Method and computing system for determining a three-dimension estimation of a data volume

Abstract

A method for performing segmentation of a data volume, said data volume comprising a plurality of 3D objects, and the method comprises segmenting at least a selected one of the plurality of 3D objects and performing segmentation of the selected 3D object within the data volume, said segmentation comprising: - for at least one image of the data volume, performing segmentation of the selected 3D object in the image, - for at least one image adjacent to the image in an acquisition direction, performing segmentation of the selected 3D object in the adjacent image, - determining an adjacent section formed by a plurality of segmented images along the acquisition direction, - updating the segmentation of the selected 3D object in the segmented images of the adjacent section, based on a constraint on the pixels belonging to the selected 3D object, considered in a direction transverse to the acquisition direction.

Description

DescriptionTitle: Method and computing system for determining a three-dimension estimation of a data volumeTechnical Field

[0001] The present disclosure relates to the processing of images in a data volume for performing segmentation of three dimensional objects in the data volume. The segmentation may notably use prior knowledge on the geometrical and / or physical properties of such objects. Such data volume may especially belong to a geological formation in order to derive information that may be used for analyzing the geological formation and for exploiting the geological formation (e.g. for soil surveys for wind farm installation, for determining if and how the geological formation can be used for hydrocarbon recovery, for hydrogen storage and / or for carbon dioxide storage).Background Art

[0002] It is known, especially in hydrocarbon exploration, to determine the position of oil reservoirs from the results of seismic measurements carried out from the surface or in well bores.

[0003] According to the technology of reflection seismology, these seismic measurements involve emitting a wave (e.g. acoustic waves) into the subsurface and measuring a signal comprising a plurality of echoes of the wave on geological structures of the geological formation. These geological structures are typically surfaces separating distinct stratigraphic layers, faults, etc. Other measurements may be carried out at wells bores.

[0004] Chrono-stratigraphic analysis is very important to understand basin evolution, predict the sedimentary facies distribution for both hydrocarbon exploration and development. This analysis is based on the fundamental assumption that seismic reflectors are surfaces of chrono-stratigraphic significance. This assumption implies that an individual seismic reflector is a "time-line" through a depositional basin that represents a surface of the same geological age (i.e. an isochronous surface in geological time).

[0005] A seismic image comprises a juxtaposition in a volume of sampled one-dimensional signals referred to as seismic traces. In a seismic trace, the value of a pixel (a.k.a. voxel for 3D images) is representative of the amplitude of the seismic measurement obtained for the portion of the geological formation represented by this pixel.

[0006] Such a seismic image may be used (possibly in combination with other information) to compute a stratigraphic image of the geological formation, i.e. to compute a representation of a stacking of estimated stratigraphic layers composing said geological formation. Determining such a stratigraphic image usually relies on estimating isochronous surfaces of the geological formation, based on the seismic image.

[0007] For instance, [LOMASK 2006] describes a method for determining seismic horizon surfaces based on a seismic image, by computing the local seismic dip at each pixel of the seismic image and searching iteratively for surfaces having local gradients approaching the local seismic dips. Such seismic horizon surfaces are examples of estimated isochronous surfaces.

[0008] Such seismic horizon surfaces can further be used to determine a relative geological time,RGT, image of the geological formation, i.e. an image in which each pixel provides an estimated geological age for the portion of the geological formation represented by said pixel. The RGT image is referred to as “relative” because the purpose of the RGT image is mainly to be able to compare the estimated geological ages of different pixels, in order to e.g. identify portions of the geological formation that have the same estimated geological age. Also, in practice, it is usually not possible to estimate an absolute geological age of any given portion of the geological formation. An RGT surface, i.e. a set of points of the RGT image which correspond to pixels having the same estimated geological age in said RGT image, is also an example of estimated isochronous surface.

[0009] Such estimated isochronous surfaces can be used to determine estimated stratigraphic layers of the geological formation. For instance, an estimated stratigraphic layer may be defined between two particular estimated isochronous surfaces which are considered to represent strong seismic reflectors (e.g. associated to high amplitude seismic values of the seismic traces), whereby strong seismic reflectors are likely to correspond to interfaces between different real stratigraphic layers of the geological formation. More precisely, such estimated isochronous surfaces can be used to estimate a geometry of said real stratigraphic layers. Other characteristics of the real stratigraphic layers, e.g. the sedimentary facies of each real stratigraphic layer, are determined by using other methods.

[0010] Various methods exist to estimate stratigraphic layers based on a seismic image of a geological formation.

[0011] For instance, publication EP0923764A1 describes a method for detecting events having a discontinuous character in a multidimensional image based on a propagation of prominent points. In another example, [GUILLON 2013] describes a tool for chronostratigraphic seismic interpretation by mapping the stratigraphic architecture of a seismic volume.

[0012] Some of such methods also estimate stratigraphic layers of a geological formation while taking into account the presence of stratigraphic discontinuities (e.g. fault, salt dome, etc.) resulting in vertical shifts of the stratigraphic layers.

[0013] For instance, [BOILLOT 2023] describes a method and a computation system for predicting the stratigraphic layers of a geological formation using artificial intelligence, based on stratigraphic stacking constraints.

[0014] However, such existing methods usually focus on stratigraphic and seismic texture continuity based on seismic images, without considering a three-dimension consistency of the seismic information, at the scale of the whole geological formation as a seismic volume.

[0015] For example, the method described in [BOILLOT 2023] proposes a mapping of the stratigraphic layers in a geological formation starting from a reference slice delimited by stratigraphic discontinuities (e.g., due to faults). Thus, such method proposes a local approach for determining seismic interfaces. Yet, considering that a three-dimensional geological formation potentially presents numerous discontinuities, such method would have to applied several times, notably by considering several reference slices, yet, such iterations would not provide a global three- dimensional consistency of the seismic information at the scale of the whole geological formation, at least not without further corrections and analyses.

[0016] A three-dimensional continuity may be obtained by performing predictions directly for each voxel of the geological formation. Yet, such prediction is computationally-complex, resource-hungry and difficult to perform in practice, as it would require labeling voxels.

[0017] As a consequence, there is a need to improve the physical and geometrical consistency in existing methods for estimating the geological formation, considered in any direction of its volume. More generally, there is a need to improve the estimation of a data volume by accurately identifying and delimiting three-dimensional objects in such data volume.Summary

[0018] This disclosure improves the situation.

