METHOD FOR ESTIMATING A DEPTH CARD OF A MONOCULAR IMAGE AND ASSOCIATED DEVICES

Abstract

Method (E100) for estimating a depth map of a monocular image (I0), comprising the following steps: a) providing (E0) a monocular color image (I0) acquired by a monocular optical capture device (0) under real observation conditions; b) performing a color correction (E1) of the monocular image (I0) from an invertible color appearance model (1a), so as to provide a color-corrected image (I1) under reference observation conditions, such that the color perception in the color-corrected image (I1) is identical to the color perception of the monocular color image (I0) acquired under real observation conditions; and c) process (E4; E4.1) the color-corrected image (I1) by applying a convolutional neural network (4; 4.1; 4.1, 4.2) to generate a depth map (I4.1; I5) of the monocular color image (I0). Figure for the abstract: Figure 1

Description

Description Title of the invention: METHOD FOR ESTIMATING A DEPTH MAP OF A MONOCULAR IMAGE AND DIS- ASSOCIATED POSITIVES technical field

[0001] = The present invention relates to the estimation of the depth of a mo- image nocular, i.e. an image acquired by an optical capture device not having than a single eyepiece, such as a camera or monocular glasses.

[0002] — The invention relates more particularly to a method for estimating a map of depth of a monocular color image and a device for setting in work of the estimation process.

[0003] = The invention finds a privileged application in the field of vision by or- dinator known as "artificial vision", particularly in the context of navigation of vehicles autonomous mobility devices, such as aircraft, drones, vehicles, or robots.

[0004] — The invention also finds application in the reconstruction of a scene in three dimensions, from two-dimensional monocular images. Technological background

[0005] = Estimating the depth of a monocular image from a single image colors, is a difficult computer vision task to enable computers to understand real-life scenes.

[0006] … For each monocular image captured, the depth designates the distance separating the A device (e.g., a camera) that captures an object identified in this image. For To simplify, the depth of a monocular image will be referred to hereafter as The expression "monocular depth" (from the English "monocular depth"). A map The depth of the monocular image represents the different levels of depth present in the image.

[0007] — Many artificial intelligence techniques, particularly through learning deep learning (from the English "deep learning") implemented by a neural network convolutional neural networks (CNNs) have been proposed for to automatically estimate monocular depth maps. In general, These techniques can be grouped into two main categories: those based on supervised learning and those based on self-supervised learning (i.e. not supervised by a human being).

