M. Brooks and B. Horn. Shape and source from shading. In Proc. Intl. Joint Conf. Artif. Intelli., pages 932--936, 1985.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....depth map of the surface is needed rather than surface features, it may be necessary to compute the light source direction. In this section, direct computation of the light source direction from the shading on occluding contours in smoothly receding objects in the image is discussed (see also [5, 24, 25]) Assume a single light source at a large distance from the surface. The source s position is defined by two angles (figure 6) tilt the angle between the projection of the light direction on the image plane (denoted the X Gamma Y plane) and the X axis, and slant the angle between the ....

M. J. Brooks and B. K. P. Horn. Shape and source from shading. In B. K. P. Horn and M. J. Brooks, editors, Shape from Shading, pages 53--68. MIT Press, Cambridge, MA, 1989.

....to provide the necessary generalized forces that will deform our model and estimate the object s 3D shape. Our methodology obviates the need for commonly used approximations (e.g. linearization) to these equations, or the solution of partial differential equations requiring boundary conditions [17]. In addition, the use of a deformable model based approachallows the numerically robust computation of the required derivatives and produces improved experimental results. Weshow how the method can be used with either orthographic or perspective projection assumptions. We also demonstrate how ....

....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 ....

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B.K.P. Horn and M.J. Brooks. Shape and source from shading. In International Joint Conference on Artificial Intelligence, pages 932--936, 1985. 36

....an object but also its corresponding shadow. Most of existing methods to estimate the illuminant direction are based on limitative assumptions related to the light source characteristics (a single point source) and the shape and reflectance of the objects (umbilical object, lambertian surface) [1] [2] 3] 4] In practice if the assumptions on the light source are often reasonable, the assumptions on the object properties are very restrictive. Pentland was one of the first who has studied this problem in 1982 [5] Since then, some authors have proposed methods to remove some assumptions of ....

Michael J. Brooks and Berthold K. P. Horn, "Shape and source from shading," Technical Report AIM-820, Massachusetts Institute of Technology, Jan. 1985.

....with directions for future work. 2 Related work Although a large body of work deals with modeling [9, 5, 20, 18, 21] animating [9, 5, 18] and rendering [15, 14, 19, 13] human hair, few articles treat the question of its acquisition. Likewise, the extensive research on Shape from Shading [3, 16] only addresses the case of relatively continuous surfaces, and doesn t offer techniques suited to hair. With [17] Nakajima is the only one, to our knowledge, having considered hair modeling from pictures. His approach is purely geometric and consists of building a 3D hair volume from pictures ....

M. J. Brooks and B. K. P. Horn. Shape and source from shading. In B. K. P. Horn and M. J. Brooks, editors, Shape from Shading, pages 53--68. MIT Press, Cambridge, MA, 1989.

....cue to account for shading variations, which are present in the set of input sample images because of a changing illumination direction. 4. 1 Shape from Shading We adopt a shape from shading technique called height from shading [21] Unlike most shape from shading and photometric stereo methods [19, 5, 40, 27], this technique computes a height field directly rather than through surface normals. This technique is efficient and robust. The geometry recovery is formulated to minimize the following energy functional [21] E # # ### # # R#p ## ;q ## # # I#i; j## # # #u # ## # v # ## ## (3) where ....

M.J. Brooks and B.K.P. Horn. Shape and source from shading. In Proc. Intern. Joint Conf. Art. Int., pages 932--936, 1988.

....2. Shape from Shading Shape from shading (SFS) has been an active subject of research for over two decades, and may be regarded as one of the classical problems of computer vision. In recent research we have developed a SFS technique based upon the variational approach of Horn and Brooks [1, 7, 8]. Our scheme addresses one of the main problems with the Horn and Brooks technique its tendency to over smooth the recovered needle map, leading to a loss of detail in regions where the surface orientation varies rapidly. Several other solutions have been proposed to this (e.g. 6] but our ....

