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Determining Optical Flow
 ARTIFICIAL INTELLIGENCE
, 1981
"... Optical flow cannot be computed locally, since only one independent measurement is available from the image sequence at a point, while the flow velocity has two components. A second constraint is needed. A method for finding the optical flow pattern is presented which assumes that the apparent veloc ..."
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Cited by 2376 (9 self)
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Optical flow cannot be computed locally, since only one independent measurement is available from the image sequence at a point, while the flow velocity has two components. A second constraint is needed. A method for finding the optical flow pattern is presented which assumes that the apparent velocity of the brightness pattern varies smoothly almost everywhere in the image. An iterative implementation is shown which successfully computes the optical flow for a number of synthetic image sequences. The algorithm is robust in that it can handle image sequences that are quantized rather coarsely in space and time. It is also insensitive to quantization of brightness levels and additive noise. Examples are included where the assumption of smoothness is violated at singular points or along lines in the image.
Numerical Shape from Shading and Occluding Boundaries
 Artifical Intelligence
, 1981
"... An iterative method for computing shape from shading using occluding boundary information is proposed. Some applications of this method are shown. We employ the stereographic plane to express the orientations of surface patches, rather than the more commonly.used gradient space. Use of the stereogra ..."
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Cited by 248 (19 self)
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An iterative method for computing shape from shading using occluding boundary information is proposed. Some applications of this method are shown. We employ the stereographic plane to express the orientations of surface patches, rather than the more commonly.used gradient space. Use of the stereographic plane makes it possible to incorporate occluding boundary information, but forces us to employ a smoothness constraint different from the one previously proposed. The new constraint follows directly from a particular definition of surface smoothness. We solve the set of equations arising from the smoothness constraints and the imageirradiance equation iteratively, using occluding boundary information to supply boundary conditions. Good initial values are found at certain points to help reduce the number of iterations required to reach a reasonable solution. Numerical experiments show that the method is effective and robust. Finally, we analyze scanning electron microscope (SEM) pictures using this method. Other applications are also proposed. 1.
Illposed problems in early vision
 Proceedings of the IEEE
, 1988
"... The first processing stage in computational vision, also called early vision, consists of decoding twodimensional images in terms of properties of 30 surfaces. Early vision includes problems such as the recovery of motion and optical flow, shape from shading, surface interpolation, and edge detect ..."
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Cited by 227 (14 self)
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The first processing stage in computational vision, also called early vision, consists of decoding twodimensional images in terms of properties of 30 surfaces. Early vision includes problems such as the recovery of motion and optical flow, shape from shading, surface interpolation, and edge detection. These are inverse problems, which are often illposed or illconditioned. We review here the relevant mathematical results on illposed and illconditioned problems and introduce the formal aspects of regularization theory in the linear and nonlinear case. Specific topics in early vision and their regularization are then analyzed rigorously, characterizing existence, uniqueness, and stability of solutions.
Survey Of Texture Mapping
 IEEE Computer Graphics and Applications
, 1986
"... This paper appeared in IEEE Computer Graphics and Applications, Nov. 1986, pp. 5667. An earlier version of thi aper appeared in Graphics Interface '86, May 1986, pp. 207212. This postscript version is missing all of the pasteup  ..."
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Cited by 226 (3 self)
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This paper appeared in IEEE Computer Graphics and Applications, Nov. 1986, pp. 5667. An earlier version of thi aper appeared in Graphics Interface '86, May 1986, pp. 207212. This postscript version is missing all of the pasteup 
Surface Reflection: Physical and Geometrical Perspectives
 IEEE Transactions on Pattern Analysis and Machine Intelligence
, 1991
"... Machine vision can greatly benefit from the development of accurate reflectance models. There are two approaches to the study of reflection: physical and geometrical optics. While geometrical models may be consumed as mere approximations to physical models, they possess simpler mathematical forms th ..."
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Cited by 152 (32 self)
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Machine vision can greatly benefit from the development of accurate reflectance models. There are two approaches to the study of reflection: physical and geometrical optics. While geometrical models may be consumed as mere approximations to physical models, they possess simpler mathematical forms that often render them more usable than physical models. However, geometrical models are applicable only when the wavelength of incident light is small compared to the dimensions of the surface imperfections. Therefore, it is incorrect to use these models to interpret or predict reflections from smooth surfaces, and only physical models are capable of describing the underlying reflection mechanism.
The variational approach to shape from shading
 Computer Vision, Graphics, and Image Processing
, 1986
"... We develop a systematic approach to the discovery of parallel iterative schemes for solving the shapefromshading problem on a grid. A standard procedure for finding such schemes is outlined, and subsequently used to derive several new ones. The shapefromshading problem is known to be mathematica ..."
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Cited by 140 (1 self)
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We develop a systematic approach to the discovery of parallel iterative schemes for solving the shapefromshading problem on a grid. A standard procedure for finding such schemes is outlined, and subsequently used to derive several new ones. The shapefromshading problem is known to be mathematically equivalent to a nonlinear firstorder partial differential equation in surface elevation. To avoid the problems inherent in methods used to solve such equations, we follow previous work in reformulating the problem as one of finding a surface orientation field that minimizes the integral of the brightness error. The calculus of variations is then employed to derive the appropriate Euler equations on which iterative schemes can be based. The problem of minimizing the integral of the brightness error term is ill posed, since it has an infinite number of solutions in terms of surface orientation fields. A previous method used a regularization technique to overcome this difficulty. An extra term was added to the integral to obtain an approximation to a solution that was as smooth as possible. We point out here that surface orientation has to obey an integrability constraint if it is to correspond to an underlying smooth surface. Regularization methods do not guarantee that the surface orientation recovered satisfies this constraint. see also "Shape from Shading" MIT Press.