[0008] = For supervised learning, depth data referred to as "ground truth" (of (English "ground truth") are required as input to the neural network for train it so that it is configured to automatically estimate the depth mo- Nocular. This training data is provided by expensive optoelectronic sensors, such as LiDAR (Laser Imaging Detection and Ranging). Consequently, obtaining meaningful data from such sensors is generally a costly and difficult operation. Furthermore, this data is often sparse compared to the original image at the pixel level. For example, in low-light areas, the LiDAR's ability to provide usable data is significantly impaired. Therefore, the performance of the neural network trained with this data is insufficient.Finally, when the trained neural network model is applied to images from another monocular camera, or when this model is used to predict the depth of a new scene under different observation conditions, the reliability of the depth estimate provided by this neural network is not guaranteed and can be greatly reduced. An example of a supervised learning method for predicting monocular depth is described in the article by D. Eigen, C. Puhrsch, and R. Fergus, entitled "Depth map prediction from a single image using a multi-scale deep network," published in Proceedings of the Advances in Neural Information Processing Systems 27, 2014, pp. 2366–2374. This article describes the use of a convolutional neural network comprising a large-scale subnetwork configured to perform an initial estimation of the scene's depth at a global level using the entire image, and a small-scale subnetwork configured to perform a second estimation that refines the global depth estimate using local information by restricting it to specific regions of the image. However, as a supervised method, this neural network requires annotated datasets for training, which is costly and time-consuming. To overcome these drawbacks, self-supervised learning methods have been proposed for estimating monocular depth. These methods generally use geometric constraints of stereoscopic image pairs (or monocular image sequences) as the sole source of supervision for the learning methods. Such learning methods require obtaining stereoscopic image pairs, for example, from two cameras observing the scene from different angles or from a single stereoscopic camera (e.g., an RGB-D camera). When using a single monocular camera, the self-supervised learning algorithm is configured to generate, from a single monocular image acquired by the camera, an image from a different viewing angle than the input image, using a view synthesis process, in order to provide a stereoscopic image pair. An example of a self-supervised method is described in the article by R. Garg, BGV Kumar, G. Carneiro and ID Reid, entitled "Unsupervised CNN for Single View Depth Estimation: Geometry to the Rescue”, published in Proceedings of the 14th European Conference Computer Vision-ECCV 2016, Volume 9912, pp. 740-756. This method uses a self-encoding neural network configured to predict the depth of the left image of a stereoscopic image pair. The self-supervised learning of the network for depth estimation is based on stereoscopic image pairs, minimizing an error function. A reconstructed left image is synthesized, for example, using an epipolar geometry constraint, with the right image from the stereoscopic image pair being used. The photometric error between the left image and the synthesized left image is used as an error function to train the autoencoding network. Thus, monocular depth estimation becomes a stereoscopic left-right matching problem with a left-right photometric loss to be minimized. To improve monocular depth estimation, the method of Godard et al. presented above was modified by introducing a depth consistency error function between the left and right images of the stereoscopic image pair, as well as a loss function for smoothing disparities between the left and right images, as constraints for performing the reconstruction of the left image. This improvement is described in the article by C. Godard, OM Aodha, and GJ Brostow, entitled "Unsupervised Monocular Depth Estimation with Left-Right Consistency," published in Proceedings of the 2017 IEEE Conference on Computer Vision and Pattern Recognition, CVPR 2017, Honolulu, HI, USA, July 21–26, 2017; pp. 6602–6611. To optimize the quality of monocular depth estimation, other approaches have been developed, such as the generation of three-dimensional virtual views from stereoscopic image pairs, as described in the article by M. Poggi, F. Tosi, and S. Mattoccia, entitled "Learning monocular depth estimation with unsupervised trinocular assumptions," published in Proceedings of the 2018 International Conference on 3D Vision (3DV), Verona, Italy, September 5–8, 2018; pp. 324–333. Appl. Sci. 2021, 11, 5383 15 of 15, This approach can be combined with the use of different types of neural networks such as: generative adversarial networks Networks") as described in the article by A. Pilzer, D. Xu, M. Puscas, E. Ricci, N. Sebe, entitled “Unsupervised adversarial depth estimation using cycled generative networks”, published in Proceedings of the 2018 Inter- national Conference on 3D Vision (3DV), Verona, Italy, 5-8 September 2018; pp. 587-595; context-sensitive networks, as described in the article by Mr. Zhai, X. Xiang, N. Lv, X. Kong, A. El Saddik, entitled “An object context integrated network for joint learning of depth and optical flow”, published in JEEFE Trans. Image Process. 2020, 29, 7807-7818. While self-supervised learning methods are simpler and less expensive to implement than supervised learning methods since they do not require data labeling, they offer the advantage of greater generalization across different cameras and / or observation conditions (e.g., viewing angle, ambient light, etc.). However, despite the improvements described above, the accuracy and reliability of monocular depth estimated by self-supervised learning methods remain lower compared to those provided by supervised learning methods. It is known that this loss of reliability and / or precision lies in a low supervision of the photometric consistency of the pixels between the input monocular image, acquired under a given shooting angle, and the image synthesized from the input image by the synthesis process under another shooting angle, so as to generate the stereoscopic image pair as a supervisory signal. Most monocular depth estimation methods using self-supervised learning rely on the assumption of color constancy, according to which variations in perceived colors remain unchanged regardless of observation conditions, such as the camera's shooting angle. Such an assumption presupposes that the input image and the synthesized image (constructed from the input image) are identical and have the same colorimetric values ​​(e.g., RGB or XYZ) at each pixel, such that the photometric error between these images is zero. However, it is known that in reality, color fluctuations in the image can be induced due to numerous factors, such as ambient light intensity, noise, and light reflection, which can cause errors in the automatic estimation of monocular depth. Since these factors are not necessarily the same for two different shooting angles, the colors perceived in the same region of the image can fluctuate depending on the shooting angle. Therefore, the disparity in perceived colors that may exist in the same image area for a pair of stereoscopic images (or equivalently for two monocular images taken under different observation conditions) is a source of error in the estimation of monocular depth. To account for photometric inconsistency due to changes in brightness, it has been proposed to incorporate either the SAD (Sum of Absolute Difference) or SSIM (Structural Similarity Index Measure) parameter into the loss function. Generally, the SSIM parameter is preferred because it incorporates more local image information than the SAD parameter, thus enabling improved monocular depth prediction performance. In the article by E. Guo, Z. Chen, Ÿ. Zhou, and DO Wu, entitled "Unsupervised Learning of Depth and Camera Pose with Feature Map Warping," published in Sensors 2021, 21(3), 923, a pyramidal loss function called FPML (Feature Pyramid Matching Loss) is proposed to address the problem of photometric inconsistency caused by changes in brightness. The FPML function is more robust than error functions based on SAD or SSIM parameters, as it leverages both local and global image information. However, the main drawback of this method is that the loss is calculated by combining a depth estimation network with a camera pose estimation network, leading to a loss of absolute scale information in the predictions. Another reason for the degradation of performance of monocular estimation performed by self-supervised learning convolutional neural networks stems from the fact that the processed images have low resolution and / or low quality (e.g. noisy and / or poorly textured image). Commercially available monocular RGB cameras can generate compression noise, increasing the signal-to-noise ratio and consequently reducing image quality. Furthermore, for resource optimization and / or cost reasons, the camera resolution may be intentionally reduced. Some regions of the image acquired by the camera may have weak textures. This can be due to low camera resolution and / or observation conditions. For example, under certain lighting conditions (e.g., low or bright sunlight), the texture of some image regions may be very weak or even virtually invisible, even when using high-resolution cameras. In this case, it is virtually impossible for prior art self-supervised convolutional neural networks to accurately predict the pixel disparity value (e.g., error function estimation) due to the limited number of features they can extract from these regions. Nearest prior art document The article by N. Yang, LV Stumberg, R. Wang, D. Cremers, entitled “D3vo: Deep depth, deep pose and deep uncertainty for monocular visual odometry”, published in Proceedings of the IEEE / CVF Conference on Computer Vision and Pattern Recognition, 2020, pp. 1281-1292, describes a method for automatically estimating the depth of a monocular image in greyscale. This document describes an adjustment of the overall brightness of the image due to changes in camera exposure to enable self-supervised