K. Ikeuchi and B. K. P. Horn. Numerical shape from shading and occluding boundaries. Artificial Intelligence, 17:141--184, 1981.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....and saddle like surfaces that appear the same from certain viewpoints . Therefore most exact shape from shading algorithms involve the propagation of information from special locations on the surface, such as occluding contours or intensity singularities, where the surface is assumed known [32, 14, 12, 22, 26]. Techniques such as the method of characteristic strips were used to solve systems of differential equations with known initial conditions. Typically these techniques are computationally expensive, requiring thousands of iterations, and rarely is it possible to prove that they converge. Because ....

K. Ikeuchi and B. K. P. Horn. Numerical shape from shading and occluding boundaries. Artificial Intelligence, 15:141--184, 1981.

....study of a number of SFS algorithms was done by [43] They classify SFS algorithms as either global or local depending on whether they use intensity information across the entire image or only in local neighborhoods. Most SFS algorithms for Lambertian surfaces follow a regularization approach [17, 18, 38, 23, 21]. Other methods are based on the use of the integrability constraint[8, 15] the intensity gradient constraint [44] and the unit normal constraint. In the above class of approaches, the method of [21] requires good initial depth values, obtained from stereo information, and results in better ....

K. Ikeuchi and B.K.P. Horn. Numerical shape from shading and occluding boundaries. Artificial Intelligence, 17:141--184, 1981.

.... called the brightness equation [18] This initial idea was limited by the particular numerical method that was used (the method of characteristics) and was enriched by posing the problem as a variational problem [17] within which additional constrains such as those provided by occluding contours [20] can be taken into account. The book [16] contains a very nice panorama of the research in this area up to 1989. Questions about the existence and uniqueness of solutions to the problem were simply not even posed at that time with the important exception of the work of Bruss [5] These questions ....

K. Ikeuchi and B.K.P Horn. Numerical shape from shading and occluding boundaries. Articial Intelligence Journal, 17:181184, 1981.

....Owing to noise in the acquisition process along with the limited resolution of cameras, only inaccurate estimates of semantic information (e.g. orientation) are possible. Furthermore, illumination variation heavily in uences the measured grey level values and is hard to model analytically [33]. Information extracted across image frames, e.g. in stereo and optic ow estimation, faces (in addition to the above mentioned problems) the correspondence and aperture problem which interfere in a fundamental and especially dicult way (see, e.g. 2, 39] However, the human visual system ....

.... these problems even increases for higher semantic information, such as curvature (see, e.g. 34, 5] or junction detection and interpretation (see, e.g. 61, 26] Furthermore, illumination variation heavily in uences the measured grey level values and is hard to model analytically (see, e.g. [33]) Extracting information across image frames, e.g. in stereo and optic ow estimation, faces (in addition to the above mentioned problems) the correspondence and aperture problem which interfere in a fundamental and especially awkward way (see, e.g. 2, 39] Furthermore, visual information is ....

K. Ikeuchi and B.K.P. Horn. Numerical shape from shading and occluding boundaries. Arti cial Intelligence, 17:141-184, 1981.

.... called the brightness equation [15] This initial idea was limited by the particular numerical method that was used (the method of characteristics) and was enriched by posing the problem as a variational problem [14] within which additional constrains such as those provided by occluding contours [17] can be taken into account. The book [13] contains a very nice panorama of the research in this area up to 1989. Questions about the existence and uniqueness of solutions to the problem were simply not even posed at that time with the important exception of the work of Bruss [4] These questions ....

K. Ikeuchi and B.K.P Horn. Numerical shape from shading and occluding boundaries. Arti cial Intelligence Journal, 17:181-184, 1981.

.... analysis (e.g. the nose appears to protrude from the face because its flanks are shaded darker than its tip) the objects in the image (e.g. the depth along the outlines of the objects) the exact shape from shading problem becomes solvable, though still computationally difficult ( 170] [69], 62] A further assumption of oblique illumination may substantially reduce the computational complexity [115] although the problem of serf shadowing, neglected by most algorithms including [115] becomes significant. In such cases, special shape from shadows algorithms [138] may be employed ....

