J. Oliensis, "Uniqueness in Shape From Shading," in the Int. Journal of Computer Vision, Vol. 6(2), pp. 75-- 104, 1991.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....a wide sense stationary process: EfR(x) R(x )g = C( 2) In this case, jR(d(x) j C(0) The shading term a(x) can thus be estimated up to a multiplicative constant from the second moment of the image E . Shape from Shading studies shape recovery from the shading term only [17, 20]. Here, we concentrate on the texture distorsion, and hence compensate for illumination changes. We estimate the second moment of the image, and then calculate 1=2 I(x) The image resulting from this local contrast renormalization is still denoted I(x) for convenience. The model therefore ....

J. Oliensis. Uniqueness in shape from shading. Int. J. Comput. Vision, 6:75-104, 1991.

....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 ....

....is behind the viewer, the surfaces z = x , z = x , and z = Gammax all appear the same. 2 Geometrical properties of surfaces near global shading maxima: Many shape from shading algorithms need, or can take advantage of, information on the shape near shading singularities (e.g. [13, 22]) A qualitative analysis of shading extrema was suggested by Koenderink van Doorn [17] showing that these singularities often cling to parabolic points. In this section, a qualitative classification of the shape of surfaces near global shading maxima is obtained from the change in the ....

J. Oliensis. Uniqueness in shape from shading. International Journal of Computer Vision, 1990. in press.

....transforming the resulting partial differential equation to obtain f 2 x f 2 y = 1 2 #f #x #f #y 2 = #1 (x, y 0 ) # 2 1 g(x) There is no room for a detailed review of this old and well studied problem. Uniqueness: Oliensis shows that if a solution exists, it is unique [11]. Note that points where g =0are particularly important, because the gradient field has a zero at these points This uniqueness result is proven by noting that (1) the characteristic strips grow from points where g =0 (but in a fashion that depends on the index of the underlying zero of the ....

....of this approach depends sharply on the use of an appropriate family of surfaces. In particular, it is important to ensure that any surface considered turns away from the eye at the boundary. This requirement substantially reduces the available ambiguities (e.g. see Oliensis uniqueness proof [11]) It is, in practice, relatively straightforward to ensure that this criterion is met. We describe our method for a circular boundary; the extension to any Jordan curve is straightforward; an extension to any boundary is technically more tricky, but appears tractable. We will work with parametric ....

J. Oliensis. Uniqueness in shape from shading. Int. J. Computer Vis ion , pages 75--104, 1991.

....GBR transformations 13 correspond to = Sigma1; 0; and = 0. A similar argument holds when the light source intensities are known. Thus, we can determine the true surface up to a sign, i.e. f(x; y) Sigmaf (x; y) This is the classical in out ambiguity that occurs in shape from shading [8, 18]. Note however, that the shadowing configurations change when changes sign, and if shadowing is present, this ambiguity can be resolved. 5 Conclusion We have shown that under any lighting condition, the shading and shadowing on an object with Lambertian reflectance are identical to the shading ....

J. Oliensis. Uniqueness in shape from shading. Int. J. Computer Vision, 6(2):75--104, June 1991.

....which to choose. The standard approach is to apply another constraint, typically the smoothness of the reconstruction, and choose the orientation to minimize the sum of the deviation from the shading model and the deviation from the extra constraint. There has been some recent work by Oliensis [ Oliensis 1991 ] to show that unique solutions can be obtained given the additional assumption that the illumination is symmetric about the viewing direction. Surface orientation approaches, including shape from shading, generally fail to handle discontinuities. They assume 0th degree smoothness in ....

J. Oliensis. Uniqueness in Shape from Shading. Int'l. J. of Computer Vision, 6(2):75--104, 1991.

....C 2 solution z with leading terms z = 1 2 (ax 2 by 2 ) O( jxj jyj) 3 ) will agree with z ; in a neighborhood of (0; 0) and on all of R 2 if z is globally de ned) with a similar statement holding for z ; See [4] or Theorem 2. 7 below for the local result and Oliensis [11] for the global version) However, the other two solutions are far from unique. In Section 3.1 we show that for the solution z ; 1 2 (ax 2 by 2 ) there is an in nite dimensional family of C 1 solutions of the form z = 1 2 (ax 2 by 2 ) O( jxj jyj) 3 ) that do not agree with ....