learning based on the assumption of constant brightness described above. This adjustment is performed by a linear transformation model, according to which the ambient brightness I of the image is adjusted according to an affine function L®, such as L®® (D= a.1+ b. However, this transformation only takes into account the ambient brightness of the image, i.e. a global light intensity which does not take into account local variations in light intensity, which has the effect of limiting the performance of predicting the monocular depth. This method is not suitable for estimating the depth of a monocular color image. It may therefore be desirable to provide a method for estimating the depth of a monocular color image that allows us to overcome at least some of the aforementioned problems and constraints. Summary of the invention A method for estimating a depth map of a monocular image is therefore proposed; said method comprises the following steps: to provide a monocular color image acquired by a device monocular optical capture under real observation conditions; to perform colorimetric correction of the monocular image from a a color-invertible appearance model, so as to provide an image color-corrected under reference viewing conditions, so that the perception of colors in the color-corrected image is identical to the color perception of a monocular color image acquired under real observation conditions; and process the color-corrected image by applying a neural network convolutional so as to generate a depth map of the image mo- nocular in color. The color correction of the monocular color image has the effect that the perception of the colors of the image remains unchanged regardless of the actual observation conditions, such as lighting conditions (e.g. ambient brightness of the scene, luminous nature of the environment, background intensity), the photometric characteristics of the camera (e.g. chromatic coordinates of the camera's RGB system) and shooting parameters, such as the shooting angle. It follows that the reliability of the depth map is increased compared to those of the self-supervised methods of the prior art which do not perform any colorimetric correction of the monocular image. Thus, the monocular depth estimation method according to the invention is more robust than those of the prior art, in the sense that the depth map is not affected by the particular conditions under which the scene is observed. The invention may further include one or more of the following optional features, in any technically possible combination. The monocular color image comprises a plurality of pixels, and the color correction includes the following steps: apply the invertible color appearance model to each pixel of the image color monocular, so as to determine at least one attribute perceptual of the pixel selected from: clarity, chromaticity, hue angle, brightness, saturation, hue composition; invert the reversible color appearance model so as to provide a inverse color appearance model; and For each pixel, apply at least one perceptual attribute to the model. of inverse color appearance configured with the observation conditions of reference, so as to provide trichromatic values ​​corrected for said pixel. The color correction further includes a frequency estimation, in which a spatial frequency of each pixel of the monocular color image is estimated, the estimated frequency being provided as input to the inverse color appearance model to obtain the corrected trichromatic values ​​of said pixel. Frequency estimation includes a decomposition of the monocular color image into a plurality of frequency domains and a decomposition of the monocular color image along several spatial orientations, the frequency being estimated taking into account the influence of frequency domains adjacent to the frequency domain to which said pixel belongs in order to obtain a spatio-frequency map of the pixels. The reversible color appearance model is the CIECAM2 model configured with at least one of the following parameters: chromaticity coordinates of a reference white, ambient brightness, background light intensity, environment indicator. The process also includes the following steps: filter the monocular color image by applying a quaternion filter linear guided by a reference image, so as to provide an image filtered quaternionic including image texture data mo- nocular; and subtract the filtered image from the color-corrected image, so as to obtain a texture map. The process also includes the following steps: oversampling the reduced-resolution depth map by ap- plication of a hierarchical network in such a way as to provide characteristics of oversampled depths; and The texture map and the oversampled depth features are concatenated to provide a residual depth map; the residual depth map and the reduced depth map are then added together to obtain a final depth map with a resolution at least equal to that of the monocular image. An original feature of the present invention is the use of a reference color model, preferably CIECAM2, to ensure invariance of perceived colors, coupled with quaternion filtering to enhance the textures of the monocular image, making it possible to extract both the color illuminating each pixel and the textures in weakly textured or noisy regions. Quaternion filtering has the advantage of improving the color accuracy of the filtered image, while optimizing image processing during filtering in terms of memory resources and computing power. The method according to the invention makes it possible to estimate the depth of low-quality (i.e., with high noise levels) and sparsely textured compressed images. The texture map obtained by subtracting the color-corrected image from the filtered image contains high spatial frequencies that facilitate the localization of depth boundaries in the monocular image. The invention also relates, in at least one embodiment, to a device for implementing the estimation process as described above. This system includes: a monocular optical capture device to obtain a mo- image nocular color in real observation conditions; a color correction module for monocular color images based on a reversible color appearance model, so as to provide a color-corrected image under reference viewing conditions, of so that the perception of colors in the color-corrected image is identical to the perception of colors in a monocular color image acquired under real observation conditions; and a depth map generation module configured to apply a convolutional neural network with color-corrected image. The device according to the invention may further include one or more of the following characteristics: The following optional risks, in any technically possible combination: a linear quaternion filtering module guided by an image of reference configured to filter the monocular image into color so as to obtain a filtered image including texture data from the mo- image nocturnal in color: and a subtraction module configured to subtract the filtered image from the image corrected in color. The invention also relates, in at least one embodiment, to an autonomous mobility device comprising a device according to the invention as described above. The invention also relates to a computer program downloadable from a communication network and / or stored on a computer-readable medium, characterized in that it includes instructions for executing the steps of a process for estimating the depth of a monocular image as described above, when said program is executed on a computer. The invention also relates to a means of storing information, removable or not, partially or totally readable by a computer or a microprocessor comprising code instructions of a computer program for the execution of the steps of the method of estimating the depth of a monocular image according to the invention as described above. Brief description of the figures The invention will be better understood with the aid of the following description, given solely by way of example and made with reference to the accompanying drawings in which: [Fig.1] schematically illustrates an estimation method according to a mode of realization of the invention: [Fig.2] schematically illustrates an example of a device for putting in works the process according to [Fig.1]; [Fig.3] schematically illustrates an example of the implementation of the step of colorimetric correction implemented in the estimation process according to the [Fig.1] ; [Fig. 4] schematically illustrates an example of the implementation of the step filtering implemented in the estimation process according to [Fig.1]; [Fig. 5] schematically illustrates an example of the implementation of a device to implement the process according to the invention; [Fig. 6] illustrates an example of the architecture of a device adapted to be put into implements the process according to an embodiment of the invention; [Fig.7] schematically illustrates a terrestrial robot in which the device according to the invention is implemented; and [Fig.8] schematically illustrates a drone in which the device according to The invention is implemented. Detailed description of the invention With reference to [Fig. 1], a method E100 for estimating the depth of a monocular image will now be described according to an embodiment of the invention. The method E100 comprises a step of obtaining E0 a monocular image I0 in color, for example in RGB (Red Green Blue) format. This monocular image I0 is acquired under so-called real-world observation conditions, for example, using a monocular camera or any other monocular optical device, such as a monocular telescope. In other embodiments (not shown), the camera O will be configured to provide a sequence of monocular images. The E100 process further includes a color correction step E1, in which the monocular image I0 is corrected to produce a color-corrected image I1. This correction is such that the color perception in the corrected image I1 under reference viewing conditions is identical to the color perception of the monocular image I0 under actual viewing conditions. This color correction step E1 will be described in more detail with reference to [Fig. 3]. During a generation step E4 and more specifically during a substep E4.1, a reduced depth map I4.1 is generated from the color corrected image I1. This depth map is described as reduced because it has a lower resolution than the