Image depth estimation method, system, device and medium based on knowledge mutual distillation

Abstract

The application discloses a kind of based on knowledge mutual distillation's image depth estimation method, system, equipment and medium, it is related to computer vision technical field, the method includes collecting single frame image, multiple frame image and stereogram, respectively obtains corresponding depth map;Single frame image pixel is converted to three-dimensional space, and the scale between inherent geometric plane and the space point corresponding to the pixel is calculated, according to the scale and the depth map of single frame, multiple frame image, the depth map of recovery scale is obtained;The depth map estimated by single frame, multiple frame and stereoscopic model is aligned;Respectively using single frame, multiple frame and stereoscopic depth estimation model corresponding scale alignment depth value reconstructs pixel, according to original pixel and reconstructed pixel constructs knowledge mutual distillation model;Depth estimation model is trained based on knowledge mutual distillation model, according to the model after training, the depth of the image to be measured is estimated;The method fuses the advantage of single frame, multiple frame and stereoscopic depth estimation model, guarantees the independence of single model.

Description

Technical Field

[0001] This invention relates to the field of computer vision technology, specifically to an image depth estimation method, system, device, and medium based on knowledge inter-distillation. Background Technology

[0002] Depth estimation is crucial in computer vision and robotics, primarily used to determine the distances from objects or surfaces in a scene to the camera. Through depth estimation, systems can understand the 3D structure of a scene, enabling more accurate object recognition, path planning, and environmental perception. Therefore, developing efficient and accurate depth estimation techniques is essential for enhancing the intelligence level of artificial intelligence systems.

[0003] Existing depth estimation methods fall into three categories: single-frame, multi-frame, and stereo. Single-frame methods estimate depth by analyzing a single image and have a strong ability to perceive image representation information. Multi-frame methods use multiple frames of images from different time points as input and can strongly perceive time information, thus enabling the analysis of dynamic scenes. Stereo methods rely on the parallax between two images taken simultaneously from two different viewpoints and can provide highly accurate depth information, making them suitable for depth estimation of static scenes.

[0004] However, in real-world engineering scenarios, both dynamic and static objects are typically present, and a strong ability to understand representational information is required. Although the three methods mentioned above each have their own advantages when used in their respective scenarios, their advantages are difficult to integrate in actual use, resulting in an inability to accurately predict the depth of dynamic objects, lighting changes, and occluded areas, thus limiting their usability. Summary of the Invention

[0005] To address the shortcomings of existing technologies where the advantages of single-frame, multi-frame, and stereo methods in image representation, temporal information, and spatial information are difficult to integrate and thus cannot meet the needs of complex scenes, this invention proposes an image depth estimation method, system, device, and medium based on knowledge inter-distillation. By constructing a training framework that enables deep knowledge inter-distillation between single-frame, multi-frame, and stereo depth estimation models, the advantages of these three models are integrated, thereby solving the problems existing in the prior art.

[0006] An image depth estimation method based on knowledge inter-distillation includes the following steps:

[0007] Acquire single-frame images, multi-frame images, and stereo images; based on the single-frame depth estimation model, multi-frame depth estimation model, and stereo depth estimation model, obtain the depth maps corresponding to the single-frame images, multi-frame images, and stereo images, respectively;

[0008] The initial pixels of a single-frame image are transformed into 3D space. The scale between the scene's inherent geometric plane and the corresponding spatial point of the pixel is calculated to obtain the scene depth scale. Based on the scene depth scale and the depth maps corresponding to the single-frame image and multiple frames, depth maps at the restored scale are obtained respectively. The depth maps corresponding to the single-frame image, multiple frames, and stereo images are aligned according to the restored scale depth maps. The initial pixels are reconstructed using the scale-aligned depth maps of the single-frame image, multiple frames, and stereo images respectively. Based on the initial pixels and the reconstructed pixels, a knowledge cross-distillation model is constructed between the single-frame depth estimation model, the multi-frame depth estimation model, and the stereo depth estimation model. The single-frame depth estimation model, the multi-frame depth estimation model, and the stereo depth estimation model are trained based on the knowledge cross-distillation model.

[0009] Depth estimation of the test image is performed based on the trained single-frame depth estimation model, multi-frame depth estimation model, and stereo depth estimation model.