K. Ikeuchi and B. K. P. Horn. Numerical shape from shading and occluding boundaries. Artificial Intelligence, 15:141-184, 1981.

....points where the surface normal is in the same direction as the light source since at these points t] R(p, q) E(x,y) The results appear qualitatively correct (Figure 5) but are slightly flattened, probably because the reflectance model is overly simple. Better reflectance models do exist [21] and we are investigating these. Figure 6 shows how brightness error and depth error change with scale as the solution for the synthetic image is tracked through scale space. SEM image of fibre Recovered surface of fibre SEM image of EM grid Recovered surface of EM grid Figure 5: Recovered ....

Ikeuchi K, Horn BKP. "Numerical Shape From Shading and Occluding Boundaries". Artificial Intelligence, Vol 17 pp141-184, 1981.

....levels. Most of the MRF models are for lowlevel processing. These include image restoration and segmentation [61,56,23,36,46,21,27,85,89,92] surface reconstruction [8,53,98,17,99,24,43] edge detection [103,131,44] texture analysis [23,30,40,34,35] optical ow [64,63,78,118,60] shape from X [9,68], active contours [74,3,123] deformable templates [97,95,70] data fusion [26] visual integration, and perceptual organization [2,125] The use of MRFs in high level, such as for object matching and recognition, has also emerged in recent years [100,29,51,4,42,76,28,87,90,91] MRF theory tells ....

....abruptly. For example, the surface of a table is at, a meadow presents a texture of grass, and a temporal event does not change abruptly over a short period of time. Indeed, we can always nd regularities of aphysical phenomenon with respect to certain properties. Since its early applications [53,64,68] aimed to impose constraints, in addition to those from the data, on the computation of image properties, the smoothness prior has been one of the most popular prior assumptions in low level problems. It has been developed into a general framework, called regularization [109,11] for ....

[Article contains additional citation context not shown here]

K. IkeuchiandB.K.P.Horn.\Numerical shape from shading and occluding boundaries". Articial Intelligence, 17:141-184, 1981.

....control parameter whichweighs the error in smoothness constraint relativ e to the error in the surface tangents equation (4) given by e t = Z Z R 2 (p# q# r)dudv (7) 3. 3 The algorithm Minimizing the error in (6) is a well known problem in variational calculus applied to computer vision [2], and the solution of which is the following iterativescheme for updating the value of (p# q# r) p (n 1) ij = p (n) ij R(p (n) ij #q (n) ij #r (n) ij ) R p (8) q (n 1) ij = q (n) ij R(p (n) ij #q (n) ij #r (n) ij ) R q (9) r (n 1) ij = r (n) ij R(p (n) ....

K. Ikeuc hi and B. K. P. Horn, "Numerical shape from shading and occluding boundaries, " Artif. Intell., vol. 19, pp. 141-185, 1981.

....across the surface. Moreover, the direction of the light source must be known in advance. Horn[1] was the first to address the shape from shading problem using a characteristic strip method. The method is notoriously sensitive to image noise. To limit the problems of noise, Ikeuchi and Horn[2] search for solutions of the image irradiance equation in which the surface normals vary smoothly. Their method is typical of a large group of regularisation methods which involve the global optimisation of a criterion which includes a data closeness term and a penalty term which penalises ....

....an empirical one. Using a digital elevation map, we investigate the scattering characteristics of the radar returns using data with known ground truth. The resulting scattering model is found to give good results when combined with the relatively simple Ikeuchi and Horn shape from shading scheme [2]. The outline of this paper is as follows. In section 2 we present the radar data and ground truth information used in this study. In section 3 we discuss the reflectance functions of surfaces illuminated by radar. In section 4, we analyse the noise properties of the images. Finally in section 5 ....