[0019] In an aspect of the present disclosure, it is proposed a computer implemented method for performing segmentation of a three-dimensional data volume, said data volume comprising a plurality of three-dimensional, 3D, objects, and the method comprises segmenting at least a selected one of the plurality of 3D objects, the method comprising: performing segmentation of the selected 3D object within the data volume, said segmentation comprising:- for at least one two-dimensional image of the data volume, performing segmentation of the selected 3D object in the image,- for at least one image adjacent to the image in an acquisition direction, performing segmentation of the selected 3D object in the adjacent image,- determining at least one adjacent section formed by a plurality of segmented images along the acquisition direction,

[0020] - updating the segmentation of the selected 3D object in the segmented images of the adjacent section, based on at least a constraint on the pixels belonging to the selected 3D object, considered in a direction transverse to the acquisition direction. As a consequence, the proposed method enables to obtain a consistent and rapidly exploitable result of volume segmentation throughout the three dimensions of a data volume, without requiring further correction and / or recalculation of the estimation. Moreover, such three-dimensional continuity is obtained while working with two-dimensional images acquired in an acquisition direction. The proposed method is thus adaptable to existing inputs and is based on partial data inputs yet enables coherent multidimensional interpretations for further analysis of the data volume.

[0021] Furthermore, this method facilitates the segmentation process by reducing the need for extensive manual corrections and iterative processes that are typically required to achieve a consistent 3D representation when using conventional methods. By constraining the segmentation in a transverse direction, the segmentation process is guided throughout the data volume, directly leading to an improved global consistency, without requiring a complex a posteriori correction of the segmentation. This leads to a reduction in computational resources and time required to achieve asatisfactory segmentation result, thereby enhancing the efficiency of the overall data volume processing workflow.

[0022] By performing segmentation of the selected 3D object in the image, the method allows for a rapid and simplified initial segmentation process. This approach leverages the efficiency of 2D image processing while setting the stage for subsequent 3D consistency. The subsequent step of performing segmentation in at least one image adjacent to the initial image in the acquisition direction enables the method to extend the segmentation process through the data volume. This iterative approach allows for the progressive building of a three-dimensional segmentation from a series of two-dimensional segmentations, which is less computationally intensive than a full 3D segmentation performed on voxels of the data volume. The complexity and computational load is thus reduced compared to direct 3D segmentation.

[0023] Determining at least one adjacent section formed by a plurality of segmented images along the acquisition direction advantageously provides a framework for assessing the continuity and consistency of the segmentation across different layers of the data volume. This step is crucial for maintaining the geometrical coherence of the segmented objects throughout the volume. For example, in the case of the data volume corresponding to a geological formation, such step enables to maintain a geological coherence of the segmented objects throughout the geological formation.

[0024] Updating the segmentation of the selected 3D object in the segmented images of the adjacent section, based on at least a constraint on the pixels belonging to the selected 3D object, considered in a direction transverse to the acquisition direction, ensures that the segmentation respects the physical and geometrical properties of the objects within the data volume. This constraint, possibly informed by physical laws or structural information of the data volume for example, enhances the accuracy and reliability of the segmentation, particularly in maintaining the three-dimensional consistency of the object features across the entire volume. Indeed, by considering a transverse direction of the data volume, the proposed disclosure enables to perform segmentation of the objects in the data volume by considering both sectional and cross-sectional consistencies of the objects.

[0025] The following features, can be optionally implemented, separately or in combination one with the others:

[0026] In an embodiment, the transverse direction corresponds to an orthogonal direction with respect to the acquisition direction.

[0027] In an embodiment, the constraint for updating the segmentation of the selected 3D object relates to a geometric continuity of the selected 3D object on the transverse direction.

[0028] By incorporating a constraint that relates to the geometric continuity of the selected 3D object on the transverse direction, the method ensures that the segmentation of the 3D object maintains its geometric integrity across different orientations. In particular, when the data volume corresponds to a geological formation, such geometrical constraint addresses the issue of maintaining the natural shapes and boundaries of geological structures, such as the dips, when viewed from various (and notably cross-sectional) angles, which is particularly important in the context of seismic datainterpretation where the accuracy of the geological model is critical. The constraint on geometric continuity allows for a more accurate representation of the 3D object within the data volume, as it enforces the alignment of the segmented object with the actual global geometric features of the data volume. This results in a more reliable and coherent 3D model of the data volume.

[0029] In an embodiment, the segmentation of the selected 3D object in the image resulting in a segmented piece, and performing the segmentation of the selected 3D object in the adjacent image comprises:-- determining at least one other piece in the adjacent image, and-- predicting said other piece as having a same label as the segmented piece.

[0030] By segmenting a selected 3D object in one image to obtain a segmented piece and then determining a corresponding piece in an adjacent image, the method ensures continuity in the labeling process across different images. This approach facilitates the creation of a coherent 3D representation of the data volume and its contained 3D objects, by maintaining consistent labeling of corresponding structures across multiple images. Such advantage is particularly beneficial in the context of geological formations, where continuity of features such as stratigraphic layers is crucial for accurate soil analysis.

[0031] The prediction of the other piece in the adjacent image as having the same label as the segmented piece allows for the extension of identified geological features across the data volume. This method effectively bridges the gap between separate images, enabling a more seamless and integrated interpretation of the data volume. This is especially advantageous when dealing with complex 3D object structures that span through multiple images, as it reduces the need for manual intervention and iterative corrections that are typically required to achieve a coherent 3D model.

[0032] In an embodiment, segmenting a selected 3D object in an image comprises assigning, to a plurality of pixels of the image, labels associated with the selected 3D object, and updating the segmentation of the selected 3D object comprises:-- determining a transverse portion of the adjacent section, said transverse portion intersecting the segmented images of said adjacent section,-- for said transverse portion, updating the segmentation of the selected 3D object by updating at least the labels assigned to the pixels belonging to said transverse portion.

[0033] The updating of the segmentation of the selected 3D object through the determination of a transverse portion of the adjacent section allows for the refinement of the segmentation in areas where the initial labeling and segmentation performed in the acquisition direction may not have fully captured the complexity of the object structures. This transverse portion intersects the segmented images of the adjacent section, providing a cross-sectional view that can reveal inconsistencies or errors in the initial segmentation performed in the acquisition direction. Updating the segmentation by adjusting the labels assigned to the pixels within this transverse portion ensures that thesegmentation is consistent and accurate across different orientations within the 3D volume. This approach improves the physical and geometrical consistency of the data volume.

[0034] By a transverse portion, it is understood a cross-sectional portion of the adjacent section included in the adjacent section and intersecting the segmented images of the adjacent section. Such transverse portion can be a plan or a 3D portion. In particular, the transverse portion can be an orthogonal portion, cross-sectioning the adjacent section in a perpendicular way, or an oblique portion, cross-sectioning the adjacent section in an oblique way. The transverse portion is not parallel to the segmented images of the adjacent section.

[0035] In an embodiment, the proposed computer implemented method further comprises: determining at least one labelled reference piece, corresponding to a part of the two- dimensional image being labelled as the selected 3D object, and the segmentation of the selected 3D object is performed based on said labelled reference piece.