[0010] Furthermore, the step of obtaining depth maps corresponding to single-frame images, multi-frame images, and stereo images based on single-frame depth estimation models, multi-frame depth estimation models, and stereo images, respectively, specifically includes:

[0011] Construct a single-frame depth estimation model, inputting a single-frame image I. a To obtain the depth map

[0012] Construct a multi-frame depth estimation model, inputting multi-frame images {I a ,I a+1 ,I a+2 ,…,I a+n}, thus obtaining the depth map

[0013] Construct a stereo depth estimation model, input stereo image pairs Obtain depth map

[0014] Furthermore, the process of converting a single frame image pixel into three-dimensional space and calculating the scale between the scene's inherent geometric plane and the corresponding spatial point of that pixel yields the scene depth scale, which is expressed as:

[0015] Image I a pixel p in i (u,v) is transformed into three-dimensional spatial coordinates P i (X,Y,Z), the specific transformation process is expressed as follows:

[0016]

[0017] Where M1 is the camera's intrinsic parameter matrix;

[0018] Select pixel p i The eight adjacent points are divided into four groups and transformed into three-dimensional space;

[0019] Based on the transformed three-dimensional spatial coordinates and pixel p i These form four planes; the average of the normal vectors of the four planes yields the pixel p. i The normal vector n(p) i The specific process is as follows:

[0020]

[0021] Where, n j Let represent the normal vector of the j-th plane;

[0022] Determine if pixel p is a valid pixel: i If the pixel matches the inherent geometric information, then the pixel is a valid pixel. The determination process is expressed as follows:

[0023]

[0024] in, τ is the normal vector of the inherent geometric plane, and τ is the angle threshold between the pixel normal vector and the inherent geometric plane normal vector;

[0025] Calculate the scale between the intrinsic geometric plane and the corresponding spatial point of the pixel, i.e., the scene depth scale f. s Specifically, it is expressed as:

[0026]

[0027] Where n represents the number of valid pixels, h i Y represents the intrinsic geometric dimension corresponding to this pixel. i This represents the three-dimensional coordinate dimension obtained by solving for this pixel.

[0028] Furthermore, based on the scene depth scale and the depth map corresponding to a single frame image and the depth maps corresponding to multiple frames images, a depth map at the restoration scale is obtained respectively; the depth map at the restoration scale is represented as follows:

[0029]

[0030] in, The depth map represents the restored scale, and D represents the relative depth map directly output by the model.

[0031] Furthermore, the step of constructing a knowledge cross-distillation model among the single-frame depth estimation model, the multi-frame depth estimation model, and the stereo depth estimation model based on the initial pixels and the reconstructed pixels specifically includes the following steps:

[0032] Depth values ​​from depth maps scaled together from single-frame, multi-frame, and stereo images, respectively. and Reconstructing pixel p i Obtain the reconstructed pixels and The specific process is as follows:

[0033]

[0034] Where Φ(·) is the reconstruction function, Based on depth value The reconstructed pixels, k∈{1,2,3} represent the corresponding depth prediction method. For the pixels in the reference image, P ab The pose between the target image and the reference image;

[0035] Constructing a quantitative evaluation of depth is represented as follows:

[0036]

[0037] Generate teacher and student pixels, represented as follows:

[0038]

[0039] Where T represents the teacher's pixel count, and Stu1 and Stu2 represent the student's pixel count. and Depth and Quantitative evaluation.

[0040] The present invention also includes an image depth estimation system based on knowledge inter-distillation, comprising:

[0041] The acquisition module is used to acquire single-frame images, multi-frame images, and stereo images; based on the single-frame depth estimation model, multi-frame depth estimation model, and stereo depth estimation model, it obtains the depth maps corresponding to the single-frame images, multi-frame images, and stereo images, respectively.

[0042] The knowledge inter-distillation model construction module is used to transform the initial pixels of a single-frame image into 3D space, calculate the scale between the scene's inherent geometric plane and the corresponding spatial point of the pixel to obtain the scene depth scale, and obtain the depth map at the restored scale based on the scene depth scale and the depth maps corresponding to the single-frame image and the multi-frame images, respectively; align the depth maps corresponding to the single-frame image, multi-frame image, and stereo image based on the restored scale depth map; reconstruct the initial pixels using the scale-aligned depth maps of the single-frame image, multi-frame image, and stereo image, respectively; construct a knowledge inter-distillation model among the single-frame depth estimation model, multi-frame depth estimation model, and stereo depth estimation model based on the initial pixels and the reconstructed pixels; and train the single-frame depth estimation model, multi-frame depth estimation model, and stereo depth estimation model based on the knowledge inter-distillation model.

