Grimson, W.E.L. (1983) "An Implementation of a Computational Theory of Visual Surface Interpolation," Computer Vision, Graphic and ImageProc#---9LT Vol. 22, pp. 39--69, April.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....Note that x and y are dependent on u and v respectively which makes the function Phi 3 (u; v) nonquadratic. We can derive the Euler Lagrange equations for the variational problem in (9) and solve the resulting system of equations [2] In this paper, we develop a more efficient approach. We follow [15] and straightaway discretize the function Phi in (9) Assuming the distance between two adjacent grid points to be u i 1;j Gamma u ij = u i;j 1 Gamma u ij = h; 10) the second order partial derivatives (u xx ) ij , u xy ) ij and (u yy ) ij at the point (i; j) can be approximated by (u xx ) ....

W. Grimson. An implementation of a computational theory of visual surface interpolation. Computer Vision, Graphics, and Image Processing, 22:39--69, 1983. 27

....interpolation has been one of the most intensely studied problems in low level computer vision. It plays a central role in the construction of a continuous 3 D surface from sparse visual data. The computational theories used in conjunction with surface interpolation include variational principles[5] and regularization theory [6,7] The common element of these computational theories is the minimization of a global energy function composed of many local energy components. This minimization usually has been implemented using iterative algorithms. Weak points in these methods are the sensitivity ....

W. E. L. Grimson. An implementation of a computational theory of visual surface interpolation. Computer Vision, Graphics, and Image Processing, 22:29--69, 1983.

....previously attained versions together. 3.2. Optimal Iterative Reconstruction The second proposed method aims at reconstructing the lost macroblocks by minimizing a cost function. This cost function, f , is the sum of the weighted square di#erences between each lost pixel value and its neighbors [17, 9], which include pixels from surrounding undamaged blocks shown in the dark region in Figure 4. Thus, f(x) 1 2 X (i,j)#D [# w i,j (x i,j x i,j 1 ) 2 # e i,j (x i,j x i,j 1 ) 2 # n i,j (x i,j x i 1,j ) 2 # s i,j (x i,j x i 1,j ) 2 ] 2) where x is a vector of ....

W. Grimson, "An implementation of a computational theory of visual surface interpolation," Computer Vision, Graphics, Image Processing, vol. 22, no. 1, pp. 39--69, April 1983. (a) (b) (c) (d)

....surface reconstruction and shape from shading problems. Performance of the preconditioning technique is demonstrated via experimental results on real and synthetic data. 2 1 Introduction In the past decade, several problems in early vision have been formulated in a regularization framework [9, 27, 26, 30, 3, 4, 12, 13]. These formulations result in partial differential equations which when discretized lead to large sparse linear systems. Numerical iterative methods such as the Gauss Seidal, Jacobi and the conjugate gradient technique [8] have been popular until the inception of multi grid methods [24] and ....

W. E. L. Grimson. "an implementation of a computational theory of visual surface interpolation ". Computer Vision, Graphics, Image Processing, 22:39--69, 1983.

....previously attained versions together. 7.2.2 Optimal Iterative Reconstruction The second proposed method aims at reconstructing the lost macroblocks by minimizing a cost function. This cost function, f , is the sum of the weighted square di#erences between each lost pixel value and its neighbors [72, 48], which include pixels from surrounding undamaged blocks shown in the dark region in Figure 7.2. Thus, 76Fig. 7.2. The cost function includes the di#erences between pixels on the boundary of the lost macroblock and their neighbors. These neighboring pixels that belong to the other macroblocks, ....

W. Grimson, "An implementation of a computational theory of visual surface interpolation," Computer Vision, Graphics, Image Processing, vol. 22, no. 1, pp. 39--69, April 1983.

....of depth. For many applications, such as surface approximation, it is desirable that continuous depth data is presented. With such demands attempts have been made to augment the depth estimates from stereo matching approaches with results from other algorithms such as surface interpolation [8] and binocular shape from shading [1] 1.1 Multi Stage Algorithm Our starting point for this work has been the auto calibration [5] and stretch correlation [4] algorithms. The requirements of this project have enabled us to further the stretch correlation algorithm and integrate it as part of ....

....already identified surface discontinuities using the stretch correlation algorithm, it seems appropriate to fit smooth functions between these estimates. The final stage is used to close the surface by averaging local areas of the image and is essentially the algorithm described by Grimson [8]. 2 Stretch Correlation The stretch correlation algorithm is an area based solution to the stereo problem, matching discrete blocks in the left image to blocks in the right. However, focusing the matching process on information rich areas of the image (those containing nonhorizontal edges) ....

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Grimson W.E.L. An implementation of a computational theory of visual surface interpolation. Computer Vision, Graphics and Image Processing, 22:39--69, 1983.

....images using approximating thin plate splines. This approach is based on the mathematical work in [19] and is an extension of the original interpolating thin plate spline approach [2] For related approaches in the context of surface approximation and modification of facial expressions, see, e.g. [8], 5] 16] 1] To find the transformation u between two images of dimension d we assume to have two sets of n landmarks p i and q i , i = 1 : n, in the first and second image, resp. as well as information about the landmark localization errors in terms of scalar weights oe 2 i . Then, u ....

W.E.L. Grimson, "An Implementation of a Computational Theory of Visual Surface Interpolation", Computer Vision, Graphics, and Image Processing 22 (1983) 39-69

....or spatial coherence constraint [71] is that most surfaces in natural scenes exhibit some geometrical smoothness and structural integrity ( rigidity ) on the whole. This approach has been successful in a wide variety of visual field reconstruction problems including depth interpolation [21, 22], shape from shading [32, 36, 37] and optical flow computation [34, 30] Mathmatically, these reconstruction problems are formulated as least squares problems in which the spatial coherence constraints are implemented as cost terms penalizing large spatial derivatives in the fields. Solution of ....