Height and gradient from shading
 International Journal of Computer Vision
, 1990
"... Abstract: The method described here for recovering the shape of a surface from a shaded image can deal with complex, wrinkled surfaces. Integrability can be enforced easily because both surface height and gradient are represented (A gradient field is integrable if it is the gradient of some surface ..."
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Cited by 135 (1 self)
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Abstract: The method described here for recovering the shape of a surface from a shaded image can deal with complex, wrinkled surfaces. Integrability can be enforced easily because both surface height and gradient are represented (A gradient field is integrable if it is the gradient of some surface height function). The robustness of the method stems in part from linearization of the reflectance map about the current estimate of the surface orientation at each picture cell (The reflectance map gives the dependence of scene radiance on surface orientation). The new scheme can find an exact solution of a given shapefromshading problem even though a regularizing term is included. The reason is that the penalty term is needed only to stabilize the iterative scheme when it is far from the correct solution; it can be turned off as the solution is approached. This is a reflection of the fact that shapefromshading problems are not illposed when boundary conditions are available, or when the image contains singular points. This paper includes a review of previous work on shape from shading and photoclinometry. Novel features of the new scheme are introduced one at a time to make it easier to see what each contributes. Included is a discussion of implementation details that are important if exact algebraic solutions of synthetic shapefromshading problems are to be obtained. The hope is that better performance on synthetic data will lead to better performance on real data.
Motion Field And Optical Flow: Qualitative Properties
 IEEE Transactions on Pattern Analysis and Machine Intelligence
, 1989
"... In this paper we show that the optical flow, a 2D field that can be associated with the variation of the image brightness pattern, and the 2D motion field, the projection on the image plane of the 3D velocity field of a moving scene, are in general different, unless very special conditions are sa ..."
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Cited by 124 (2 self)
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In this paper we show that the optical flow, a 2D field that can be associated with the variation of the image brightness pattern, and the 2D motion field, the projection on the image plane of the 3D velocity field of a moving scene, are in general different, unless very special conditions are satisfied. The optical flow, therefore, is illsuited for computing structure from motion and for reconstructing the 3D velocity field, problems that require an accurate estimate of the 2D motion field. We then suggest a different use of the optical flow. We argue that stable qualitative properties of the 2D motion field give useful information about the 3D velocity field and the 3D structure of the scene, and that they can be usually obtained from the optical flow. To support this approach we show how the (smoothed) optical flow and 2D motion field, interpreted as vector fields tangent to flows of planar dynamical systems, may have the same qualitative properties from the point of view of the theory of structural stability of dynamical systems. () Massachusetts Institute of Technology 1986 This report describes research done within the Artificial Intelligence Laboratory. Support for the A.I. Laboratory's artificial intelligence research is provided in part by the Advanced Research Projects Agency of the Depart ment of Defense under Oilice of Naval Research contract N00014S5K0124. Support for this research is also provided by a grant from the Oilice of Naval Research, Engineering Psychology Division and by gift of the Artificial Intelligence Center of Hughes Aircraft Corporation to T. Poggio.
Exaggerated Shading for Depicting Shape and Detail
 PROC. OF ACM SIGGRAPH, ACM TRANS. ON GRAPHICS
, 2006
"... In fields ranging from technical illustration to mapmaking, artists have developed distinctive visual styles designed to convey both detail and overall shape as clearly as possible. We investigate a nonphotorealistic shading model, inspired by techniques for cartographic terrain relief, based on dy ..."
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Cited by 67 (5 self)
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In fields ranging from technical illustration to mapmaking, artists have developed distinctive visual styles designed to convey both detail and overall shape as clearly as possible. We investigate a nonphotorealistic shading model, inspired by techniques for cartographic terrain relief, based on dynamically adjusting the effective light position for different areas of the surface. It reveals detail regardless of surface orientation and, by operating at multiple scales, is designed to convey detail at all frequencies simultaneously.
deFigueiredo, “A theory of photometric stereo for a class of diffuse nonlambertian surfaces
 IEEE Transactions on PAMI
, 1991
"... AbstractPhotometric stereo is a method of reconstructing a surface from the amount of light reflected by it. This is done by using prior knowledge of the surface reflectance to estimate the surface normal at all visible points. The theory of photometric stereo has been extensively developed for sur ..."
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Cited by 54 (0 self)
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AbstractPhotometric stereo is a method of reconstructing a surface from the amount of light reflected by it. This is done by using prior knowledge of the surface reflectance to estimate the surface normal at all visible points. The theory of photometric stereo has been extensively developed for surfaces and illumination geometries that give rise to a Lambertian reflectance map. For nonLambertian reflectance maps, the theory has been developed for specific cases, but a general theory has not been presented in the literature. In this paper, we propose a theory of photometric stereo for a large class of nonLambertian reflectance maps. First, we review the different reflectance maps proposed in the literature for modeling reflection from realworld surfaces. From this, we obtain a mathematical class of reflectance maps to which the maps belong. Next, we show that three lights can be sufficient for a unique inversion of the photometric stereo equation for the entire class of reflectance maps. We also obtain a constraint on