[0043] The depth estimation module is used to estimate the depth of the image under test based on the trained single-frame depth estimation model, multi-frame depth estimation model, and stereo depth estimation model.

[0044] The present invention also includes a computer device for image depth estimation based on knowledge interdistillation, comprising: a memory, a processor, and a computer program stored in the memory, wherein the processor executes the computer program to implement the steps of the image depth estimation method based on knowledge interdistillation.

[0045] The present invention also includes a readable storage medium storing a computer program, the computer program including program instructions, which, when executed by a processor, are used to perform the steps of the image depth estimation method based on knowledge inter-distillation.

[0046] This invention provides an image depth estimation method, system, device, and medium based on knowledge inter-distillation, which has the following beneficial effects:

[0047] This invention constructs a training framework for inter-distillation of depth knowledge among single-frame, multi-frame, and stereo depth estimation models, enabling synchronous training of these models. Based on inherent scene geometric information, it restores the scale of the output depth maps from the single-frame and multi-frame depth estimation models, avoiding the problem of inconsistent scales in the output depth maps of the single-frame, multi-frame, and stereo models. A knowledge inter-distillation model is constructed for training among the single-frame, multi-frame, and stereo depth estimation models, avoiding the unidirectional flow of knowledge in traditional knowledge distillation processes. This allows the single-frame, multi-frame, and stereo depth estimation models to act as both student and teacher models for each other. During training, only advantageous knowledge flows between models, avoiding mutual interference. This achieves the fusion of the advantages of single-frame, multi-frame, and stereo depth estimation models in image representation, temporal information, and spatial information, while ensuring the independence of each individual model. Attached Figure Description

[0048] Figure 1 This is a diagram of a neural network training framework based on knowledge inter-distillation in an embodiment of the present invention;

[0049] Figure 2 This is a depth map scale recovery and alignment map based on the inherent geometric information of the scene in this embodiment of the invention;

[0050] Figure 3 This is a structural diagram of the deep knowledge inter-distillation model in an embodiment of the present invention. Detailed Implementation

[0051] The technical solutions of the present invention will be clearly and completely described below with reference to the accompanying drawings of the embodiments of the present invention. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments.

[0052] This invention proposes an image depth estimation method based on knowledge inter-distillation, which can integrate the advantages of single-frame, multi-frame, and stereo depth estimation models in image representation, temporal information, and spatial information, respectively, and obtain independent single-frame, multi-frame, and stereo depth estimation models, such as... Figure 1 As shown, the model training process includes three independent depth estimation models: a single-frame depth estimation model, a multi-frame depth estimation model, and a stereo depth estimation model. After the three models independently complete depth estimation, scale recovery and alignment are performed based on the inherent geometric information of the scene. Finally, a knowledge cross-distillation loss function is constructed to supervise the training of the single-frame, multi-frame, and stereo models. This method specifically includes the following steps:

[0053] S1. Construct a deep knowledge mutual distillation neural network training framework, including the following specific steps:

[0054] a) Construct a single-frame depth estimation model, inputting a single-frame image I. a To obtain the depth map

[0055] b) Construct a multi-frame depth estimation model, inputting multi-frame images {I} a ,I a+1 ,I a+2 ,…,I a+n}, thus obtaining the depth map

[0056] c) Construct a stereo depth estimation model, inputting stereo images... Obtain depth map

[0057] d) Construct a deep knowledge inter-distillation module to realize the exploration and mutual transfer of deep knowledge advantages of single-frame, multi-frame and stereo models.

[0058] S2. Depth map alignment based on scene-specific geometric information (such as camera height above the ground, lane line width, lane width, etc.), including single-frame, multi-frame, and stereo model estimations. Figure 2 As shown; including the following specific steps:

[0059] a) For image I a pixel p in i (u,v), transform it into three-dimensional spatial coordinates P i (X,Y,Z), the specific transformation process can be represented as:

[0060]

[0061] In the formula, M1 is the intrinsic parameter matrix of the camera, which is composed of the camera's inherent parameters.