....any regularization function, and is a Lagrange multiplier. The first term of this functional encodes the image irradiance equation. The second term penalizes sharp changes of orientation according to the function ae oe . Ifae oe (j) j 2 , the functional is the same as used by Horn and Brooks [1]. However, any other function may be used as the regularization term, and we have investigated several robust measures, including the classical Tukey [5] and Huber [9] and the Adaptive Prior Potential Functions of Li [13] We also introduced [25] a continuous version of the piecewise Huber robust ....

M. Brooks and B. Horn. Shape and source from shading. IJCAI, pages 932--936, 1986.

....brightness as the input image at each surface point, while the smoothness constraint forces the gradient of the surface to change smoothly. The shape was computed by minimizing an energy function which consists of the above two constraints. Also using these same constraints, Brooks and Horn (B H) [2] minimized the same energy function, in terms of surface normal instead of surface gradient. Frankot and Chellappa [5] enforced the integrability in B H s algorithm in order to recover integrable surfaces (surfaces for which z xy = z yx ) Surface slope estimates from the iterative scheme were ....

M. J. Brooks and B. K. P. Horn. Shape and source from shading. In Proceedings of International Joint Conference on Artificial Intelligence, pages 932--936, 1985.

....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, the brain can be fooled and a shape that is different from the real one may result. This phenomenon ....

....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 ....

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M. Brooks and B. Horn. Shape and source from shading. In Proceedings of the 1985 International Joint Conference on Artificial Intelligence, pages 932--936, Los Angeles, CA, 1985. Artificial Intelligence Conference Inc., Morgan Kaufmann Publishers.

....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. Calibration: ....

Brooks M. and Horn B.K.P. Shape and Source from Shading. In Proceedings of the International Joint Conference on Artificial Intelligence, Los Angeles, CA, USA, pp. 5--12, August 1985.

....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. Calibration: Computer ....

Brooks M. and Horn B.K.P. Shape and Source from Shading. In Proceedings of the International Joint Conference on Artificial Intelligence, Los Angeles, CA, USA, pp. 5--12, August 1985.

....objects. 2 Shape from Shading Shape from shading (SFS) has been an active subject of research for over two decades, and may be regarded as one of the classical problems of computer vision. In recent research we have developed a SFS technique based upon the variational approach of Horn and Brooks [1, 7, 8]. Our scheme addresses one of the main problems with the Horn and Brooks technique its tendency to over smooth the recovered needle map, leading to a loss of detail in regions where the surface orientation varies rapidly. Several other solutions have been proposed to this (e.g. 6] but our ....

.... # # ## #k# i;j ## # # # # # # # # # # #k# i;j## # # #k# i;j## # # # # # # ## #k# i;j ## # # # # # ## # ## #k# i;j ## # # # # #k# i;j ## # # ## #k# i;j ## # # # In the quadratic case where # ### # # # , this becomes the update equation used by Horn and Brooks [1]. However, any other function may be used as the regularization term, and we have investigated several robust measures, including the classical Tukey [5] and Huber [9] and the Adaptive Prior Potential Functions of Li [13] We also introduced [25] a continuous version of the piecewise Huber robust ....

M.J. Brooks and B.K.P. Horn. Shape and source from shading. IJCAI, pages 932--936, 1986.

....approximate surface orientation, as specified in a DEM, and an estimate of the direct illumination direction. Sun angle is often provided with satellite data. For USGS orthoimages, it must be estimated from the imagery. Computer vision shape from shading methods can be used to solve this problem [3]. If shadows are present and one or more matches can be established between points on shadow generating contours and the corresponding point on the trailing edge of the shadow, then the direction of direct illumination can be inferred from the DEMspecified elevations of the corresponding points. ....

BROOKS, M. J., AND HORN, B. K. P. Shape and source from shading. In Shape from Shading, B. K. P. Horn and M. J. Brooks, Eds. MIT Press, Cambridge, MA, 1989.

....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 ....

....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 methods for the estimation of the light source direction. [3] proposes an iterative method that updates both the shape and the illuminant direction at every iteration. To avoid local minima a good initial state is often necessary, and furthermore, the requirement for a light source vector of unit length is not enforced. 10] used a Gaussian sphere model for ....

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M.J. Brooks and B.K.P. Horn. Shape and source from shading. In Proceedings of International Joint Conference on Artificial Intelligence, pages 932-936, 1985.