K. Ikeuchi and B. K. P. Horn, "Numerical Shape from Shading and Occluding Boundaries," Artificial Intelligence,Vol. 17, pp 141--184 1981.

....to be used in the rendering process. There is a tremendous amount of work in the computer vision literature on model reconstruction from intensity images with di erent paradigms such as structure from motion (e.g. 55, 108, 19, 105] shape from stereo (e.g. 70, 79] shape from shading (e.g. [49, 84]) and other model reconstruction methods (e.g. 13, 104] The extracted model may be a complete CAD model or just the positions of some geometric features like points and lines. Once the 3D model representing the scene has been reconstructed, a new view of the scene can be obtained by rst ....

K. Ikeuchi and B.K.P. Horn. Numerical shape from shading and occluding boundaries. Articial Intelligence, 17:141-184, 1981. 138

....survey of SFS methods can be found in [14] 2. 1 Minimization Approaches Based on one of the earliest minimization methods, the SFS problem is formulated as a function of surface gradients, while brightness and smoothness constraints are added to overcome the underdeterminedness condition [15]. The brightness constraint ensures the reconstructed shape produce the same brightness as the input image. The smoothness constraint in terms of second order surface gradients helps in reconstruction of a smooth surface. The shape at the occluding boundary was used for initialization to imply a ....

....ensures the reconstructed shape produce the same brightness as the input image. The smoothness constraint in terms of second order surface gradients helps in reconstruction of a smooth surface. The shape at the occluding boundary was used for initialization to imply a correct convergence [15]. Other minimization approaches use more or less the same logic to deal with the SFS problem. However, some variations in either formulation of the problem or the constraints (or both) are usually implemented. 2.2 Propagation Approaches In this approach there is a characteristic strip along ....

Ikeuchi, K., Horn, B. K. P.: Numerical Shape from Shading and Occluding Boundaries. Artificial Intelligence, Vol. 17, Nos. 1-3 (1981), pp. 141-184

....initial calibration registration of models to objects and the subsequent dynamic update of these models based on tracking the corresponding real objects. The general shape of the environment may also be directly acquired with a variety of techniques (e.g. shape fromshading, Oliensis Dupuis 93; Ikeuchi Horn 81] 3. Correct lighting is an essential part of generating virtual objects with convincing shading. It is therefore important to properly model the lighting of a real environment and project it onto the virtual objects. It is equally important and difficult to modify the shading of real objects ....

K. Ikeuchi, B.K.P. Horn, Numerical Shape from Shading and Occluding Boundaries. Artificial Intelligence 17, 1981, pp. 141--184.

....propagate the shape information from known surface points (e.g. singular points) to the whole image. Local approaches derive shape only from the intensity information of the surface points in a small neighborhood. One of the earlier global minimization approaches was by Ikeuchi and Horn [10]. Since each surface point has two unknowns for the surface normal, and each pixel in the image provides one gray value, therefore image gray levels alone are not enough to recover the shape. To overcome this, Ikeuchi and Horn introduced two constraints: The brightness constraint and the ....

K. Ikeuchi and B.K.P. Horn. Numerical shape from shading and occluding boundaries. Artificial Intelligence, 17(1-3):141--184, 1981.

....levels. Most of the MRF models are for low level processing. These include image restoration and segmentation [61,56,23,36,46,21,27,85,89,92] surface reconstruction [8,53,98,17,99,24,43] edge detection [103,131,44] texture analysis [23,30,40,34,35] optical ow [64,63,78,118,60] shape from X [9,68], active contours [74,3,123] deformable templates [97,95,70] data fusion [26] visual integration, and perceptual organization [2,125] The use of MRFs in high level, such as for object matching and recognition, has also emerged in recent years [100,29,51,4,42,76,28,87,90,91] MRF theory tells ....