monocular image IO or the color corrected image II. Thanks to the colorimetric adjustment performed during the color correction step El, the estimated monocular depth in the reduced depth map 14.1 does not depend on the actual observation conditions. This correction is particularly advantageous for ensuring the color consistency of a stereoscopic image pair obtained from the monocular image IO for the self-supervised learning of neural networks. The E100 process can be supplemented by the following optional steps grouped on [Fig.1] by a frame of dotted lines. During a filtering step F2, the monocular image IO is filtered to provide a filtered image 12 that corresponds to the monocular image 10. One of the objectives of the filtering is to obtain a high-frequency image I2, known as a "high-pass" image, in which the textures and / or edges of the object are well-defined, i.e., better defined than in the original monocular image IO. Once the textures and / or edges of the object are well- Once the edges of the various objects constituting the image are obtained, a better estimation of the monocular depth can be obtained for each object in the image. This E2 filtering step will be described in more detail with reference to [Fig. 4]. During a subtraction step E3, the color-corrected image I1 is subtracted from the filtered image I2, so as to obtain a texture map I3 of the monocular image 10. The texture map I3 is a color-corrected image in which the textures of the monocular image I0 are highlighted. The E100 process further includes a generation step E4 in which at least one enhanced depth map is determined. More specifically, this step E4 includes a substep E4.2 in which a residual depth map I4.2 is generated based on the reduced depth map [4.1] and the texture map I3. The generation step F4 will be described in more detail with reference to [Fig. 5]. The E100 process further includes an ES addition step, in which the reduced depth map 14.1 is added to the residual depth map I4.2, so as to provide a final depth map I5 with a resolution at least equal to that of the monocular image IO provided in step E0. With reference to [Fig.2], an example of device 100 for implementing the process according to [Fig.1] as described above will now be described. In the present example, the device 100 according to the invention comprises a monocular camera 0 configured to acquire the monocular image 10. As previously stated, any other monocular image-capturing device suitable for capturing monocular images may be used instead of the camera. In the present example, the camera 0 is part of the device 100. However, in other embodiments (not shown), the camera 0 or any other monocular image-capturing device may be external to the device 100, in which case the device 100 will include a means for obtaining the monocular image IO previously acquired by the camera 0. The device 100 further includes a color correction module 1 for the monocular image IO. This module 1 is configured to provide a color-corrected image I1, such that the color perception in the color-corrected image I1 under reference viewing conditions is identical to the color perception of the monocular image IO under actual viewing conditions. This color correction module 1 will be described in more detail with reference to [Fig. 3]. The device 100 further includes a filtering module 2 for filtering the monocular image IO, so as to provide the filtered image I2. Preferably, the filtering module 2 is configured to implement a guided quaternion filter which will described in more detail with reference to [Fig.4]. The color correction module | and the filtering module 2 are connected to the same output of the monocular camera 0, so as to receive and process the same monocular image IO simultaneously. Device 100 further includes a subtraction module 3 connected to the output of the color correction module 1 and the filtering module 2. The subtraction module 3 is configured to subtract the color-corrected image I1 and the filtered image I2, so as to provide the texture map I3, such that I3 = I2 - I1. An example of the texture map I3 is shown in [Fig. 2], in which textures and possibly borders of the monocular image I1 have been highlighted. The resulting I3 texture map is a filtered image, such that low frequencies have been removed, so that the I3 texture map only includes high-frequency components useful for estimating the depth of field of the image. Device 100 further includes a convolutional neural network 4 comprising a first subnetwork 4.1 to estimate the depth of the monocular image I0 and a second subnetwork 4.2 to improve the depth estimated by the first subnetwork 4.1. The first subnetwork 4.1 is configured to provide the reduced depth map 14.1. The second subnetwork 4.2 is configured to provide the residual depth map I4.2. The first subnetwork 4.1 is connected to the output of the color correction module 1 so as to receive the color-corrected image 11 as input. The second subnetwork 4.2 is connected to the output of the subtraction module 3 so as to receive the texture map I3 as input. The second subnetwork 4.2 is connected to the first subnetwork 4.1 so that the first subnetwork 4.1 provides the reduced depth map I4.1 to the second subnetwork 4.2. The implementation of the convolutional neural network 4, and more specifically of the first subnetwork 4.1 and the second subnetwork 4.2, will be described in more detail with reference to [Fig.5]. Device 100 further includes an addition module 5 connected to the output of the first and second subnetworks 4.1, 4.2. The addition module 5 is configured to obtain the final depth map IS by adding the reduced depth map I4.1 to the residual depth map I4.2. With reference to [Fig.3], an example of the implementation of the color correction step El by the color correction module 1 will now be described. In this example, it is assumed that the monocular image IO provided by the monocular camera 0 is encoded in the RGB color space. During a substep of the E10 conversion, the monocular image IO is converted into the XYZ color space, so as to provide a converted I1.1 image comprising a plurality of pixels Pij in XYZ coordinates. This conversion is performed using the chromaticity coordinates of the camera's RGB system (Xw, Yw, Zw) for the R, G, and B components: (Xp, Yr), (Xe, Ya), and (Xe, Ya), respectively, and using the chromaticity coordinates of the reference white level (Xw, Yw, Zw), according to the standards of the International Commission on Illumination (CIE). This conversion is obviously not required if the monocular image (IO) is already provided in the XYZ color space. During a substep El1, perceptual attributes, such as clarity J, chromaticity C, hue angle h, brightness Q, saturation s, hue composition H are determined by applying to the converted image I1.1, a reversible color appearance model (CAM: "Color Appearance Modelling" in English). Preferably, this model is the CIECAMO2 model, as published in 2022 by Technical Committee 8-01 ("Color Appearance Modelling for Color Management Systems") of the International Commission on Illumination (CIE). The CIECAMO2 model is particularly well-suited for reliably accounting for the environment of a colored object in order to compensate for the influence of its surroundings on color perception. Among the advantages of the CIECAMO2 model compared to the CIECAMO7 model are a linear chromatic adaptation transform, which allows for easier model inversion, and a simplified adaptation factor D. The aforementioned perceptual attributes can be calculated according to CIE standards, e.g. according to the CIECAM2 model, but will not be detailed here for the sake of brevity. In this example, the CIECAM2 model is configured using at least one of the following configuration parameters: the chromaticity coordinates of the reference white level Xy, Yw, Zw, the ambient brightness (or luminous intensity) L, of the image expressed in lux or cd / m², a background luminous intensity Y, of the image, an average illumination indicator of the viewing environment E (e.g., bright, dark, medium, standard daylight). Preferably, all these parameters are taken into account when configuring the model, as they influence color vision (colorimetric perception). Some of these configuration parameters are user-defined, such as those relating to the viewing environment (E), ambient brightness (L), and reference white (Xw, Yw, Zw). To define the viewing parameters (E), three additional parameters can be set: the environmental impact (c), the chromaticity induction factor (N), and the adaptation factor (F), following the standard recommendations of the CIECAM97 and / or CIECAMO2 models. All these parameters can be pre-set during substep E11. Other model configuration parameters can be determined during substep El1 by the color correction module 1, such as the image background brightness Y. For each pixel Pij, the Y value of this parameter is determined by selecting a window Wij formed by a set of pixels in the vicinity of pixel Pij and calculating E110 the average intensity of the pixels belonging to the window Wij. Alternatively, the intensity Y is determined using a Gaussian-weighted average. Preferably, the calculated Y value is less than 100, e.g., Y=2 for black, Y=20 for mid-gray, Y=90 for near-pure white. According to a particular feature of the invention, the CIECAM2 model referenced is applied to each pixel Pij of the image I1.1. Thus, for each pixel Pij, the perceptual attributes are determined and provided at the end of step E11. In general, perceptual attributes can be selected from: lightness J, chromaticity C, hue composition H (or quadrature hue), hue angle or angular hue h, brightness G, saturation s. In this example, the perceptual attributes considered for each pixel Pij are brightness Jij, chromaticity Cij, and hue angle hij. In other implementations, other perceptual attributes may be considered as a substitute for or in addition to these parameters. During an inverse step E12, the CIECAM2 model is inverted. This operation is facilitated by the fact that the model uses a linear matching transformation, which is itself easy to invert. The inverse model 1b is denoted CIECAM2! In the inverse step E12, the perceptual attributes Jij, Cij, hij previously calculated in step E1 are then provided as input to the inverse model Ib, denoted CIECAMZ, in order to determine trichromatic values ​​X'ij, Y'ij, Z'ij