....function, or both. Likewise, intensity varies because of changes in the shape, illumination, transfer function, or any combination of the three. Many algorithms, in particular shape from shading, work because they assume the image variation is due to changes in only one element of the hypothesis [9]. With a general scene model and the hypothesis framework we can begin to relax these assumptions. The task ahead is to enumerate the set of hypotheses contained in each hypothesis list, or the set of physical explanations in each equivalence class. We want to base these hypotheses on the general ....

....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 ....

M. J. Brooks and B. K. P. Horn, "Shape and Source from Shading," in Proceedings, Int'l Joint Conf. on Artificial Intelligence, August 1985, pp. 932-936.

....to provide the necessary generalized forces that will deform our model and estimate the object s 3D shape. Our methodology obviates the need for commonly used approximations (e.g. linearization) to these equations, or the need to solve partial differential equations requiring boundary conditions [4]. We use deformable models or grids with both global and local deformations [19, 20] During shape estimation, we first fit the model s global parameters given the illumination constraints, and then we refine its shape based on the model s local deformations, using a coarse to fine grid. Use of a ....

....as either global or local, depending on whether they use intensity information across the entire image or only in the local neighborhood of each pixel. Most SFS algorithms for Lambertian surfaces follow a regularization approach using the image brightness and surface smoothing constraints [4, 14, 27, 17, 15]. Some methods make use of the integrability constraint [8, 12] the intensity gradient constraint [31] and the unit normal constraint [4] while [18] provides a numerically efficient solution to regularization. In the above class of approaches, 15, 10] combine stereo and shading. These methods ....

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M.J. Brooks and B.K.P. Horn. Shape and source from shading. In Proceedings of International Joint Conference on Artificial Intelligence, pages 932936, 1985.

....We present typical simulation results to validate the proposed scheme. 1. INTRODUCTION Various schemes exist in the literature to track the motion of an object from a sequence of its images [1] 2] A lot of work has also been done in the estimation of illuminant direction from a single image [3] [4], 5] However, the problem addressed in this paper is that of estimation of the motion of the illuminant itself by observing an image sequence of an unknown object illuminated by it. The camera and the object are both fixed and the light source illuminating the object is moving. This problem is ....

....The major advantage of the solution to the problem addressed in this paper is that the problem of feature correspondence does not arise. Use of a single image frame to estimate the illuminant direction leads to an ill posed problem. This problem was first addressed by Pentland [3] Brooks and Horn [4] have proposed an iterative scheme to alternately estimate the direction of light source and the shape of the object from a single image. Here the cost functional includes a smoothness term resulting in a particularly smooth estimate of shape. Zheng and Chellappa s [5] scheme estimates the ....

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M.J.Brooks and B.K.P.Horn, "Shape and source from shading," Proc. of the Intern. Joint Conf. on Artificial Intelligence, Los Angeles, CA, August 18-23, 1985, pp 932-936.

....condition in terms of the derivatives of the function z(x; y) This condition can then be manipulated into an iterative solution method. Unfortunately, the iteration equations derived from Euler s equation yield methods equivalent to gradient descent. For example, the difference equations in Brooks and Horn (1985) can be derived by taking the gradient of their objective function with respect to each z ij . Gradient descent algorithms are known to have poor convergence properties for systems of many variables. To avoid this problem we formulate a shape from shading objective function in a purely discrete ....

....numerical methods for minimizing the objective function, as discussed in Section 4. 3. 2 Source Direction and Albedo Though the above discussion assumes a known light source direction and albedo l = ha; b; ci we can also consider minimizing E with respect to these parameters, as did Horn and Brooks (1985) within their variational formulation. In fact, the processing of real imagery usually requires such estimation since light source direction and albedo are rarely known accurately. Furthermore, one can show that the objective function is highly sensitive to errors in albedo. To avoid this problem ....

Brooks, M. J. and Horn, B. K. P. (1985). Shape and source from shading. In Proc. Intern. Joint Conf.