[0036] By determining at least one labelled reference piece corresponding to a part of the two- dimensional image being labelled as the selected 3D object, the segmentation process is anchored to a specific, known part within the data volume. This approach leverages the labelled reference as a starting point for the segmentation, which can enhance the accuracy of the segmentation process by providing a reliable reference that the algorithm can use to extend the segmentation throughout the 3D data volume. The use of a labelled reference piece also allows for the application of hybrid supervised and unsupervised machine learning techniques. Supervised learning can be applied directly to the labelled lines, for example providing a foundation for the algorithm to calibrate the geological dips (dips) subsequently in the case of the data volume corresponding to a geological formation. This can result in a more coherent 3D segmentation output that aligns with the structure of the data volume.

[0037] In an embodiment, the data volume is a seismic acquisition of a geological formation and the selected 3D object is a geological object present within the geological formation.

[0038] Thus, the aforementioned advantages of the proposed method are particularly useful in the field of seismic analysis, thereby improving the geological interpretation and analysis of the subsurface formation. Such improved knowledge about the geological structure are notably essential for assessing the potential of aquifers, reservoirs and other subsurface formations for applications such as hydrocarbon recovery, hydrogen and / or carbon dioxide storage, or for soil characterization for wind farm installation for example.

[0039] The proposed method advantageously relies of two dimensional images that may typically correspond to seismic images, which are systematically retrieved in the field of geophysics. The method thus ensures compatibility with standard practices in the field.

[0040] In an embodiment, the selected 3D object is at least part of a stacking of estimated stratigraphic layers.

[0041] In such embodiment, performing segmentation of the selected 3D object in the image further includes: determining, in the image, at least one labelled reference slice corresponding to part of the stacking of estimated stratigraphic layers, segmenting at least another slice in the image corresponding to an adjacent part of the stacking of estimated stratigraphic layers in the image, determining the image as a reference segmented image.

[0042] By determining at least one labelled reference slice corresponding to part of the stacking of estimated stratigraphic layers, the method provides a basis for the segmentation process that is grounded in the physical structure of the geological formation. This approach leverages the inherent stratigraphic information within the seismic data to guide the segmentation, ensuring that the identified 3D objects are consistent with the geological context. Segmenting another slice in the image corresponding to an adjacent part of the stacking of estimated stratigraphic layers allows for the extension of the segmentation process to neighboring areas. This step ensures that the segmentation takes into account the continuity of geological features across adjacent slices, thereby enhancing the accuracy and relevance of the segmentation in a three-dimensional context.

[0043] By relying the segmentation on a reference part of the stacking of estimated stratigraphic layers, the method facilitates a coherent and consistent approach to the delineation of stratigraphic layers throughout the entire geological formation.

[0044] In an embodiment, the segmentation of the selected 3D object is performed by using a segmentation model corresponding to a physics-informed neural network, PINN, trained to update the segmentation of the selected 3D object according to the constraint, said constraint being related at least to a geometric continuity of interfaces delimiting said estimated stratigraphic layers. Alternatively or cumulatively, said constraint may also be related to the conservation of local entropy when segmenting the selected 3D object.

[0045] By employing a physics-informed neural network (PINN) as the segmentation model, the method ensures that the segmentation of the selected 3D object adheres to physical constraints inherent to the geological formation. This approach allows for the incorporation of geological knowledge, and notably the geometric continuity of interfaces, into the segmentation process. Such physical constraint may also be reflected in the conservation of local entropy in different portions of the geological formation. As a result, the segmentation output is more likely to reflect the true and continuous three-dimensional structure of the geological formation, leading to more accurate and reliable interpretations of seismic data.

[0046] The use of a PINN also enables the segmentation model to be trained with a combination of labeled data and the physical constraints derived from the geological formation characteristics. This hybrid training approach can potentially reduce the amount of labeled data required, as the model leverages both data-driven learning and domain-specific rules to refine the segmentation.Consequently, the method can provide a coherent 3D segmentation of geological formations with less manual labeling effort.

[0047] This leads to a more physically plausible segmentation that respects the inherent structure of the geological formation.

[0048] In an embodiment, the segmentation is performed by implementing a machine learning model, preferably a neural network, NN, trained on at least pixel values of training images related to the data volume.

[0049] In an embodiment, updating the segmentation of the selected 3D object is performed using a semi supervised machine learning model, implementing at least unsupervised learning on at least pixel values of the adjacent section.

[0050] In another aspect of the present disclosure, it is proposed a computer program product comprising instructions which, when executed by at least processor, configure said at least one processor to carry out the proposed method.

[0051] In another aspect of the present disclosure, it is proposed a computer-readable non-transient storage medium comprising instructions which, when executed by at least one processor, configure said at least one processor to carry out the proposed method.

[0052] In another aspect of the present disclosure, it is proposed a computing system comprising at least one memory and at least one processor configured to carry out the proposed method.Brief Description of Drawings

[0053] Other features, details and advantages will be shown in the following detailed description and on the figures, given that such features are examples that are no way limiting:Fig. 1

[0054] [Fig. 1] is an example of a two-dimensional image according to an embodiment.Fig. 2

[0055] [Fig. 2] is an example of a data volume according to an embodiment.Fig. 3

[0056] [Fig. 3] is a flowchart illustrating steps for segmenting a 3D object in a data volume according to an embodiment.Fig. 4

[0057] [Fig. 4] illustrates examples of adjacent images in the data volume according to an embodiment.Fig. 5

[0058] [Fig. 5] illustrates examples of reference elements in an image according to an embodiment.Fig. 6

[0059] [Fig. 6] illustrates an adjacent section according to an embodiment.Fig. 7

[0060] [Fig. 7] illustrates examples of the use of a transverse portion in the segmentation method according to an embodiment.Fig. 8

[0061] [Fig. 8] illustrative comparative segmentation results.

[0062] In these figures, references identical from one figure to another designate identical or analogous elements. For reasons of clarity, the elements shown are not to scale, unless explicitly stated otherwise.

[0063] Also, the order of steps / phases represented in the figures is provided only for illustration purposes and is not meant to limit the present disclosure which may be applied with the same steps / phases executed in a different order.Description of Embodiments

[0064] As discussed above, the present disclosure relates to a computer implemented method 30 for performing segmentation of a three-dimensional (or 3D) data volume comprising a plurality of three dimensional (or 3D) objects. The method 30 and its detailed steps will be further illustrated by examples and figures with a data volume corresponding to a seismic acquisition of a geological formation. Yet, the proposed method 30 is not purely restricted to the seismic field. Indeed, the method 30 may also be applied in the field of medicine, where the data volume may for example correspond to the fundus of an eye or to parts within a body. The 3D objects to be segmented with such data volume may then correspond to tissues, organs and skeleton structures for instance. The images of such data volume may be acquired via magnetic resonance imaging (or MRI) and / or computed tomography (or CT) for example. More generally, the data volume may correspond to any 3D volume containing objects to be segmented and within which images may be acquired by any imaging means. Such imaging means are configured to acquire two-dimensional (or 2D) images in a direction referred to as the acquisition direction.