corrected for pixel Pij. The inverse model Ib is configured by applying environmental parameters E*, ambient brightness L;', and white level X* 49 Y'w, Z'w +. These parameters are adjusted according to reference observation conditions. During an inverse conversion step E14, the trichromatic values ​​X'ij, Y'ij, Z'ij provided by the inverse model CITECAM2* are converted into the RGB color space, so as to provide the corrected image II in RGB format, i.e. in the same color domain as that of camera 0. Optionally, the color correction step El also includes a frequency estimation E13, during which a spatial frequency Fij of each pixel Pij of the monocular image IO, here the monocular image converted I1.1 to RGB format, is estimated. The estimated frequency Fij at the end of step E13 is provided as input to the CIECAM2* inverse color appearance model referenced 1b to obtain the corrected trichromatic values ​​X°ij, Y'ij, Z'ij of pixel Pij. An example of frequency estimation E13 will now be described in more detail, again with reference to [Fig.3]. During an E13.1 spectral decomposition, the monocular image I1.1 in XYZ colorimetric format is transformed by applying a two-dimensional Fourier transform (2D-Fourier Transform) to obtain a spectrum I1.2 of the monocular image I1.1. The spectrum I1.2 includes the spatial frequency components of the image I1.1 in Fourier space. During a spatio-frequency distribution step E13.2, these frequency components are distributed in different spectral domains and according to different spatial orientations, so as to form a plurality of sectors, thus providing a spectrum ordered in frequencies and in space I1.3. In this example, the ordered spectrum I1.3 comprises three spectral regions: a zero-frequency region D, containing the continuous (i.e., zero-frequency) components; a low-frequency region Ds containing frequency components below a predetermined threshold; and a high-frequency region Dur containing frequency components above said threshold. For example, the threshold is set to be equal to the average frequency of the entire frequency range (the median frequency of a histogram of the frequencies in spectrum I1.3). As illustrated, the zero-frequency domain D is delimited by a central circle CO. The low-frequency domain Day lies between the central circle CO and an intermediate circle Ci concentric with the central circle CO. The high-frequency domain Dyr lies between the edges of image 11.3 and the intermediate circle Ci. For each frequency domain Dpr, Dyp, and Dyr, an average frequency is calculated and denoted Far and Fur, respectively, for the low-frequency and high-frequency domains. For each domain, the average frequency Far and Fur is calculated based on the size of the original monocular image IO. In undescribed embodiments, several frequency thresholds may be defined to distribute the frequency components across a larger number of frequency domains. For example, by defining two frequency thresholds, three frequency domains (excluding the zero frequency domain) may be defined (e.g., low frequencies, medium frequencies, high frequencies), each with an average frequency associated with it. During step E13.2, the (spatial frequencies are distributed in the geometric space of the two-dimensional image (X,Y). To achieve this, the image is divided into several sectors centered along different principal orientations, so as to form a plurality of sectors {s,}. Thus, each sector s, (k being a natural number, varying for example from 0 to 16) groups spatial frequencies in Fourier space that correspond to an area of ​​the image Originally, in geometric space, the transition between a sector s and the associated image area is achieved through an inverse Fourier transform. In this example, the number of sectors with non-zero frequencies is 16 (with k ranging from 1 to 16). However, in other embodiments, this number can be adjusted, for example, to values ​​greater than 16 for finer sampling, further improving the monocular depth estimation results. The spatial decomposition of the image into several sectors is relatively simple to implement and requires no parameters other than the spatial frequency, unlike other prior art models (e.g., Daly's model), which require a plurality of parameters, such as radial frequency, orientation, luminance, area, observation distance (i.e., distance between the camera and the objects in the image), and eccentricity. This simplicity is particularly advantageous for enabling real-time depth-of-field determination, especially in the context of autonomous vehicle navigation. In this example, we consider the following principal orientations: 0°, +45°, -45°, +90°, -90°, 135°, -135°, 180°. Thus, zero frequencies are distributed in sector 5. Low frequencies are distributed in sectors numbered s1, 82, 3, 84, 5, 5, 6. High frequencies are distributed in sectors numbered s9, 10, 51, 5, 12, 13, 14, 15, 16. Once the ordered spectrum I1.3 is obtained at the end of step E13.2, the frequency of each pixel P, is determined during step E13.3. For this, it is necessary to determine, for each sector s,,the value v+ (ay) Que possesses the pixel Pij considered (knowing that a pixel can contribute frequencyly to several sectors simultaneously). The frequency of the colorimetric component X of pixel P;, denoted F,(ij), is obtained by averaging the contributions of pixel P; over the image area associated with each of the sectors s,. Each pixel P; of the original image is found in one of the predefined frequency domains and the task is to precisely determine the frequency of this pixel. For example, the frequency F,(i,J) is calculated by averaging the influences of each zone associated with sector s, on pixel P, according to the following equation 1: [Math 1] ht, t=ié, ki imétri F an= EurFasEis VuiXFar where Vi) denotes the colorimetric value X <() GER La Via of pixel P; on the image area associated with sector s,. The frequency F,(i,j) thus obtained corresponds to the sum of the average of the low-frequency and high-frequency domains, weighted respectively by the sum of the colorimetric values ​​of the pixels in the associated sectors. This frequency is normalized in the sense that it includes in the denominator the sum of the k » VÉn over the set of sectors s,. For example, if pixel P; is strongly represented in sector s, it will show a strong correlation with horizontal low-frequency components, i.e. in a substantially horizontal direction along the X-axis. The same operations are performed for the colorimetric components Y and Z, in order to obtain the frequency components of each pixel P;; according to the equations : F tes. wheat “ following: [Math 2] z cn BE *FartEs VanXEur lis) fee, FILE rl Vita k Éci Vi (a) respectively denote the kB k=ts 4, 4 End = Er ConsFertEio Vétu<Eur OÙ Vi > z(àj) Fa k ve qi VER colorimetric values ​​Ÿ, Z of pixel P;; on the image area associated with sector s,. Finally, the frequency F(i,j) of pixel P is determined by calculating the average of the frequencies previously calculated for each of the three colorimetric components X, Y, Z, according to the following equation: [Math 4] Funz Est FocpitFoiap) ti) > 3 Thus, the distribution of spatial frequencies into different spatial sectors constitutes a crude decomposition of the Fourier space, allowing the extraction of areas from the original image using an inverse Fourier transform. Such a decomposition enables the reliable calculation of the frequency of each pixel in the original image while optimizing computation time and memory resources. Indeed, grouping spectral components into different frequency domains is more advantageous than a conventional approach that considers the influence of each point in the spectrum on the pixel in question. This calculation technique is all the more advantageous because it is necessary to repeat the calculations for each of the three colorimetric components X, Y, Z of pixel P. The frequency F;; calculated for each pixel P; is applied as input to the CIECAM inverse model;! during the inverse step E12 to determine the perceptual attributes of the pixel P;, taking into account its frequency F;. Thus, at the end of the conversion step E14, the corrected colorimetric coordinates X°;, Y';, Z'; of the pixel P; converted to RGB format take into account the frequency of each pixel P;,,. Taking into account the frequency F; for each pixel P; allows advantageously to adjust the color correction in an adaptive way which best preserves the color details of the image. Steps E10, El1, E12, E13, E14 are performed for each of the pixels P;; of the original image IO or IL.1. With reference to [Fig. 4], an example of the implementation of the E2 filtering step is shown. work in the estimation process according to [Fig.1] will now be described in detail. The E2 filtering step is configured to filter the monocular image I0 to obtain a filtered image I2, including at least texture data and possibly edge data from the monocular image IO. During a quaternion coding step E20, each pixel P; of the original RGB color image IO is converted into a pure quaternion encoding the three colorimetric components R, G, B according to the following equation: [Math 5] Pij=iPp(ij)+jP6(b 7) +KP2(1 j).where Pplt j). Peli j) and Pp(i, j) are the red, green and blue components respectively. By definition, a quaternion q is a hypercomplex number comprising a real part and three imaginary parts, as expressed by the following formula: [Math 61g=g,+iq,+ Ja, + kg, where 9, is the real part, 4, 7, and 4, are the three imaginary parts and ;, j, A are three complex operators according to the following rules: (Mah7] 2= P=12=ijk=-1 and [ij=-ji=k | jk=-s=i ki=-ik=; If the quaternion q has a unitary norm, i.e., ||q|| = L, we say that q is a unitary quaternion. If the real part of q is zero, i.e., 4, = 0, we say that g is a pure quaternion. The modulus and conjugate of the quaternion @ are defined respectively according to the following expressions: [Math 8] Il q Il = Jaq ES Va? + + A + PR ; [Math 914=q,-i4,-jq,-kq,. Using a quaternionic representation of the monocular image to perform filtering is advantageous because quaternionic processing is particularly efficient at optimizing memory and computing power resources, and with better accuracy on color information than conventional approaches, because each pixel P; is presented by a vector in a three-dimensional space (RGB) which is treated as a single entity. Preferably, the filtering is guided quaternion filtering. This filter is configured during a prior configuration step E02 according to a predefined model. Preferably, the guided quaternion filter is a linear and local model between a guide image / and the filter response q which is a linear transform in a pixel window W; centered around a pixel k according to the following equation: [Math 10] g, =aJ1+b, : Vie W,; where (ab;) are linear coefficients and pure quaternions in the window W;. In this example, for each pixel p to be filtered, during step E21, the quaternion filter is applied locally to a plurality of pixel windows including pixel p;. The guide image I, called the reference image to guide the filtering, is the image II obtained after applying the color correction. The linear coefficients (ab) are determined by minimizing the difference between the filter response g;=a,p;+b, and its input p,. During an E22 step, a quaternionic cost function Eç expressing this difference is calculated in W;, for example, according to the following equation: [Math 11] Eglay bi) =Ejew,( | Im(ad+b)-p, | ?