....and difficult to solve. All available methods impose some constraints. Variational methods, require boundary conditions, which are points where the surface normal can be determined, in order to find a unique solution, if at all possible. These are typically singular points, or limb boundaries [3, 4]. Local methods make assumptions about local surface geometry, and do not generally produce exact estimates of shape [5, 6] Linear approximations to the reflectance model allow a closed form solution. However, such approaches have problems when the light source is not oblique to the viewer [7] ....

....about local surface geometry, and do not generally produce exact estimates of shape [5, 6] Linear approximations to the reflectance model allow a closed form solution. However, such approaches have problems when the light source is not oblique to the viewer [7] or with noise [8] Brooks and Horn [3] derived a method for finding surface shape and light source direction for a smooth, lambertian surface where boundary conditions are set. They use a global scheme based on the image irradiance equation with a regularisation component. The surface is found iteratively by minimising the error in ....

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M J Brooks and B K P Horn, "Shape and source from shading", in Shape From Shading, B K P Horn and M J Brooks, Eds., pp. 53--68. The MIT Press: Cambridge Massachusetts, London England, 1989.

....depth map of the surface is needed rather than surface features, it may be necessary to compute the light source direction. In this section, direct computation of the light source direction from the shading on occluding contours in smoothly receding objects in the image is discussed (see also [5, 24, 25]) Assume a single light source at a large distance from the surface. The source s position is defined by two angles (figure 6) tilt the angle between the projection of the light direction on the image plane (denoted the X Gamma Y plane) and the X axis, and slant the angle between the ....

M. J. Brooks and B. K. P. Horn. Shape and source from shading. In B. K. P. Horn and M. J. Brooks, editors, Shape from Shading, pages 53--68. MIT Press, Cambridge, MA, 1989.

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Brooks, M.J. & B.K.P. Horn (1985) "Shape and Source from Shading,"ProcCV;J## of the International JointConferenc onArtific(J Intelligenc , Los Angeles, CA, August 18--23, pp. 932--936. Also MIT AI Laboratory Memo 820 January. Bruss, A.R. & B.K.P. Horn (1983) "Passive Navigation," Computer Vision,Graphic# and , Vol. 21, No. 1, pp.3--20 January.

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M. Brooks and B. Horn. Shape and source from shading. In Proc. Intl. Joint Conf. Artif. Intelli., pages 932--936, 1985.

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M.J. Brooks and B.K.P. Horn, "Shape and source from shading," Proc. IJCAI, pp.932--936, 1985.

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M. Brooks and B. Horn. Shape and source from shading. In Proc. Intl. Joint Conf. Artif. Intelli., pages 932--936, 1985.

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M. J. Brooks and B. K. P. Horn. Shape and source from shading. In B. K. P. Horn and M. J. Brooks, editors, Shape from shading, chapter 3. MIT Press, Cambridge, MA, 1989.

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M.J. Brooks and B.K.P. Horn. Shape and source from shading. In Proc. Int. Joint Conf. on Artif. Intell., pages 932--936, Aug. 1985.

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B.K.P. Horn and M.J. Brooks. Shape and source from shading. In IJCAI85, pages 932--936.

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M. J. Brooks and B. K. P. Horn. Shape and source from shading. In Proc. Int. Joint Conf. Aritficial Intell., pages 932--936, 1985.

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M. J. Brooks and B. K. P. Horn. Shape and source from shading. In B. K. P. Horn and M. J. Brooks, editors, Shape from Shading. MIT Press, Cambridge, MA, 1989.

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M. J. Brooks and B. K. P. Horn. Shape and source from shading. In B. K. P. Horn and M. J. Brooks, editors, Shape from shading, chapter 3. MIT Press, Cambridge, MA, 1989.

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M. J. Brooks and B. K. P. Horn, "Shape and Source from Shading," IJCAI, pp932-936, August 1985.

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M.J. Brooks and B.ICP. Horn, Shape and source from shading, in: Proceedings IJCAI-85, Los Angeles, CA (1985) 932-936.

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Brooks, M. J. and Horn, B.K.P. 1985. Shape and source from shading. In: Proc. Int. Joint Conf. Artificial Intell., Los Angeles, pp. 932--936.

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