[0062] b) Select pixel p i The eight adjacent points are divided into four groups and transformed into three-dimensional space according to equation (1). The joint pixel p i This forms four planes. (Description of pixel p) i The normal vector n(p) i This can be obtained by averaging the normal vectors of the four planes. The specific process can be expressed as follows:

[0063]

[0064] In the formula, n j Let represent the normal vector of the j-th plane.

[0065] c) If pixel p i If the pixel matches the inherent geometric information, then the pixel is a valid pixel. The process of determining a valid pixel can be represented as follows:

[0066]

[0067] In the formula, τ is the normal vector of the intrinsic geometric plane, and τ is the angle threshold between the pixel normal vector and the intrinsic geometric plane normal vector.

[0068] d) Scene depth scale f s The scale between the intrinsic geometric plane and the corresponding spatial point of the pixel can be represented as follows:

[0069]

[0070] In the formula, n represents the number of effective pixels, and h i Y represents the intrinsic geometric dimension corresponding to this pixel. i This represents the three-dimensional coordinate dimension obtained by solving for this pixel.

[0071] e) Recover the scale information of depth estimated by single-frame and multi-frame models. The specific process can be represented as follows:

[0072]

[0073] In the formula, The depth map represents the restored scale, and D represents the relative depth map directly output by the single-frame or multi-frame model.

[0074] f) Align depth maps estimated from single-frame, multi-frame, and stereo models.

[0075] S3. Construct a knowledge cross-distillation loss function to supervise single-frame, multi-frame, and stereo model training, such as... Figure 3 As shown; including the following specific steps:

[0076] a) Recover the scaled depth values ​​using both single-frame and multi-frame methods. and And the depth value output by the 3D model Reconstructing pixel p i Obtain the reconstructed pixels and The specific process can be represented as follows:

[0077]

[0078] In the formula, Φ(·) is the reconstruction function. Based on depth value The reconstructed pixels, k∈{1,2,3} represent the corresponding depth prediction method. For the pixels in the reference image, P ab The pose between the target image and the reference image;

[0079] b) Constructing a quantitative evaluation of depth, the specific process of which can be expressed as follows:

[0080]

[0081] c) Define the teacher's pixel and the student's pixel. The specific process can be represented as follows:

[0082]

[0083] In the formula, T represents the teacher's pixel count, and Stu1 and Stu2 represent the student's pixel count. and Depth and Quantitative evaluation.

[0084] This invention provides an image depth estimation method based on knowledge inter-distillation. It leverages the advantages of single-frame, multi-frame, and stereo depth estimation models in image representation, temporal information, and spatial information, respectively, to establish a pixel-based knowledge distillation mechanism. This mechanism enables knowledge inter-distillation among the three methods, ultimately allowing a single model to simultaneously possess advantages in image representation, temporal information, and spatial information. This addresses the instability of existing methods in real-world engineering scenarios containing both dynamic and static objects. The invention constructs a model training framework based on knowledge inter-distillation; achieves synchronous training of single-frame, multi-frame, and stereo depth estimation models; constructs a depth scale recovery method based on inherent scene information, achieving scale alignment of the output depth maps of the single-frame, multi-frame, and stereo depth estimation models; and constructs a pixel-based quantitative depth evaluation standard, enabling knowledge inter-distillation among the single-frame, multi-frame, and stereo depth estimation models. Based on knowledge inter-distillation, mutual constraints are added to the single-frame, multi-frame, and stereo depth estimation models during training, achieving mutual learning through knowledge optimization and complementary advantages. Compared with existing technologies, this invention solves the problem of the difficulty in integrating the advantages of single-frame, multi-frame, and stereo depth estimation models in image representation, temporal information, and spatial information.

[0085] Based on the same inventive concept, this invention also proposes an image depth estimation system based on knowledge inter-distillation, comprising:

[0086] The acquisition module is used to acquire single-frame images, multi-frame images, and stereo images; based on the single-frame depth estimation model, multi-frame depth estimation model, and stereo depth estimation model, it obtains the depth maps corresponding to the single-frame images, multi-frame images, and stereo images, respectively.