[0065] A schematic illustration of a data volume 1 is represented on figure 2. The shape of the data volume 1 is purely illustrative and non-limitative. The data volume 1 is modelized as a cuboid volume positioned in an orthogonal reference frame (X, Y, Z). Alternatively, the reference frame (X,Y,Z) may be different, with secant yet non-orthogonal axes X, Y, Z for example. Images 2 of such data volume 1 may be acquired according to the acquisition direction X. The number, resolution and repartition of acquired images of the data volume may vary depending on the nature of the data volume and on the imaging means notably.

[0066] In the following description, the data volume 1 is considered to be a geological formation. Images acquired in such geological formation correspond to seismic images. A seismic image, as synthetized and represented on figure 1 as an example, represents a picture of the subsoil arising from a seismic exploration survey. The seismic image represented by figure 1 is 2D and maycorrespond to a 2D seismic image or to a 2D section of a 3D seismic image, in a vertical plane. Such seismic image is composed of pixels regularly distributed according to a horizontal resolution on a horizontal dimension (represented by direction Y on figure 2) of the image and a vertical resolution on a vertical dimension (represented by direction Z on figure 2) of the image. The seismic image comprises: a number of columns of pixels which is equal to the quotient of the horizontal extension along the horizontal dimension divided by the horizontal resolution along the horizontal dimension; and a number of pixels per column which is equal to the quotient of the vertical extension divided by the vertical resolution.

[0067] Each pixel is associated with a seismic value which is representative of the amplitude of the seismic signal measured for the portion of the geological formation represented by the corresponding pixel.

[0068] In the sequel, a point corresponds to a set of coordinates in the grid of the seismic image, i.e. a set comprising a horizontal position along each horizontal dimension and a vertical position along the vertical dimension. A pixel therefore corresponds to a point with a value associated thereto (i.e. a seismic value in the case of a pixel of the seismic image, an estimated geological age in the case of a pixel of an RGT image, etc.).

[0069] In the context of a data volume corresponding to a geological formation, images 2 may thus correspond to seismic images composed on pixels associated to seismic values. As can be seen in figure 1 , the seismic values highlight the composition of the geological formation, since high amplitude seismic values are usually associated to strong seismic reflectors.

[0070] The geological formation includes a plurality of 3D geological objects. In particular, such 3D objects may include a stacking of estimated stratigraphic layers.

[0071] The present disclosure notably relates to the segmentation of objects contained in the data volume. In particular, the present disclosure relates to the segmentation of the estimated stratigraphic layers in the geological formation.

[0072] Figure 3 represents schematically an exemplary embodiment of a segmentation method 30 for segmenting the data volume 1. In particular, the segmentation method 30 enables determining the estimated stratigraphic layers of the geological formation.

[0073] By segmenting the data volume 1 , it is understood assigning labels to at least part of a plurality of delimited unitary portions of the data volume 1 associated to respective 3D objects. In the case of a geological formation, such delimited unitary portion may for example be geological units. Each delimited unitary portion of the data volume 1 may be associated to a voxel corresponding to a 3D pixel having a value highlighting the composition or other physical properties of the delimited unitary portion. A geological unit may be associated to a voxel having a seismic value. Segmenting the geological formation may be understood as assigning different geological units of the geological formation to geological objects, such as estimated stratigraphic layers for example.

[0074] By segmenting a 3D object in an image 2 or an adjacent image 2’, it is understood assigning labels to a plurality of pixels o the image 2, 2’ associated to a 3D object. Such segmentation may beperformed for a same 3D object in different images and / or for different 3D objects in a same image. Segmenting a 3D object in several images of the data volume 1 is relevant in the context of a 3D object spanning through the data volume over different images. This is typically the case of a stacking of estimated stratigraphic layers in a geological formation, with stratigraphic layers extending through the geological formation with varying dips throughout the geological formation. This is also the case of a 3D object such as a blood vessel extending within a body and which spans over different CT scan images.

[0075] The segmentation method 30 is carried out by a computing system (not represented in the figures). In some examples, the computing system comprises one or more processors (which may belong to a same computer or to different computers) and one or more memories (which may belong to a same computer or to different computers). The one or more processors may include for instance a central processing unit (CPU), a digital signal processor (DSP), a field-programmable gate array (FPGA), an application specific integrated circuit (ASIC), etc. The one or more memories may include any type of computer readable volatile and non-volatile memories (magnetic hard disk, solid-state disk, optical disk, electronic memory, etc.). The one or more memories may store a computer program product, in the form of a set of program-code instructions to be executed by the one or more processors in order to implement all or part of the steps of the segmentation method 30. In other words, the computing system comprises a set of means configured by software (specific computer program product) and / or by hardware (CPU, DSP, FPGA, ASIC, etc.) to implement the steps of the segmentation method 30.

[0076] As illustrated by figure 3, the segmentation method 30 comprises a step S30 of obtaining at least one image 2 of the data volume. Such image 2 may be directly acquired by imaging means or may result from a preprocessing and / or processing of an acquired image. For example, the image 2 obtained at step S30 may correspond to a seismic image acquired from a data volume 1 corresponding to a geological formation. Such seismic image is represented on figure 1.

[0077] The image 2 obtained at step S30 may also correspond to a stratigraphic image obtained by processing the seismic image of figure 1 , using any method known to the skilled person. The stratigraphic image corresponds to a stacking of estimated stratigraphic layers of the geological formation and is for example illustrated on figure 5.

[0078] Step S30 may include obtaining a plurality of images 2 of the data volume 1 . Such plurality of images 2 may result from an image acquisition of different parts of the data volume, as represented on figure 2.

[0079] The image 2 or plurality of images 2 obtained at step S30 is / are acquired in the acquisition direction. Such acquisition direction is understood as the principle (or optical) axis of the imaging means acquiring the image of the data volume. The images 2 are considered to have a same acquisition direction. Such acquisition direction is for example illustrated as direction X on figure 2.

[0080] The segmentation method 30 then comprises a step S31 of segmenting at least one selected 3D object in the at least one image 2 obtained at step S30. The selected 3D object may correspondto an object of interest to be identified and / or which contour is to be delimited within the data volume1. For example, the selected 3D object may be a specific tissue, organ, blood vessel or structure to be delimited within a body part corresponding to the data volume 1 . The selected 3D object may also correspond to a stacking of estimated stratigraphic layers or to one or several specific stratigraphic layers in a geological formation corresponding to the data volume 1. Step S31 and the next steps will be further described for one selected 3D object and considering one image 2. Yet, segmentation method 30 may also be performed for a plurality of 3D objects and starting from a plurality of images2, in which case step S31 and the next steps S32 to S34 may be repeated for each selected 3D object in each image 2.