....abruptly. For example, the surface of a table is at, a meadow presents a texture of grass, and a temporal event does not change abruptly over a short period of time. Indeed, we can always nd regularities of a physical phenomenon with respect to certain properties. Since its early applications [53,64,68] aimed to impose constraints, in addition to those from the data, on the computation of image properties, the smoothness prior has been one of the most popular prior assumptions in low level problems. It has been developed into a general framework, called regularization [109,11] for a variety of ....

[Article contains additional citation context not shown here]

K. Ikeuchi and B. K. P. Horn. \Numerical shape from shading and occluding boundaries". Articial Intelligence, 17:141-184, 1981.

....information from different image cues like stereo, shading and motion, the solution may be significantly improved. Surprisingly, it is only recently that researchers in Computer Vision have started realizing the benefits of integrating information from separate modules. These are the work of Horn [10] on combining shading with contour, Grimson s [6] use of shading in determining the surface orientation of feature point contours obtained from stereo, Aloimonos s methods [1] for combining shading and motion, texture and motion, and motion and contour, and Waxman s approach for combining stereo ....

....necessary to fine tune the thresholds for each and every set of data. 5 Discussion There are several other possibilities for integrating stereo and shading. The stereo depth map can be used to improve the shape from shading algorithm. For instance, in IkeuchiHorn s shape from shading algorithm [10] it is assumed that the depth at the occluding contours is available. Their method iteratively computes the surface orientation at the remaining locations by propogating the depth at the occluding contours. The contour depth map computed by the feature based stereo can be used for this purpose. In ....

Ikeuchi, K. and Horn, B.K.P. Numerical shape from shading and occluding Boundaries. Artifical Intelligence, Vol. 17, No. 1-3, pp. 141-184, 1981.

....as brightness now depends only on surface orientation and reflectance properties. It also means that orthographic projection can be employed, which further simplifies the problem. Early shape from shading algorithms assume that the direction of the light source is available to the algorithm [20, 23]; recently algorithms have been developed to recover the direction of the light source [6, 29, 38, 43] The human visual system assumes that the reflecting properties are homogeneous over the object s surface. If this is not the case, i.e. the reflectance properties vary on the object s surface, ....

....where the surface normals are parallel to the image plane is called the occluding contour. The occluding contour provides vital information because the gradient is known on this curve. This information is used by many shape from shading algorithms as a means to initialize an iterative solution [6, 17, 20, 23, 36]. However, depending on the direction of the light source, the occluding contour can be obscured from view by self shadowing. Points lie on the self shadowed boundary if the surface normals at these points form a 90 degree angle with the light source. The problem at these points is that the ....

[Article contains additional citation context not shown here]

K. Ikeuchi and B. Horn. Numerical shape from shading and occluding boundaries. Artificial Intelligence, 17(1-3):141--184, 1981.

.... or motion are evaluated independently in almost completely separate pathways [21, 5, 10] Curvature is supposed to be processed by such a separate channel in early vision, too [23, 2, 3] Methods to reconstruct a three dimensional scene from single features are known as shape from X methods [6, 8, 1, 9]. Usually, they lead to so called illposed problems since the mapping of a three dimensional image onto a gray scale (contour, texture, image has no unique inversion. A well known approach to deal with this problem is called regularization. It removes the non uniqueness by imposing a ....

K. Ikeuchi and B.K.P. Horn. Numerical shape from shading and occluding boundaries. Artificial Intelligence, 17:141--184, 1981.

....to converge to the true solution in the CG type algorithms. In fact, we always use 0 as the initial guess in our experiments. To resolve the above problem for minimizing the SFS energy function by gradient based methods, we include the boundary conditions obtained from the occluding boundary [14] as an additional data constraint in the energy function to be minimized. By incorporating the boundary conditions into the SFS energy function, the CG type algorithms can approach the true solution. In our experiment, we use the active contour model [16] to locate the occluding boundary at first. ....