[0087] The knowledge inter-distillation model construction module is used to transform the initial pixels of a single-frame image into 3D space, calculate the scale between the scene's inherent geometric plane and the corresponding spatial point of the pixel to obtain the scene depth scale, and obtain the restored scale depth maps based on the scene depth scale and the depth maps corresponding to the single-frame image and the multi-frame images, respectively; align the depth maps corresponding to the single-frame image, multi-frame image, and stereo image based on the restored scale depth maps; reconstruct the initial pixels using the scale-aligned depth maps of the single-frame image, multi-frame image, and stereo image, respectively; construct a knowledge inter-distillation model among the single-frame depth estimation model, multi-frame depth estimation model, and stereo depth estimation model based on the initial pixels and the reconstructed pixels; and train the single-frame depth estimation model, multi-frame depth estimation model, and stereo depth estimation model based on the knowledge inter-distillation model.

[0088] The depth estimation module is used to estimate the depth of the image under test based on the trained single-frame depth estimation model, multi-frame depth estimation model, and stereo depth estimation model.

[0089] The present invention also proposes a computer device for image depth estimation based on knowledge inter-distillation, comprising: a memory, a processor, and a computer program stored in the memory, wherein the processor executes the computer program to implement the steps of the image depth estimation method based on knowledge inter-distillation.

[0090] The present invention also proposes a readable storage medium storing a computer program, the computer program including program instructions, which, when executed by a processor, are used to perform steps of an image depth estimation method based on knowledge inter-distillation.

[0091] The above description is only a preferred embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any equivalent substitutions or modifications made by those skilled in the art within the scope of the technology disclosed in the present invention, based on the technical solution and inventive concept of the present invention, should be covered within the scope of protection of the present invention.

Claims

1. An image depth estimation method based on knowledge inter-distillation, characterized in that, Includes the following steps: Acquire single-frame images, multi-frame images, and stereo images; based on the single-frame depth estimation model, multi-frame depth estimation model, and stereo depth estimation model, obtain the depth maps corresponding to the single-frame images, multi-frame images, and stereo images, respectively; The initial pixels of a single frame image are transformed into three-dimensional space. The scale between the scene's inherent geometric plane and the corresponding spatial point of the pixel is calculated to obtain the scene depth scale. Based on the scene depth scale and the depth map corresponding to the single frame image and the depth maps corresponding to multiple frames, the depth maps of the restored scale are obtained respectively. Align the depth maps corresponding to single-frame images, multi-frame images, and stereo images based on the depth map of the restored scale; The initial pixels were reconstructed using the scale-aligned depth maps of single-frame images, multi-frame images, and stereo images, respectively. Based on the initial pixels and reconstructed pixels, a knowledge cross-distillation model is constructed among the single-frame depth estimation model, the multi-frame depth estimation model, and the stereo depth estimation model. The single-frame depth estimation model, the multi-frame depth estimation model, and the stereo depth estimation model are then trained based on the knowledge cross-distillation model. The construction of the knowledge cross-distillation model among the single-frame depth estimation model, the multi-frame depth estimation model, and the stereo depth estimation model specifically includes the following steps: using the depth values ​​of the scale-aligned depth maps of the single-frame image, the multi-frame image, and the stereo image, respectively. , and Reconstructing pixels Obtain the reconstructed pixels , and The specific process is as follows: ;in, For reconstruction function, Based on depth value Reconstructed pixels, This represents the corresponding depth prediction method. For the pixels in the reference image, Given the pose between the target image and the reference image; construct a quantitative evaluation of depth, expressed as: Generate teacher and student pixels, represented as: ;in, For teacher pixels, and For student pixels, , and Depth , and Quantitative evaluation; Depth estimation of the test image is performed based on the trained single-frame depth estimation model, multi-frame depth estimation model, and stereo depth estimation model.

2. The image depth estimation method based on knowledge inter-distillation according to claim 1, characterized in that, The process of obtaining depth maps corresponding to single-frame images, multi-frame images, and stereo images based on single-frame depth estimation models, multi-frame depth estimation models, and stereo images, respectively, specifically includes: Construct a single-frame depth estimation model, inputting a single-frame image. To obtain the depth map ; Construct a multi-frame depth estimation model, taking multiple frames of images as input. To obtain the depth map ; Construct a stereo depth estimation model, input stereo image pairs To obtain the depth map .