[0081] During step S31 , labels are assigned to at least part of the pixels of the image 2 associated to the selected 3D object. For example, referring to figure 5, all pixels of the image 2 may be assigned to labels associated to the different estimated stratigraphic layers forming the represented stacking of stratigraphic layers. Pixels comprised in referenced zones 211 and 21 T notably, may be assigned to a same label associated to a same stratigraphic estimated layer.

[0082] To that end, the segmentation method 30 may rely on a segmentation model configured to at least perform segmentation of the selected 3D object in the image 2. Such segmentation model may be a machine learning model, such as a neural network model. In such implementation, the segmentation model may be trained beforehand on pixel values of a plurality of training images. Such training images may notably relate to the data volume 1 , which means that the training images are based on images acquired in the data volume 1 and / or in other volumes potentially presenting similar properties and / or 3D objects with respect to the data volume 1 . For example, when the data volume1 is a geological formation, the training images may be images acquired from another geological formation, from an aquifer or a subsoil. Such segmentation model may also be or include a physics- informed neural network, or PINN in the case of a geological formation, or any other informed or finetuned model adapted for segmentation of 3D objects in the specific field of exploitation of the data volume 1. The segmentation model may thus be a pre-trained model configured to perform segmentation of at least the selected 3D object at step S31 .

[0083] Furthermore, in a possible embodiment of the segmentation method 30 (referred to as the supervised embodiment), step S31 may be performed based on supervised means (or equivalently, based on a supervised unit of the segmentation model). To that end, the segmentation model may include supervised learning means which may be pre-trained on labelled training images.

[0084] In the supervised embodiment, step S31 may also include a step of determining at least one labelled reference element in the image 2 (or in each image 2), corresponding to a part of the image2 being labelled as the selected 3D object. Such labelled reference element may be determined by any means known to the skilled person. For example, in the case of stratigraphic images of a geological formation, a labelled reference element may be delimited laterally in a stratigraphic image by one or more stratigraphic discontinuities or faults, as illustrated on figure 5 by the oblique lines extending across the stacking.

[0085] In a first example, referring to figure 5, the selected 3D object may be a specific stratigraphic layer and the labelled reference element is a labelled reference piece 211 , which corresponds to a portion of the image 2 which pixels are labelled in association with such specific stratigraphic layer.

[0086] In a second example, still referring to figure 5, the selected 3D object may be a part of the stacking of estimated stratigraphic layers and the labelled reference element is a labelled reference slice 21 , corresponding to a portion of the image 2 in which pixels are labelled in association with identified stacked stratigraphic layers. A slice corresponds to a local (vertical) stacking of pieces of estimated stratigraphic layers of the stratigraphic image 2. The pieces of estimated stratigraphic layers of the labelled reference slice 21 are considered as reference pieces, which are assumed to belong to (that is, are labelled as belonging to) different respective real stratigraphic layers.

[0087] In such supervised embodiment, step S31 then includes segmenting the selected 3D object in the image 2 by segmenting at least another element in the image 2 corresponding to an adjacent part of the labelled reference element.

[0088] Pursuing with the first example, referring to figure 5, the other element to be segmented is another piece 211 ’ in the image 2, adjacent to the labelled reference piece 211 .

[0089] Pursuing with the second example, still referring to figure 5, the other element to be segmented is another slice 2T in the image 2, adjacent to the labelled reference slice 21.

[0090] Step S31 may then be performed by successively segmenting the whole image 2 starting from a reference element 21 , 211 , which is used as a reference and a landmark for characterizing the respective contents of the 3D objects of the data volume.

[0091] After step S31 , the image 2 is segmented, based on supervised or unsupervised means, and may be referred to as a reference segmented image. The reference segmented image notably includes at least one segmented piece, corresponding to pixels of the reference segmented image associated to the selected 3D object. The reference segmented image may naturally comprise several distinct segmented pieces if the segmentation is performed on the image 2 for several selected 3D objects.

[0092] Such reference segmented image may then serve as a landmark for segmenting other parts of the data volume 1 in the following next steps. Such step may advantageously be performed for a few images 2 acquired in the data volume 1 , which avoids a resource-hungry labelling of the complete data volume 1 , while enabling to obtain several anchors throughout the data volume 1.

[0093] In another embodiment, such step S31 of segmenting the image 2 may be performed using other methods or by considering other labelled reference elements in the image 2.

[0094] At a step S32, segmentation of the at least one selected 3D object is performed in at least one image adjacent to the image 2 in the acquisition direction X, referred to as an adjacent image 2’.

[0095] In order to perform segmentation of at least the selected 3D object in at least one adjacent image 2’, step S32 includes determining at least one other piece in the adjacent image 2’ and predicting such other piece as having the same label as the segmented piece of the referencesegmented image (in the image 2). Such step S32 may be performed by the segmentation model and more particularly by unsupervised means of such segmentation model. Such step S32 may for example be performed using the PINN means of the segmentation model in order to perform segmentation in the adjacent images 2’.

[0096] Examples of such adjacent images 2’ for a given image 2 are illustrated in figure 4 in dotted lines. By an adjacent image 2’, it is understood a 2D section of the data volume forming a parallel plan with the plan containing the image 2. Moreover, such adjacent image 2’ may be defined as having a distance with the image 2 according to the acquisition direction X below a predefined distance d. Such predefined distance d may depend for instance on a required level of accuracy of the segmentation, or on the exploitation purpose of the data volume 1. In an embodiment, such predefined distance d may be defined so that the whole data volume 1 is covered by adjacent images 2’ starting from one image 2.

[0097] Thus, the image 2 and its adjacent images 2’ are parallel according to the acquisition direction X. In other words, an image 2 and its adjacent images 2’ have the same main direction corresponding to the acquisition direction X. It is underlined that the image 2 results from an acquisition (for example by imaging means) while the adjacent images 2’ are considered with respect to the image 2 and are thus estimated images. The image 2, and more particularly the image 2 after segmentation of step S31 , thus serves as an anchor (or a landmark) for considering the adjacent images 2’ and their segmentation at step S32.

[0098] The distance separating the image 2 and an immediate adjacent image 2’ depends on a predefined granularity defined for the data volume 1. For example, two images of the data volume 1 may be considered as immediately successive if there is a continuity for a 3D object spanning through both images in the data volume 1 .

[0099] In particular, an adjacent image 2’ may then correspond to an immediately successive image with respect to the image 2, but may also correspond to an image spaced from the image 2 by one or several other adjacent images 2’ but which distance to the image 2 is still below the predefined distance d. Thus, for each image 2, it may be defined several adjacent images 2’, depending on the granularity to be considered for the segmentation method 30.

[0100] Such step S32 may thus be performed for a plurality of adjacent images 2’ of an image 2. Such segmentation in the adjacent images 2’ are performed successively, starting from the adjacent images 2 being the closest to the image 2. The segmentation of further adjacent images 2’ may then be performed based on already segmented adjacent images 2’ which are immediate adjacent images to the adjacent image to be segmented. More generally, the segmentation in a given adjacent image 2’ relies on a segmented image immediately adjacent to such given adjacent image 2’.