....hf = 0 corresponds to the brightness change constraint equation in which g(s) and h(s) are obtained from the temporal and spatial gradients of the image brightness. Another example is the generation of sparse measurements of the depth field by stereo matching of feature points in a pair of images [21, 22]. In this case, the unknown f(s) represents the depth field while g(s) is the sparse measurement of f(s) and h(s) is a binary function such that h(s) 8 : 1; if the depth is measured at s 0; otherwise. Note that at the points s where h(s) 0, f(s) is unconstrained by the measurement ....

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W. E. L. Grimson. An implementation of a computational theory of visual surface interpolation. Computer Vision, Graphics, and Image Processing, 22:39-- 69, 1983.

....where the surface is the graph of a function of two variables: z = f(x; y) In the second category the surface is described by the equation f(x; y; z) const, the so called implicit form. In these definitions x; y; z are the Cartesian coordinates. Algorithms such as the ones proposed by Grimson [4] and Terzopoulos [11] model the surface in an explicit form by calculating the z values over a (x; y) grid. This is achieved by minimizing a defined energy functional, which produces a smooth interpolation of the sparse range data. Vemuri [13] uses a different approach where viewpoint independence ....

.... Delta h k ; k = 1; 2. By applying this extension of the Kohonen algorithm it is possible to describe surfaces of fairly complex objects. At this point it is interesting and necessary to assess the novel method on the background of some previous work in that field. Standard algorithms, such as in [4] or [11] assume a given rectangular grid (x; y) By minimizing certain functionals they determine the function f to describe z = f(x; y) Viewpoint dependence is inherent to these methods, because the (x; y) plane has to be defined a priori. Fusion of data from different sources creates ....

W.E.L. Grimson, An Implementation of a Computational Theory of a Visual Surface Interpolation in: Computer Vision, Graphics, and Image Processing, vol. 6, no. 22, pp. 39-69, 1983.

....object manipulation) segmentation of multiple objects (in object recognition) There have been several studies on inferring object surfaces from sparse 3 D data obtained by passive ranging methods including stereo vision. Their works are broadly classi ed into three approaches. The rst approach[1][2] is to attach the surface to sparse edge points by regularization with some additional constraints such as smoothness constraint. This approach, however, has the following problems. Firstly, the additional constraints to regularize the problem are not always true for every scene. Secondly, it ....

W. E. L. Grimson. An implementation of a computational theory of visual surface interpolation. Comput. Vision Graph. Image Process., Vol. 22, pp. 39-69, 1983.

....in two dimensions. Hence, we reduce the deformation model described in Section 3.1 to the thin plate surface model[14] which is simpler and enables a more efficient numerical method. The thin plate surface model has been used in computer vision to solve the visual surface reconstruction problem[10, 20, 21]. Let Omega be a rectangular thin plate on the uv plane and p = u; v) a point on Omega . If the plate is allowed to be deformed only in the direction perpendicular to the uv plane, a shape of the plate can be represented by a function, f(p) The function f specifies a real value for each point on ....

W. Grimson. An implementation of a computational theory of visual surface interpolation. Computer Vision, Graphics, and Image Processing, 22:39--69, 1983.

....of high confidence, the depth estimates are qualitatively correct. In order to fill in the missing ADELSON AND WANG: SINGLE LENS STEREO WITH A PLENOPTIC CAMERA 105 regions, one would need to use techniques such as those that have been described in other domains of computational vision (e.g. [17] [l9] VIII. CONCLUSIONS The structure of light that fills the space around an obiect contains a great deal of information that can help characterize the object s 3 D shape. Ordinary camera systems capture only a tiny portion of the information. Binocular stereo systems capture information about ....

W. E. L. Grimson, "An implementation of a computational theory of visual surface interpolation," Comput. Vision Graphics, Image Processing, vol. 2, pp. 39-69, 1983.

....and so on. This is an ill posed problem. Regularization is usually applied to make it well posed. Then, various methods can be used to discretize the problem into an objective function of discrete nodal variables such that an approximated solution which can be solved numerically is possible [1] [3], 6] 7] 9] 10] 13] In this paper, we introduce a novel insight into studying this problem. Specifically, we try to tackle this problem by parallel information based complexity techniques. The computational complexity of a problem is its intrinsic difficulty as measured by the time, space, ....

W.E.L.Grimson(1983), An implementation of a computational theory of visual surface interpolation, Computer Vision, Graphics, Image Procssing, vol.22, pp. 39-69.

....interpolating features making it much easier to use than the previous techniques. 2 Deformable surface construction The construction of a smooth surface which interpolates a set of scattered points has been investigated in computer vision to solve the visual surface reconstruction problem. Grimson[8] first applied the thin plate surface model[9] to the problem and used the conjugate gradient method for a numerical solution. Terzopoulos extended the result to accommodate discontinuities[10] and presented a multilevel algorithm for quickly solving a hierarchy of discrete problems[11] We adopt ....

W. Grimson. An implementation of a computational theory of visual surface interpolation. Computer Vision, Graphics, and Image Processing, 22:39--69, 1983.

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Grimson, W.E.L. (1983) "An Implementation of a Computational Theory of Visual Surface Interpolation," Computer Vision, Graphic and ImageProc#---9LT Vol. 22, pp. 39--69, April.

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W. E. L. Grimson, "An implementation of a computational theory of visual surface interpolation," Comput. Vision, Graphics, and Image Processing 22, 39--69 ~1983!.

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