3. The image depth estimation method based on knowledge inter-distillation according to claim 2, characterized in that, the initial pixels of a single frame image are converted into three-dimensional space, and the scale between the scene's inherent geometric plane and the corresponding spatial point of the pixel is calculated to obtain the scene depth scale, which is expressed as: Image Pixels Convert to three-dimensional space coordinates The specific conversion process is as follows: ； in, This is the intrinsic parameter matrix of the camera; Select pixels The eight adjacent points are divided into four groups and transformed into three-dimensional space; Based on the transformed 3D spatial coordinates and pixels These form four planes; the average of the normal vectors of the four planes is used to obtain the pixel. normal vector The specific process is as follows: ； in, Indicates the first The normal vector of the plane group; Determine if the pixel is a valid pixel: If the pixel If the pixel matches the inherent geometric information, then the pixel is a valid pixel. The determination process is expressed as follows: ； in, The normal vector of the inherent geometric plane. This is the angle threshold between the pixel normal vector and the inherent geometric plane normal vector; Calculate the scale between the intrinsic geometric plane and the corresponding spatial points of pixels, i.e., the scene depth scale. Specifically, it is expressed as: ； in, Indicates the number of valid pixels. This indicates the inherent geometric size of the pixel. This represents the three-dimensional coordinate dimension obtained by solving for this pixel.

4. The image depth estimation method based on knowledge inter-distillation according to claim 3, characterized in that, The depth map at the restoration scale is obtained by using the depth map corresponding to the scene depth scale and the depth maps corresponding to the single-frame image and the multi-frame images, respectively; the depth map at the restoration scale is represented as follows: ； in, A depth map representing the recovery scale. This represents the relative depth map directly output by the model.

5. An image depth estimation system based on knowledge inter-distillation, characterized in that, include: The acquisition unit is used to acquire single-frame images, multi-frame images, and stereo images; based on the single-frame depth estimation model, multi-frame depth estimation model, and stereo depth estimation model, it obtains the depth maps corresponding to the single-frame images, multi-frame images, and stereo images, respectively. The knowledge inter-distillation model construction module is used to transform the initial pixels of a single frame image into three-dimensional space, calculate the scale between the scene's inherent geometric plane and the corresponding spatial point of the pixel to obtain the scene depth scale, and obtain the depth map of the restored scale based on the scene depth scale and the depth map corresponding to the single frame image and the depth maps corresponding to multiple frames images respectively. Align the depth maps corresponding to single-frame images, multi-frame images, and stereo images based on the depth map of the restored scale; The initial pixels were reconstructed using the scale-aligned depth maps of single-frame images, multi-frame images, and stereo images, respectively. Based on the initial pixels and reconstructed pixels, a knowledge cross-distillation model is constructed among the single-frame depth estimation model, the multi-frame depth estimation model, and the stereo depth estimation model. The single-frame depth estimation model, the multi-frame depth estimation model, and the stereo depth estimation model are then trained based on the knowledge cross-distillation model. The construction of the knowledge cross-distillation model among the single-frame depth estimation model, the multi-frame depth estimation model, and the stereo depth estimation model specifically includes the following steps: using the depth values ​​of the scale-aligned depth maps of the single-frame image, the multi-frame image, and the stereo image, respectively. , and Reconstructing pixels Obtain the reconstructed pixels , and The specific process is as follows: ;in, For reconstruction function, Based on depth value Reconstructed pixels, This represents the corresponding depth prediction method. For the pixels in the reference image, Given the pose between the target image and the reference image; construct a quantitative evaluation of depth, expressed as: Generate teacher and student pixels, represented as: ;in, For teacher pixels, and For student pixels, , and Depth , and Quantitative evaluation; The depth estimation unit is used to estimate the depth of the image under test based on the trained single-frame depth estimation model, multi-frame depth estimation model, and stereo depth estimation model.

6. A computer device for image depth estimation based on knowledge inter-distillation, characterized in that, include: A memory, a processor, and a computer program stored in the memory, wherein the processor executes the computer program to implement the steps of the image depth estimation method based on knowledge inter-distillation as described in any one of claims 1-4.

7. A readable storage medium, characterized in that, The readable storage medium stores a computer program, which includes program instructions that, when executed by a processor, perform the steps of the image depth estimation method based on knowledge inter-distillation as described in any one of claims 1-4.

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