[0101] In case of several images 2, step S32 may be performed for the adjacent images 2’ of each of the images 2. For example, referring to figure 2, three images 2 are considered in the data volume 1. Three batches of adjacent images 2’ respectively associated to each of the three images 2 may then be considered and segmented at step S32.

[0102] After step S32, the data volume 1 includes one or several reference segmented images corresponding to images 2 and corresponding segmented adjacent images, in which at least part of the selected 3D object is segmented.

[0103] At a step S33, at least one adjacent section 3 is determined. Such adjacent section 3 is formed by a plurality of segmented images along the acquisition direction X. More specifically, such adjacent section 3 is formed by a segmented reference image (corresponding to the image 2) and segmented adjacent images (corresponding to adjacent images 2’) based on such segmented reference image.

[0104] An example of an adjacent section 3 is represented on figures 6 and 7. The adjacent section 3 is thus a sub-volume of the data volume 1 , having a thickness K defined according to the acquisition direction X. Such thickness K directly depends on the predefined distance d delimiting the number of adjacent images 2’ for a given image 2.

[0105] In case of several images 2, step S33 includes determining several adjacent sections 3 associated to the respective segmented reference images corresponding to the several images 2. Such several adjacent sections 3 may overlap or not.

[0106] At a step S34, the segmentation method 30 includes updating the segmentation of the selected 3D object in the segmented images of the adjacent section 3, based on at least a constraint on the pixels belonging to the selected 3D object, considered in a direction transverse, to be understood as secant or oblique, to the acquisition direction X. Such direction is referred to as the transverse direction Y.

[0107] To that end, step S34 may include:- determining at least one transverse portion 31 of the adjacent section 3, as illustrated on figure 7 which represents two distinct examples 31a, 31 b of transverse portions 31 , and,- based on such transverse portion 31 , updating segmentation of the selected 3D object by updating labels assigned to pixels of the image 2 and adjacent images 2’ of the adjacent section 3 by constraining pixels belonging to such transverse portion 31.

[0108] The transverse portion 31 determined at step S35 may be a cross-sectional plan or a cross- sectional 3D volume transverse (or oblique) with respect to a front part of the adjacent section 3. For example, referring to figure 7, the adjacent section 3 is formed by a plurality of parallel images 2, 2’ along the acquisition direction X. The adjacent section 3 thus has a thickness K, which depends on the number of images 2, 2’ considered to form the adjacent section 3. A front part of the adjacent section 3 may be understood as the plan parallel to the images 2, 2’ forming the adjacent section 3, here the plan formed by axes (Y,Z). In such context, the transverse portion 31 may be defined as cross-sectional portion included in the adjacent section 3. For example, referring to figure 7, such transverse portion 31 may be parallel to the plan formed by axes (X,Z), as illustrated by transverse portion 31a on figure 7. In another example, the transverse portion 31 may also be unparallel to the plan formed by axes (X,Z), as illustrated by orthogonal portion 31 b on figure 7.

[0109] More generally, the transverse portion 31 of an adjacent section 3 may be understood as a plan or 3D portion included in the adjacent section 3, as a sectional plan or a 3D volume, and providing a cross-sectional view of the adjacent section 3.

[0110] In a possible embodiment, a plurality of transverse portions 31 are determined in the adjacent section 3, and the segmentation is updated by constraining pixels in such parts of the adjacent section 3, the transverse portions 31 serving as anchors for updating segmentation in the adjacent section 3. In another embodiment, a plurality of transverse portions 31 are determined to cover the whole or most parts of the adjacent section 3 and the segmentation is updated based on all transverse portions 31 , so that the segmentation is updated by considering constraints on many pixels belonging to the adjacent section 3.

[0111] Updating the segmentation based on the transverse portion 31 implies constraining the segmentation of the selected 3D object in such transverse portion 31 so as to minimize a transverse loss function. Such transverse loss function reflects the gap between the predicted 3D dip in the transverse portion 31 and the real 3D dip based on physical knowledge of the geological formation.

[0112] The step of updating the segmentation on the transverse portion 31 is equivalent to applying a smoothing constraint by the local geometry of the data volume 1. More precisely, step S34 notably includes extracting, for each transverse portion 31 , the labels predicted for pixels of the images 2 and adjacent images 2’ belonging to such transverse portion 31. Such extracted labels then serve as a smoothing constraint for updating the predicted labels images 2 and adjacent images 2’ in such adjacent portion 3 during step S34, so as to minimize the transverse loss function.

[0113] Figure 7 illustrates such updating of the segmentation step S34 of the selected 3D object in the segmented images of the adjacent section 3, using a transverse portion 31. Referring to figure 7, it is considered one adjacent section 3 and step S34 is detailed for one considered transverse portion 31a.

[0114] Figure 7(a) illustrates a (synthesized) seismic portion as viewed from the perspective of the transverse section 31a (for example, as would the pixels be viewed at step S30, but from a cross- sectional view of the transverse section 31a). It is noted that such seismic portion spans over the image 2 considered at step S31 and the adjacent images 2’ considered at step S32.

[0115] The edges of the at least one selected 3D object (here, the stacking of estimated stratigraphic layers) in such transverse section 31a can be detected by calculating a structure tensor on the seismic portion image of figure 7a), such structure tensor being approximated as gradients respectively calculated on vertical (here, along the Z-axis) and horizontal (here, along the X-axis) directions of the transverse section 31a. For example, a Sobel filter may be used. Figure 7b) illustrates arrows (i.e., gradient vectors) resulting from the product of such (vertical and horizontal) gradients and represents the edge (contour) detection of the selected 3D object in the seismic portion of figure 7a) (that is, before the segmentation steps of S31 and S32), viewed in the transverse portion 31a.

[0116] Figure 7c) illustrates the labels predicted for pixels of the images 2 and adjacent images 2’ belonging to such transverse portion 31a. Such labels are notably the result of step S32 viewed from the perspective of the transverse portion 31a.

[0117] Then, figure 7d) illustrates arrows resulting from the product of (vertical and horizontal) gradients calculated on the predicted image portion of figure 7c). In other words, similarly to figure 7b), figure 7d) provides an edge detection of the selected 3D object in the labelled portion of figure 7c) (that is, after the segmentation steps of S31 and S32), viewed in the transverse portion 31a.

[0118] The comparison of the detected edges of the selected 3D object before (figure 7b)) and after (figure 7d) the segmentation of the selected 3D object performed in the acquisition direction X via steps S31 and S32 enables to assess such segmentation in the acquisition direction X, so as to update (i.e., correct) such segmentation during step S34. To that end, a scalar product of the gradient vectors as shown on figures 7b) and 7c) results in the transverse loss function as represented on figure 7e) (the represented scale being a metrics reflecting a level of edge segmentation error). The transverse loss function as represented on figure 7e) thus reflects the edge detection errors of the segmentation in the acquisition direction X, with respect to the seismic dips observed in the actual seismic portion of figure 7a) (segmentation errors occur when the labelled object edges do not match with the seismic dips of the seismic portion).