+2 | Re(ai+ bi) 1+e lac 17) , where the coefficients as, b, of the guided quaternionic filter, the pixels I; of the guide image and the pixel p; of the original image to be filtered are expressed respectively in a quaternionic form as follows: [Math 12] a, = ia} + jaz+ ka} ; [Math 13] by =ibl + jb2 + kb} 3 [Math 14] 1,= ir} + 717 + KI} ; [Math 15] p,=ip}+ jp? + kp} ; where Im(), Re() denote respectively the imaginary part and the real part; and À and € are parameters allowing the result of the filtering to be adjusted so that it is constant in the window W, ; € being in addition a regularization parameter to prevent “& from being too large. During a minimization step E23, the quaternionic cost function Eç is minimized with respect to the quaternionic components of the coefficients (ay, b), i.e., ak a a, bi, bi b; by solving the following set of equations: [Math 16] 2Eg _ ÿ, 2E2 _ p. 2E2 - pp 9e _ pp 2e _ ny eg _ 4 07-07-95 70% 0% 0 Thus, the coefficients a, b, minimizing the quaternionic cost function Eç are; pis us Z determined by the quaternionic coefficients a}, a?, a, bl> BR, b}- During step E24, the filtered pixel q; at the output of the guided quaternion filter is determined from the coefficients a,, b, previously obtained during step E23, such that q=a,1+b,. As a quaternion image element, this filtered pixel q; is expressed in the following quaternion form [Math 17]: ÿ, = iq! + Ja? + KP. During an E25 step, the quaternionic coefficients a, by and the filtered pixel q; are stored in association with the window W.. Steps E21, E22, E23, E24, E25 are repeated for each window W,. However, for the different windows W covering the same pixel Pij, denoted p for simplicity, the previously calculated values ​​of Ÿ are not identical. Therefore, the process further includes a step E26 configured to calculate the average of these different values ​​of Ÿ obtained for different windows. For example, step E26 provides, for each pixel p; of the original image IO, a filtered and averaged pixel according to the following expression: [Math 18] 45 Emo la + 650 = FE Esp Ca + jaÿ 4 ht CT TÈ PR + (10e REA RDE) ) = "Cote ii) + (TP 8) + IL AE) fade 6) During the calculation of the quaternionic cost function Eç in step E22, the parameter A can be adjusted so that the real part of @,1;+ b; approaches 0 without being zero. For example, when the coefficient A is relatively large, preferably between 0.1 and 0.5, the image details in the real part of 1;+ b; are practically zero. Therefore, the energy of the color image is largely carried by the imaginary part of the pixels q; after filtering. In this case, the filtered pixel can be considered as a pure quaternion of the following form: 4,5igi+ Ja + ka} where: [Math 11 gi 5 @F-a7+bj 5 = 1-0} + Dj; 5172102714 p* el to 5 mr to gi med: q=al-a1;+ bj with al= Fr re, al 'a= FT Drew, saj= Trj Era 6; etpi_ 1 Ipne 2 pui 3 bi= rérbren Pi bi = TWi Erewi bj= wi Levi Thus, the quaternion filter makes it possible to provide a low-pass image in which details are preserved. With reference to [Fig.5], a detailed example of the embodiment of a device for implementing the process according to the invention will now be described in detail. This device is an example of the implementation of device 100 previously described generically with reference to [Fig. 2]. The general architecture and operating principle remain identical. With reference to [Fig. 5], the focus is primarily on the implementation of neural network 4, more specifically the first subnetwork 4.1 and the second subnetwork 4.2 in the same context as before. The first subnetwork 4.1 includes a first convolution layer 4.10 taking as input the color corrected image Il from the color correction module 1. For example, the first convolution layer 4.10 has a convolution kernel of size 7x7 pixels allowing to provide a data block 1410 of reduced size by a factor of 2 compared to that of the image Il. At the output of the first convolution layer 4.10, the first subnetwork 4.1 includes a "pooling" layer 4.11 configured to reduce the image data size by a factor, for example, equal to 2. Thus, the "pooling" layer 4.11 produces a data block I411 with a size reduced by a factor equal to 4 compared to that of the image II. At the output of the pooling layer 4.11, the first subnetwork 4.1 includes a second convolution layer 4.12. For example, this layer is configured with a convolution kernel of a size equal to 3x3 pixels, to reduce the data volume by a factor of 2. Thus, the second convolution layer 4.12 produces a data block I412 with a size reduced by a factor of 8 compared to that of the image II. At the output of the second convolution layer 4.12, the first subnetwork 4.1 comprises two dilated convolution layers 4.13 and 4.14, supplied sequentially. These dilated convolutions provide two final subsampling layers, eliminating the need for the stride operators used to translate the convolution kernel of conventional convolution layers. By definition, a dilated convolution is a convolution technique in which the convolution kernel is expanded by inserting gaps between its consecutive elements. In other words, it is a convolution involving a pixel jump, in order to cover a larger area of ​​the input image. The two dilated convolution layers 4.13, 4.14 have the effect of maintaining constant the size of the data blocks at the output of these layers 1413, 1414 respectively, which advantageously limits the reduction of the resolution of the reduced depth map I4.1 provided at the output of the first subnetwork 4.1. In the present example, the resolution of the image at the output of the two layers 4.13, 4.14 is maintained at 1 / 8 of that of the image II provided at the input of the neural network 4. At the output of the two dilated convolution layers 4.13, 4.14, the first subnetwork 4.1 includes in parallel a plurality, preferably four, of dilated convolution layers 4.15a, 4.15b, 4.15c, 4.15d. Advantageously, the dilated convolution layers have dilation factors fixed at distinct values. For example, the four dilated convolution layers 4.15a, 4.15b, 4.15c, 4.15d have dilation factors equal to 6, 12, 18 and 24 respectively. The dilated convolution layers 4.15a, 4.15b, 4.15c, and 4.15d form a pyramidal structure that allows the extraction of four subsampled depth feature maps, I415a, I415b, I415c, and I415d, respectively, with different receptive fields. A "receptive field" is understood to be a sensor field designed to capture more or less global (or local) image features. For example, receptive fields can be considered that correspond to different levels of image detail, i.e., finer or coarser. The set of these layers 4.15a, 4.15b, 4.15c, and 4.15d constitutes a "multi-scale" scheme that advantageously ensures that image regions at an arbitrary scale can be accurately retrieved. Indeed, predicting a depth map from a fixed camera cannot exploit objects captured at different scales, unlike a moving camera. To overcome this limitation, one solution is to use the same convolutional neural network architectures on different resized versions of the same datasets, and then concatenate the feature maps from different convolutional neural networks to obtain a final result. This set of layers also eliminates the need for fully connected layers, which are the terminal layers of a classic convolutional neural network. Thus, this set of layers 4.15a, 4.15b, 4.15c, and 4.15d advantageously simplifies the neural network structure and consequently facilitates its implementation, particularly in embedded applications such as autonomous vehicle navigation with real-time obstacle detection. At the output of the dilated convolution layers, the first subnetwork 4.1 includes a fusion module 4.16 configured to merge the four depth maps I415a, I415b, I415c, I415d, so as to provide the reduced depth map I4.1. Due to the aggregation of the undersampled depth features obtained by the fusion module 4.16, the resolution of the reduced depth map 14.1 is equal to only 1 / 8 of the resolution of the image I1 supplied as input to the first sub-array 4.1. To increase the resolution of the reduced depth map 14.1, the first sub-array 4.1 is connected at the output of the fusion module 4.16 to the second sub-array 4.2. Preferably, the second sub-array 4.2 is a hierarchical array rather than a bicubic interpolation to progressively reconstruct a depth map to the same size as that of the input color image II. The term "hierarchical" refers to the hierarchical or pyramidal structure of subnetwork 4.2, i.e., exhibiting several levels of resolution increasing progressively with the constituent neural layers of the subnetwork so as to achieve a resolution at least equal to that of the color-corrected image II. For example, the second sub-array 4.2 comprises three successive oversampling layers 4.20, 4.21, 4.22 to progressively upsample the reduced depth map [4.1] from the first sub-array 4.1 in three levels. Preferably, each of these three oversampling layers comprises a convolutional layer followed by a transposed convolutional layer. Each oversampling layer 4.20, 4.21, 4.22 is configured such that it increases the size of the depth map or, equivalently, the resolution by a factor, preferably equal to 2. Thus, the reduced depth map I4.1 provided as input to the second sub-array 4.2 consists of a data block