....CG type algorithms can approach the true solution. In our experiment, we use the active contour model [16] to locate the occluding boundary at first. By using the property that the surface normal at a point on the occluding boundary is parallel to the normal of the silhouette in the image plane [14], we impose the Direchelet boundary condition on (p; q) along the occluding boundary. In addition, we use the occluding boundary to incorporate the discontinuities in (p; q) or z representing orientation discontinuities or depth discontinuities respectively. In this experiment, we incorporate the ....

K. Ikeuchi and B. K. P. Horn. "Numerical shape from shading and occluding boundaries". Artificial Intelligence, 17:141--184, 1981.

....binary edge maps from images. 3. Shape from Shading: Iterative algorithm for recovering a gradient map from a brightness image reflectance map. 10] Chapter 11) 4. Shape from Shading: Recovering depth maps from gradient maps, e.g. by characteristic strip expansion. 10] Chapter 11) [14], 12] 4] 5. Optical Flow: Iterative Gradient based (Direct) algorithm for computing dense optical flow fields. 10] Chapter 12) 13] 15] Chapter 14) 6. Optical Flow: Linear algorithms for recovering motion and surface structure from optical flow fields. 8] Chapter 15) 7. ....

Ikeuchi K. and Horn B.K.P. Numerical Shape from Shading and Occluding Boundaries. Artificial Intelligence, 17:141--187, August 1981.

....the object or it can not be captured in natural position. That is why we prefer the passive technique (e.g. stereo) Two basic approaches can be distinguised according to a way, how to interpret the input data: i) stereo according to geometrical information, and (ii) shape from shading [IH81, LR85, OD93] according to photometric properties. There are two main kinds of output model reprezentations: volume based and surface based. Volume based models (e.g. general cylinders, quadrics and CSG) strongly generalize the object shape. That is why the surface based models (e.g. ....

K. Ikeuchi and B. K. P. Horn. Numerical shape from shading and occluding boundaries. Artificial Intelligence, 17:141--184, 1981.

....binary edge maps from images. 3. Shape from Shading: Iterative algorithm for recovering a gradient map from a brightness image reflectance map. 10] Chapter 11) 4. Shape from Shading: Recovering depth maps from gradient maps, e.g. by characteristic strip expansion. 10] Chapter 11) [14], 12] 4] 5. Optical Flow: Iterative Gradient based (Direct) algorithm for computing dense optical flow fields. 10] Chapter 12) 13] 15] Chapter 14) 6. Optical Flow: Linear algorithms for recovering motion and surface structure from optical flow fields. 8] Chapter 15) 7. ....

Ikeuchi K. and Horn B.K.P. Numerical Shape from Shading and Occluding Boundaries. Artificial Intelligence, 17:141--187, August 1981.

....absorbed into l . In order to improve the numerical stability of the Stereo Matching by Discontinuity Preserving Regularization JOURNAL OF ELECTRICAL ENGINEERING AND INFORMATION SCIENCE, vol. 4, no. 4, pp. 452 458, Aug. 1999. 4 algorithm, we resort to the slightly different relaxation formula [3,7]: 1 1 y u x L y u x L y x R u u x n n = l (7) where u is used in evaluating both L and x L . A synthetic stereo image pair and its disparity map are obtained by using (7) are shown in Fig. 1. The true disparity map is shown,too. In the true ....

B. K. P. Horn and K. Ikeuchi, "Numerical Shape from Shading and Occluding Boundaries," Artificial Intelligence 17, pp. 141-184, 1981.

....shape from shading (SFS) within the deformable models framework. Most of the earlier work on SFS has been compiled in [7] the first comprehensive comparative study of a number of SFS algorithms is [21] Most of the methods use a regularization approach combined with some additional constraints [3, 8, 11, 9, 22, 12]. 9, 4] combine stereo and shading; 4] handles perspective projection in their stereo and shading mesh. Other approaches are described in [6, 16, 10, 20] A useful discussion of the ambiguities involved in light source estimation can be found in [2] A number of researchers have proposed ....

K. Ikeuchi and B.K.P Horn. Numerical Shape from shading and occluding boundaries. Artificial Intelligence, 17(13) :141-184, 1981.