[0119] In such view, step S34 performs a correction of such segmentation errors by minimizing the transverse loss function, resulting in an updated segmentation of the selected 3D object. Notably, such updating step is performed by constraining the labels of the pixels in the transverse portion 31 (as shown on figure 7c for example) to follow the seismic dips of the actual seismic portion in the transverse portion 31 (as shown on figure 7a for example). The updating step S34 thus performs a segmentation of the pixels in the adjacent section 3 (thus, pixels in image 2 and a plurality of adjacent images 2’) based on some constrained pixels (which are the transverse portion(s) 31 of the adjacent section 3. In particular, such updating step S34 is performed in the transverse direction Y, since the adjacent section 3 and the corresponding transverse portion 31 are considered in such transverse direction Y. Such updated segmentation S34 advantageously relies on the cross-sectional view of the data volume and the selected 3D objects (here, the geological formation and the stacking of estimated stratigraphic layers).

[0120] Step S34 results in an updated segmentation of the data volume in the adjacent section 3. Such step S34 may also be performed so as to update the segmentation on the whole 3D volume, by considering constraints in the one or several transverse portions 31 of one or several adjacent sections 3, as well as a continuity hypothesis between transverse portions 31 and between adjacent sections 3.

[0121] In another embodiment, the update of the segmentation at step S34 may be performed directly on the whole adjacent section 3, by updating the segmentation in the transverse direction Y. Yet, the use of transverse portions 31 is more time and resource efficient, while providing more precise segmentation results.

[0122] The constraint for updating the segmentation of the selected 3D object may especially relate to a geometric continuity of the selected 3D object on the transverse direction Y. Such constraint on the transverse direction Y then adds a cross-sectional view with respect to the previous steps. Indeed, segmentation of the selected 3D object performed in previous steps relies on a segmentation continuity of the selected 3D object in the acquisition direction X, since segmentation is performed for images 2 and their adjacent images 2’ according to the acquisition direction X. Yet, due to the three-dimensional nature of the data volume 1 , such continuity is not yet guaranteed in the transverse direction Y, that is when considering transverse portions of the adjacent section 3, as illustrated on figure 7.

[0123] When considering the data volume 1 as a geological formation, the constraint for updating the segmentation of the selected 3D object in the adjacent section 3 may relate to a stacking order of estimated stratigraphic layers present in the geological formation. Such constraint may also relate to a geometric continuity of interfaces delimiting said estimated stratigraphic layers. Indeed, when considering the geological formation in the transverse direction Y (as stratigraphic images 2 are defined in the acquisition direction X illustrated on figures 2, 4, 6 and 7), geometric lines delimiting the interfaces of the different stratigraphic layers are considered. Segmentation of a selected 3D object corresponding to the stacking of such stratigraphic layers or to a considered stratigraphic layer should thus take the consistency (or continuity) of such geometric lines into account.

[0124] By updating the segmentation of the selected 3D object in the segmented images of the adjacent section 3, it is understood rechallenging the labels assigned to the pixels in the segmented images of the adjacent section 3. Such label rechallenging may thus lead to modifying the assigned labels or maintaining the assigned labels.

[0125] To that end, step S34 may rely on the segmentation model as mentioned for updating the labels of the pixels belonging to each of the transverse portions 31. In particular, such updating may rely on unsupervised means of the segmentation model since no labelling consistent in the transverse direction Y has been fed to the segmentation model beforehand.

[0126] Such unsupervised means of the segmentation model for performing step S34 may rely on a physics-informed neural network, PINN, trained to update the segmentation of the selected 3D object according to the constraint in the transverse direction Y.

[0127] As illustrated on figure 7, updating the segmentation of the selected 3D object enables to integrate the geometrical constraint of the data volume reflected as the geometrical loss function to be optimized , thus improving the segmentation of the different estimated stratigraphic layers in the transverse direction Y.

[0128] Such step S34 may be performed for updating the segmentation of several 3D objects.

[0129] In an embodiment, several adjacent sections 3 are determined at step S33 and the segmentation of the selected 3D object is updated for each of such adjacent sections 3.

[0130] In such case, at an optional step S35, a global segmentation is performed by gathering the distinct segmented adjacent sections 3, so as to obtain a whole segmented data volume.

[0131] The proposed segmentation method 30 thus enables to perform segmentation on a whole data volume 1 and to perform segmentation of one or several selected 3D objects within such data volume 1. In particular, in the case of a geological formation, such segmentation method 30 enables to obtain an improved estimation of the different stratigraphic layers stacked in the geological formation, and thus provides more accurate knowledge of the subsoil formation.

[0132] The proposed segmentation method 30 advantageously relies of a segmentation model, which may be a semi-supervised machine learning model. Indeed, supervised means (or a supervised learning unit) of the segmentation model may be used for segmenting the selected 3D objects in the acquisition direction, typically within an image 2 starting from a labelled reference element 21 , 211. Unsupervised means (or an unsupervised learning unit) of the segmentation model may be used for segmenting the selected 3D object in adjacent images 2’, as well as for updating segmentation of the selected 3D object in the adjacent section 3).

[0133] The semi-supervised machine learning model used in the segmentation method 30 as proposed may globally aim at minimizing a global loss function £ which could be schematized as: where:£531is a loss function to be minimized when performing segmentation in the image 2 at step S31 ,£S32is a loss function to be minimized when performing segmentation in the adjacent images 2’ at step S32,£534is the transverse loss function to be minimized when updating segmentation in the adjacent section 3 at step S34,Ay31, Ay32and A534are loss weights reflecting the weight of each learning unit used in respective steps S31 , S32, S34. Such weights are adjusted during steps S31 , S32 and S34 respectively.

[0134] £ may be optimized during step S31 via £531(A531is adjusted, A532and A534are null), using supervised training of the segmentation model (for example, based on labelled elements 21 , 211 ).

[0135] £ may be optimized during step S32 via £531and £S32(A531and A532are adjusted, A534is null), using semi-supervised training of the segmentation model, so that supervised learning means enable segmentation of the 3D objects in the image(s) 2 while unsupervised learning means (such as PINN) enable segmentation of the 3D objects in the adjacent image(s) 2’.

[0136] £ may be optimized during step S34 via all £531, £S32and £534(A531, A532and A534are adjusted), using unsupervised training of the segmentation model, so that supervised learning means enable segmentation of the 3D objects in the image(s) 2 while unsupervised learning means (such as PINN) enable segmentation of the 3D objects in the adjacent image(s) 2’ and in the transverse portions 31.