[420] with a resolution equal to 1 / 8 that of the image T1 provided as input to the first sub-array 4.1. The data block 1421 provided as output to layer 4.20 has a size (or resolution) equal to 44 that of the input image I1. The data block I422 provided as output to layer 4.21 has a size (or resolution) equal to 1 / 2 that of the input image I1. Thus, the second sub-array 4.2 allows for the progressive upsampling of the depth map. intermediate 14.1 provided by the first subnetwork 4.1 to increase the size, and consequently the resolution of the depth map. The second subnetwork 4.2 further includes a convolution layer 4.23 connected to the output of the subtraction module 3, so as to provide an intermediate map l'3. For example, this convolution layer 4.23 has a convolution kernel of size equal to 3x3. The second subnetwork 4.2 further includes a concatenation module 4.24 connected to the convolution module 4.23 and the upsampling layer 4.22. From the upsampled features 1424 provided by layer 4.22, the concatenation module 4.24 is configured to increase the resolution of the depth map so that it has a resolution equal to that of the color-corrected image map 11 (or the original monocular image 10). The concatenation module 4.24 outputs a data block 1425. At the output of the concatenation module 4.24, the second subnetwork 4.2 further includes several (preferably two) convolution layers 4.25, 4.26, so as to provide the residual depth map I4.2. For example, each of these layers 4.25, 4.26 has a convolution kernel of size equal to 3x3 pixels. The output of the first subnetwork 4.1 and the second subnetwork 4.2 is connected the addition module 5, so as to provide the final depth map IS by adding the residual depth map 14.2 to the reduced depth map I4.1. Thus, the second subnetwork 4.2 improves the depth estimation performed by the first subnetwork 4.1. In particular, the second subnetwork 4.2 provides residual learning, enabling fast and stable training, which contributes to improved depth estimation results. Training The neural network 4 as a whole is trained using a machine learning tool, such as TensorFlow developed by Google. The first subnetwork, 4.1, is initialized using a residual deep neural network (ResNet), for example, the ResNet-101. This network is then trained using a first L2-norm loss function El applied between subsampled depth images and corresponding depth outputs subsampled by a factor of 8. For example, the KITTI training database is used to provide subsampled images and their corresponding depth maps. The second sub-lattice 4.2 is initialized randomly and trained using a second L2 norm loss function E2 applied between the low resolution depth pair (1 / 8) corresponding to the reduced depth map I4.1 and the high resolution depth pair corresponding to the residual depth map I4.2. As with the first 4.1 subnetwork, the KITTI training database is used to obtain these high-resolution (HR) and low-resolution (LR) depth pairs. The first 4.1 and second 4.2 subnetworks are jointly fitted using a single loss function, common to both subnetworks 4.1 and 4.2. Preferably, this loss function, denoted L, is defined as follows [Math 20]: a EN 9 cu” nf) 1(à,à, d,d)=E 1400 y +20” At A = where d denotes 421, ground truth depth map subsampled by a factor (e.g., 8); & denotes the output depth map of the network; 4 denotes the ground truth depth map; %} — el c.8) denotes the depth map obtained by a mapping function g, such that a = e(c,0) resembles the ground truth depth map d as a function of the input image c (in RGB format) and the set of parameters 6 of the network to be optimized; A is a balancing parameter between the two loss terms (1) 2 and i) … _ 2: N is the number of samples 12401 NA 004, learning. The goal of the training is to learn the mapping function # to generate the depth map a =2 (e, 8) with an optimum degree of similarity to the depth map d of the ground truth. One of the advantages of the so-called "double loss" strategy as proposed according to equation [Math 20] above is that it allows supervision of intermediate layers, that is to say simultaneous supervision of the two subnetworks 4.1, 4.2. In addition, all the convolutional filters used for feature extraction, sampling and the multiscale scheme are trained together in an end-to-end manner. The complete architecture is trained using, for example, the TensorFlow platform (or framework). Each subnetwork 4.1, 4.2 is first trained separately. Regarding the first depth prediction subnetwork 4.1, the "ResNet 101" network is used to initialize this subnetwork. The model of this subnetwork is then refined with a calculated L2 norm loss between the subsampled depth images and the corresponding 1 / 8 depth outputs. Regarding the second depth enhancement subnetwork 4.2, the model of this subnetwork 4.2 is randomized. This subnetwork 4.2 is then trained with a calculated L2 norm loss function between the so-called LR-HR depth pairs, i.e. low-resolution (LR) - high-resolution (HR). Next, the two subnetworks 4.1, 4.2 are jointly adjusted using the proposed L loss function with dual supervision. Preferably, the inertia parameter (nomentum in English) is set to 0.9 and the learning rate is initialized to 104 for all layers of both subnetworks 4.1, 4.2 and then decreased by 0.90 at each epoch or iteration (epoch in English). Results and performance Neural network 4, more specifically the two subnetworks 4.1, 4.2 are trained using a known training database, such as the KITTI database. The results of neural network 4 according to the invention are compared with those of three state-of-the-art methods designated below as A, B and C and respectively described in the following articles: [A]: H. Fu, M. Gong, C. Wang, K. Batmanghelich, and D. Tao, “Deep ordinal regression network for monocular depth estimation,” in Proc. IEEE / CVF Conf. Computer Vision Pattern Recognition, Jun. 2018, p. 2002-2011. [B]: JH Lee, M.-K. Han, DW Ko, and L H. Suh, 'From big to small: Multi-scale local planar guidance for monocular depth estimation” 2019, arXiv:1907.10326. [C]: £ Hao, Y. Li, S. You, and F. Lu, “Detail preserving depth estimation from a single image using attention guided networks,” in Proc. Int. Conf. 3D Screw. (DV), Sep. 2018, p. 304-313. Six evaluation metrics as described below are used to compare the results of the present invention with those obtained by the three prior art methods A, BC: The absolute relative error (ARE): 5 met ù i Abs Rel = Taj hherl$- y / y where T denotes a set of pixels of reference for which ground truth depth values ​​are known, [TI denotes the number of valid pixels of the “ground truth” and Y” refers to the "ground truth" at depth. The squared absolute relative error ("Squared Absolute Relative Error" in sp 2j4x (English): Sq Re} = Yesterday Ly->"17 / The root mean square error (RMSE) + || 2- English) *RMSE= Her lv-xl = 2. RMSEp,= rh L,er | logv-log 3" || The mean logarithmic deviation: Jpg10 = Tri bser Hogy- log y*| « Accuracy is a ratio, which can be expressed as a percentage of Ÿ under the condition max(}, ë ) = 5< Th » Where Th denotes a predetermined threshold. Typically, the Th threshold is set at 1.25, which corresponds to a prediction accuracy of {+0.25, +0.5625, +0.9531} compared to the reality on the ground. The performance of the invention is compared to that of the three methods A, B, C for the parameters β, Abs, Rel, Log10 and RMSE as shown in Table 1 below. In particular, the accuracy parameter β is estimated for three distinct thresholds: Th=1.25; Th=1.252=1.5623; Th=1.253=1.95. Method |6<1.25 |5<1.25° |5<1.25* |AbsRel|logl0 |RMSE A 0.828 Jo965 Jo992 Jo11s Jo05s1 Jo.509 B 0.882 [0979 — |o995 = lo112 |0047 |o.352 c 0841 10.966 0991 [0.127 Jons3 |o.555 Invention [0.885 | [0.979 jo99s Jo.110 [0.047 |0.393 [Table 1] Table 1: Performance In view of these results, the present invention provides better performance than that obtained by the prior art methods A, B and C. In particular, the accuracy values ​​are maximum for each of the three conditions tested, i.e. According to one embodiment of the invention, the device 100 as described with reference to [Fig.2], is at least partly implemented by a computer system or computer 6 which will now be described in more detail with reference to [Fig.6]. This computer system 600 includes a data processing unit 6.1 (e.g., a microprocessor, denoted CPU, from the English "Central Processing Unit") and a main memory 6.2 (e.g., RAM, from the English "Random Access Memory") and a read-only memory 6.3 (e.g., ROM, from the English "Read Only Memory"), accessible by the processing unit 6.1. The computer system 6 also includes, for example, a network interface 6.4, and / or a computer-readable medium, such as a local medium, like a local hard disk 6.6, or a remote medium (such as a remote hard disk accessible via the network interface 6.4 through a communication network) or a removable medium (such as a USB key, from the English "Universal Serial Bus", or a CD, from the English "Compact Disc" or a DVD, from the English "Digital Versatile Disc") readable by means of an appropriate reader of the computer system 6 (such as a USB port or a CD and / or DVD disc drive). . A computer program Q containing instructions for the processing unit 6.1 is stored on the medium 6.6 and / or downloadable via the network interface 6.4. This computer program Q is, for example, intended to be loaded into main memory 6.2, so that the processing unit 6.1 executes its instructions. These instructions can be organized into software modules, as described previously with reference to Figures 2 and 5, in particular, the color correction module 1, the filtering module 2, the neural network 4 including the first subnetwork 4.1 and the second subnetwork 4.2, the subtraction module 3, the addition module 5, to implement the steps E1, E2, E3, E4, ES of the E100 process as described with reference to [Fig. 1]. Thus, steps E1, E2, E3, E4, ES of process E100 are implemented by computer. However, this presentation does not prejudge the form of the computer program, which can be any form. Alternatively, all or part of these modules could be implemented as hardware modules, that is to say as an electronic circuit, for example micro-wired, not involving a computer program. With reference to [Fig.7], a 700 ground robot in which the invention is implemented will now be described. The 700 ground robot is adapted to move autonomously on the ground. For example, it includes device 100 according to [Fig.2] to determine the depth of field of images captured by camera 0. It is adapted to detect obstacles, estimate its distance from the various obstacles detected and adjust its trajectory accordingly so as to avoid any collision with one of the detected obstacles. With reference to [Fig. 8], an 800 drone in which the device according to the invention is The implementation will now be described. The 800 drone is adapted to move autonomously through the air. For example, it includes device 100 according to [Fig.2] to determine the depth of field of images captured by camera 0. It is also adapted to detect fixed or moving obstacles, estimate its distance from the various obstacles detected and adjust its trajectory accordingly so as to avoid any collision with an obstacle. It should also be noted that the invention is not limited to the embodiments described above. Indeed, it will be apparent to those skilled in the art that various modifications can be made to the embodiments described above, in light of the information just disclosed to them. Industrial applications According to a first industrial application, the monocular depth estimation method according to the invention can be implemented for the navigation of a mobility device in three dimensions, for example, based on the reception of satellite signals (e.g., GPS: "Global Positioning System" in English). The device according to the invention can be integrated into an artificial vision system embedded in the mobility device and configured to detect the presence of obstacles from a monocular color image captured by a monocular camera and estimate the distance between the device and the detected obstacle as a function of the monocular depth estimated according to the method of the invention. The device and method according to the invention find a privileged application for mobility devices (e.g. aircraft, drones, robots) called autonomous, i.e. adapted to move autonomously. Once a potential obstacle is identified, the autonomous mobility device must be able to estimate monocular depth with increased reliability to deduce the distance separating the obstacle from the mobility device, in order to adjust its trajectory in real time and avoid any collision. According to a second industrial application, the monocular depth estimation method according to the invention can be implemented for the automatic reconstruction of a three-dimensional scene from one or more two-dimensional images captured by a monocular camera (i.e., a stream of monocular images). In the detailed presentation of the invention given above, the terms used shall not be interpreted as limiting the invention to the embodiments set forth in this description, but shall be interpreted as including all equivalents that can be foreseen by a person skilled in the art by applying their general knowledge to the implementation of the teaching that has just been given. disclosed.