....they attempt to minimize the error function while conforming to the specific constraints of the technique. Global minimization techniques often require an initial estimate of the depth map and do not run quickly. Examples of global minimization include the work of Ikeuchi Horn and Brooks Horn [21] [9] Global propagation techniques, on the other hand, use singularity points and occluding boundaries to get surface gradient estimates for a few points in the scene. Then they propagate this information throughout the image, again using smoothness or integrability constraints to control the ....

K. Ikeuchi and B. K. P. Horn, "Numerical shape from shading and occluding boundaries," Artificial Intelligence, 17(1-3), 1981, pp.141-184.

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Ikeuchi, K. & B.K.P. Horn (1981) "Numerical Shape from Shading and Occluding Boundaries,"ArtifichJ Intelligenc , Vol. 17, No. 1--3, pp. 141--184, August. Also in Computer Vision, Brady, J.M. (ed.), North-Holland Publishers.

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K. Ikeuchi and B.K.P Horn. Numerical shape from shading and occluding boundaries. Artificial Intelligence Journal, 17:181--184, 1981.

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K. Ikeuchi and B.K.P. Horn. Numerical Shape from Shading and Occluding Boundaries. Artificial Intelligence, 17:141--185, 1981.

....K. Ikeuchi School f Computer Science, Carnegie Mellon University, Pittsburgh, PA 15213, USA Abstract Ikeuch. K. Comment on Numerical shape from shading and occluding boundaries , Artificial Intelligence 59 (1993) 89 94. The paper Numerical shape from shading and occluding boundaries [10] proposed a method to determine the 3D shape of an object from a single brightness image using the smoothness constraint on surface orientations, and the orientations of the surface given along an occluding boundary. This paper contributed both a specific algorithm for solving a specific problem, ....

K. Ikeuchi and B.ICP. Horn, Numerical shape from shading and occluding boundaries, Artif. Intell. 17 (1981) 141-184.

....the image plane can be easily converted into the image on the image sphere. Let a point on the image plane be (u, v) Then the point is mapped into (u X 1 u2 v 2, v X l u2 v 2, l X 1 u2 v2) 1.3. Gaussian sphere and image sphere Surface orientation is expressed using the Gaussian sphere [14]. The Gaussian sphere is a sphere of unit radius whose z axis is taken as an extended line through the north and south poles of the sphere. Assume that we put a surface patch of an object at the center of the sphere and that the direction of the viewer is the direction from the center to the north ....

....3. Constraints and the Propagation of Constraints 3.1. The smoothness constraints Surface smoothness requires that the surface orientation be continuous over the image sphere. Our smoothness requirement is equivalent to the requirement that the surface height function be c I on the image sphere [14]: 1) Surface is continuous on an image sphere (c o w.r.t. height) 2) Surface orientation is continuous on an image sphere (c w.r.t. height) The definition of continuity can be expressed in a more convenient form: A function F is continuous at (x0, y0) if, given 0, there exists a 5 such that ....

[Article contains additional citation context not shown here]

Ikeuchi, K. and Horn, B.K.P., Numerical shape from shading and occluding boundaries, Artificial Intelligence 17 (1981) 141-184.

.... reflectance from brightness (with a known shape and illumination) illumination from brightness (with a known shape and reflectance) The first two kinds of analyses, shape from brightness and reflectance from brightness, have been intensively studied using the shape from shading method [4, 7, 8, 18], as well as through reflectance analysis research [1, 9, 11, 13, 16, 22] In contrast, relatively limited amounts of research have been conducted in the third area, illumination frombrightness [3, 7, 12, 15, 17, 19, 25] This is because real scenes usually include both direct and indirect ....

K. Ikeuchi and B. K. P. Horn, "Numerical shape from shading and occluding boundaries," Artificial Intelligence 17(1-3), pp.141-184, 1981.