[0137] Figure 8 shows comparative results of segmentation using different segmentation means performed based on stratigraphic images 2 for estimating stacked stratigraphic layers, which are represented on figure 8 in different shades of grey and delimited by the dotted lines representing the different stratigraphic interfaces.

[0138] Figure 8(a) provides a baseline showing a classic segmentation performed solely with a supervised segmentation model. Such segmentation results may typically be obtained by optimizing the loss function £531solely. Figure 8(a) results show major segmentation inconsistencies in both the texture prediction for each stratigraphic layers and the dips of the interfaces separating the latter. Such inconsistencies are notably enhanced in the presence of faults or seismic irregularities causing discontinuities in stratigraphic interfaces of the geological formation.

[0139] Figure 8(b) provides results of a segmentation method as performed in [BOILLOT 2023], where segmentation performed on images in the same acquisition direction is performed. PINN means are also used for predicting 3D objects in images in the acquisition direction. Such segmentation results may typically be obtained by optimizing the loss functionsand £S32solely. Figure 8(b) results show an improved segmentation compared to the baseline of Figure 8(a), notably regarding texture segmentation. Yet, such segmentation remains inconsistent, notably with respect to the stratigraphic interfaces in dotted lines and the dips of such interfaces, which do not correctly delimitate the different stratigraphic layers. Such segmentation results thus require further heavy corrections in order to be fully exploitable for precise analyses of the geological formation.

[0140] Figure 8(c) provides results of the segmentation method 30 as proposed. Such segmentation results notably add the optimization of a transverse loss function £534. Figure 8(c) results show a much improved segmentation of the stratigraphic layers which are furthermore consistent with the delimitation of stratigraphic interfaces. While still processing 2D images, such segmentation results enable a direct exploitation of the estimated stratigraphic layers having a 3D consistency for further analyses of the geological formation.Reference Signs List

[0141] -1 : data volume-2: images-2’: adjacent images-21 : labelled reference slice-2T: another slice-211 : labelled reference piece-21 T: other piece-3: adjacent section-31a, 3ab, 31 : transverse portion-X: acquisition direction-Y: transverse direction-d: predefined distance-K: thickness of the adjacent sectionReferences

[0142] [LOMASK 2006] Lomask, et al.: "Flattening without picking", Geophysics Volume 71 Issue 4(July-August 2006), Pages 13-20.

[0143] [GUILLON 2013] Guillon, et al.: “Geotime: A 3D automatic tool for chronostratigraphic seismic interpretation and filtering”, Geophysics, 32, 154-159

[0144] [BOILLOT 2023] Boillot, et al.: “Stratigraphic constraint for deep learning image segmentation of geological units”, 3rd International Meeting for Applied Geoscience

Claims

Claims

1. A computer implemented method (30) for performing segmentation of a three-dimensional data volume (1 ), said data volume (1 ) comprising a plurality of three-dimensional, 3D, objects, and the method (30) comprises segmenting at least a selected one of the plurality of 3D objects, the method (30) comprising: performing segmentation of the selected 3D object within the data volume, said segmentation comprising:- for at least one two-dimensional image of the data volume, performing segmentation (S31 ) of the selected 3D object in the image (2),- for at least one image adjacent (2’) to the image (2) in an acquisition direction (X), performing segmentation (S32) of the selected 3D object in the adjacent image (2’),- determining (S33) at least one adjacent section (3) formed by a plurality of segmented images along the acquisition direction (X),- updating the segmentation (S34) of the selected 3D object in the segmented images of the adjacent section (3), based on at least a constraint on the pixels belonging to the selected 3D object, considered in a direction transverse (Y) to the acquisition direction (X).

2. The computer implemented method (30) according to claim 1 , wherein the constraint for updating the segmentation (S34) of the selected 3D object relates to a geometric continuity of the selected 3D object on the transverse direction (Y).

3. The computer implemented method (30) according to any one of the preceding claims, the segmentation (S31 ) of the selected 3D object in the image (2) resulting in a segmented piece, and wherein performing the segmentation (S32) of the selected 3D object in the adjacent image (2’) comprises:-- determining at least one other piece in the adjacent image (2’), and-- predicting said other piece as having a same label as the segmented piece.

4. The computer implemented method (30) according to any one of the preceding claims, wherein segmenting (S31 ) a selected 3D object in an image (2) comprises assigning, to a plurality of pixels of the image, labels associated with the selected 3D object, and updating the segmentation (S34) of the selected 3D object comprises:-- determining a transverse portion (31 ) of the adjacent section (3), said transverse portion (31 ) intersecting the segmented images of said adjacent section (3),-- for said transverse portion (31 ), updating the segmentation of the selected 3D object by updating at least the labels assigned to the pixels belonging to said transverse portion (31 ).

5. The computer implemented method (30) according to any one of the preceding claims further comprising:determining at least one labelled reference piece (21 1 ), corresponding to a part of the two- dimensional image (2) being labelled as the selected 3D object, and wherein the segmentation (S31 ) of the selected 3D object is performed based on said labelled reference piece (211 ).

6. The computer implemented method (30) according to any one of the preceding claims, wherein the data volume (1 ) is a seismic acquisition of a geological formation and the selected 3D object is a geological object present within the geological formation.

7. The computer implemented method (30) according to claim 6, wherein the selected 3D object is at least part of a stacking of estimated stratigraphic layers.

8. The computer implemented method (30) according to claim 7, wherein performing segmentation (S31 ) of the selected 3D object in the image (2) further includes: determining, in the image, at least one labelled reference slice (21 ) corresponding to part of the stacking of estimated stratigraphic layers, segmenting at least another slice (2T) in the image corresponding to an adjacent part of the stacking of estimated stratigraphic layers in the image (2), determining the image (2) as a reference segmented image.

9. The computer implemented method (30) according to any one of claims 6 to 8, wherein the segmentation of the selected 3D object is performed by using a segmentation model corresponding to a physics-informed neural network, PINN, trained to at least update the segmentation of the selected 3D object according to the constraint, said constraint being related at least to a geometric continuity of interfaces delimiting said estimated stratigraphic layers.

10. The computer implemented method (30) according to any one of the preceding claims, wherein the segmentation is performed by implementing a machine learning model, preferably a neural network, NN, trained on at least pixel values of training images related to the data volume (1 ).

11. The computer implemented method (30) according to any one of the preceding claims, wherein updating the segmentation (S34) of the selected 3D object is performed using a semi supervised machine learning model, implementing at least unsupervised learning on at least pixel values of the adjacent section (3).

12. A computer program product comprising instructions which, when executed by at least processor, configure said at least one processor to carry out a method (30) according to any one of the preceding claims.

13. A computer-readable non-transient storage medium comprising instructions which, when executed by at least one processor, configure said at least one processor to carry out a method (30) according to any of claims 1 to 11 .

14. A computing system comprising at least one memory and at least one processor configured to carry out a method (30) according to any one of claims 1 to 11 .

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