Claims

Claims

1. Method (E100) for estimating a depth map of an image monocular (I0), said method being characterized in that it comprises the following steps: provide (E0) a monocular color image (I0) acquired by a monocular optical capture device (0) in real observation conditions; carry out a colorimetric correction (E1) of the mo- image nocular (10) from a color appearance model in- reversible (the), so as to provide a corrected image in colors (11) under reference viewing conditions, so that the perception of colors in the corrected image in colors (It) is identical to the perception of colors of the monocular color image (IO) acquired in the real observation conditions; and process (E4; E4.1) the color-corrected image (II) by ap- replicating a convolutional neural network (4; 4.1; 4.1, 4.2) of way to generate a depth map (14.1; I5) of the monocular color image (I0).

2. A method according to claim !, wherein the monocular image in colors (I0) comprises a plurality of pixels (P;;) and the color correction rimetric (El) comprising the following steps: apply (E11) the invertible color appearance model (la) at each pixel (P;;) of the monocular color image (IO; 11.1), so as to determine at least one perceptual attribute of the pixel (J;;, Cu, h;y) selected from: lightness (J), chromaticity (C), hue angle (h), brightness (Q), saturation (s), com- tint position (H); invert (E12) the invertible color appearance model (the) so as to provide an inverse color appearance model t{Iib) :and for each pixel (P;;), apply (E12) said at least one perceptual attribute (J;;, Cy, h;) to the color appearance model inverse (1b) configured with the observation conditions of reference, so as to provide trichromatic values corrected (X>;, Y';;, 2') of said pixel (P;;).

3. The method of claim 2, wherein the color correction- metric (El) further includes a frequency estimation (E13), at which a spatial frequency (F,;) of each pixel (P;) of the monocular color image (IQ; I1.1) is estimated, the frequency estimated (F;;) being provided as input to the color appearance model inverse (1b) to obtain the corrected trichromatic values ​​(X®;, Yi, Z';) of said pixel (P,,;).

4. The method of claim 3, wherein the frequency estimation (E13; E13.1, E13.2) includes a decomposition (E13.1) of the image monocular in colors (T0; T1.1) in a plurality of fre- quentials (So-S;6 ; S,) and a decomposition (E13.2) of the mo- image nocular in colors {IO; 11.1) according to several spatial orientations (E13.2), the frequency (F,;) being estimated taking into account the influence frequency domains adjacent to the frequency domain to which ap- part of said pixel (P,;) so as to obtain a spatio-frequency map- pixel quantity (11.3).

5. A method according to any one of claims 1 to 4, wherein the invertible color appearance model (the) is the CIECAM2 model configured with at least one of the following parameters: co- chromatic ordinates of a reference white (Xy, Yw Zw), lU- ambient light intensity (L,), background light intensity (ŸY,), indicator environment (E).

6. A method according to any one of claims 1 to 5, comprising in in addition to the following steps: filter (E2) the monocular color image (I0) by applying a linear quaternion filter guided by an image of reference (I), so as to provide a quaternionic image filtered (q; I2) including texture data from the image monocular (10); and subtract (E3) the filtered image (I2) from the corrected image in colors (11), so as to obtain a texture map (I3).

7. The method of claim 6, further comprising the steps following: upsample (E; E4.2) the depth map, to re- reduced solution, (14.1) by application of a hierarchical network archique (4.2) so as to provide characteristics of oversampled depth (1424); concatenate (E4.24) the texture map (I3; l'3) and the charac- oversampled depth characteristics (1413) to provide a residual depth map (14.2); and add (ES) the residual depth map (14.2) and the reduced depth map (14.1), so as to obtain a final depth map (I5) of at least equal resolution to that of the monocular image (10).

8. Device (100; 600) for implementing the estimation method according to any one of claims 1 to 7, comprising: a monocular optical capture device (0) to obtain a monocular color image (10) under conditions of real observations; a color correction module (1) of the mo- image color nocular (IO) based on an appearance model invertible color (the), so as to provide an image color corrected (II) under viewing conditions of reference, so that the perception of colors in the image corrected in colors (I1) is identical to the perception of colors in the acquired monocular color image (10) under real observation conditions; and a module for generating (4) a depth map (14.1; 15) configured to apply a convolutional neural network (4; 4.1, 4.2) to the color-corrected image (I1).

9. Device (100; 600) according to claim 8, further comprising: a linear quaternionic filtering module (2) guided by a reference image {T) configured to filter the mo- image nocular in colors (I0) so as to obtain an image filtered (q; 12) including texture data from the image color monocular (IQ); and a subtraction module (3) configured to subtract the filtered image (I2) of the color-corrected image (I1).

10. Autonomous mobility device (700; 800) comprising a device (100; 600) according to claim 8 or 9.