....even under a complex illumination environment. 1 Introduction Image brightness is a function of shape, reflectance, and illumination [4] The relationship among them has provided three major research areas in physics based vision: shape from brightness (with a known reflectance and illumination) [6, 7, 8, 16], reflectance from brightness (with a known shape and illumination) 9, 1, 11, 12, 15, 17] and illumination from brightness (with a known shape and reflectance) In the past, shape from brightness and reflectance frombrightness have been extensively explored. In contrast, relatively limited ....

K. Ikeuchi and B. K. P. Horn, "Numerical Shape from Shading and Occluding Boundaries," Artificial Intelligence 17(13) , pp.141-184, 1981.

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K. Ikeuchi and B. K. P. Horn. Numerical shape from shading and occluding boundaries. Artificial Intelligence, 17:141--184, 1981.

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K. Ikeuchi and B.K.P. Horn, "Numerical shape from shading and occluding boundaries," Artificial Intelligence, v. 17, pp. 141-184, 1981. RMS distance (mm) 0.1 0.2 0.3 0.4 5 10 15 20 Mean normal error (deg) 1.2 1.3 1.4 1.5 1.6 1.7 300 310 320 330 340 350 360 Refractive Index Total reconstruction Minimum = 1.33

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Katsushi Ikeuchi and Berthold K. P. Horn. Numerical shape from shading and occluding boundaries. In Michael Brady, editor, Computer Vision, pages 141--184. Elsevier Science Publishing Company, New York, NY, August 1981.

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K. Ikeuchi and B. K. P. Horn, "Numerical shape from shading and occluding boundaries," Artificial Intelligence, Vol. 17, pp. 141-184, August 1981.

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K. Ikeuchi & B. Horn, Numerical Shape from Shading and Occluding Boundaries, Arti cial Intelligence, 17(1-3):141-184, 1981

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K. Ikeuchi and B.K.P. Horn. Numerical shape from shading and occluding boundaries. Artificial Intelligence, 17:141--184, 1981.

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K.Ikeuchi and B.K.P.Horn. Numerical shape from shading and occluding boundaries. Artif. Intell, 17:141--184, 1981.

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K. Ikeuchi and B.K.P. Horn, "Numerical shape from shading and occluding boundaries," Artificial Intelligence, vol. 17, pp. 141--184, 1981.

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K. Ikeuchi and B.K.P. Horn. Numerical shape from shading and occluding boundaries. Arti cial Intelligence, 17:141-184, 1981.

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K. Ikeuchi and B.K.P. Horn. Numerical shape from shading and occluding boundaries. Artificial Intelligence, 17:141--184, 1981.

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K. Ikeuchi and B.K. Horn, "Numerical shape from shading and occluding boundaries, " Artificial Intelligence, vol. 17, pp. 141--184, 1981.

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K. Ikeuchi and B.K.P. Horn. Numerical shape from shading and occluding boundaries. Artificial Intelligence, 17:141--184, 1981.

No context found.

K. Ikeuchi and B.K.P. Horn, "Numerical Shape from Shading and Occluding Boundaries," Artificial Intelligence, vol. 17, pp. 141-184, 1981.

No context found.

K. Ikeuchi and B.K.P. Horn. Numerical shape from shading and occluding boundaries. Artificial Intelligence, 17:141--184, 1981.

No context found.

K. Ikeuchi and B.K.P. Horn. Numerical shape from shading and occluding boundaries. Artificial Intelligence, 17:141--184, 1981.

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K. Ikeuchi and B.K.P. Horn. Numerical shape from shading and occluding boundaries. Artificial Intelligence, 17(1-3):141--184, Aug. 1981.

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K. Ikeuchi and B.K.P. Horn, "Numerical shape from shading and occluding boundaries," Artificial Intelligence, Vol. 17, pp. 141-184, 1981.

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Ikeuchi K. and Honi B. K. P. "Numerical shape from shading and occluding boundaries," Artificial Intelligence 17 (1981), 141-184.

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