J. Oliensis, Uniqueness in shape from shading, IJCV 6 (1991), no. 2, 75-104.

.... classical problem in nonlinear Partial Differential Equation (PDE) of first order F (X; Y; Z; p; q) 0; p j ZX ; q j Z Y (1) requiring the formal assumption of F 2 p F 2 q 6= 0 and C 2 continuity of F at each local point and in some neighborhood of this point for the existence of solution[17, 21, 20]. This problem is interpreted geometrically, in X,Y ,Z space, as finding the C 2 continuous surface Z(X;Y ) contacted by local tangent patch which has normal vector (p; q; 1) and which satisfies eq. 1) This problem is a widely studied one in mathematics, physics, and computer vision. ....

....the Monge cone and contacts tangent surface. these usually require a lots of iterations without guarantee of convergence. Geometrical approaches, a way of directly solving this problem, have been started from CSEM[9] and an analysis about properties of characteristic strip has been studied by [17]. Recently, the number of iterations have been considerably reduced by introducing stable approaches based on viscosity solution[21] and or LCPM[1, 20, 14] Nevertheless, we believe that the study about uniqueness and existence of analytical solution of SFS problem have not been fully proceeded ....

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J. Oliensis, "Uniqueness in shape from shading", IJCV, 6(2):75--104, 1991.

....problem of these approaches is that these usually require a lots of iterations without guarantee of convergence. Geometrical approaches, a way of directly solving the problem, have been started from CSEM[11] and an analysis about properties of characteristic strip has been studied by [22]. Recently, the number of iterations have been considerably reduced in addition to guarantee of convergence by introducing stable approaches based on viscosity solution[26, 21, 6, 9] and or LCPM[1, 25, 8, 18, 28] All these approaches are basically similar in the global propagation and or ....

....and or iteration with a given initial condition which is a non characteristic curve or a singular point. Nevertheless, we believe that the study about uniqueness and existence of locally analytic solution of SFS problem have not been fully proceeded until now regardless of recent contributions[22, 23, 5, 6, 20]. The topic about existence and uniqueness of the SFS problem will be discussed based on a typical geometrical interpretation of PDE by assuming known position of light source, normalized albedo, and the orthographic projection. It will be shown by this discussion that the solution of this problem ....

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J. Oliensis, "Uniqueness in shape from shading", IJCV, 6(2):75--104, 1991.

....of the algorithm of Oliensis and Dupuis, is based on a minimum downhill principle which guarantees continuous surfaces and stable results. The algorithm is applicable to a broad variety of objects and reflectance maps. 1 Introduction Until the recent publications of Oliensis and Dupuis [ 5] 6] [7]] most researchers in shape from shading were convinced that recovering depth from a brightness image necessarily required some regularization technique in order to guarantee a physically plausible surface [4] It also seemed evident that only an iterative process with typically several thousand ....

J. Oliensis, "Uniqueness in Shape from Shading," International Journal of Computer Vision, Vol. 6(2), pp. 75-104, 1991.

....correspond to = Sigma1; 0; and = 0. A similar argument holds about G GammaT when the light source intensities are known. Thus, we can determine the true surface up to a sign, i.e. f(x; y) Sigmaf (x; y) This is the classical in out ambiguity that occurs in shape from shading [6, 14]. Note however, that the shadowing configurations change when changes sign, and if shadowing is present, this ambiguity can be resolved. 5 Discussion We have shown that under any lighting condition, the shading and shadowing on an object is identical to the shading and shadowing on any ....

J. Oliensis. Uniqueness in shape from shading. Int. J. Computer Vision, 6(2):75--104, June 1991.

.... y = R q q = E y If the surface normal were known at a pixel (x 0 ; y 0 ) then the differential equations could be integrated to obtain a curve on the surface using the method of characteristic strips[27, 18] Conditions under which these known points uniquely constrain the solution are proved in [6, 73, 66, 67]. The second approach is to concede that (3.4) is an approximation and to compute a surface for which the error, k R(p; q) Gamma E(x; y) k 2 , is as small as possible, that is, to compute a surface whose rendered image is similar to the actual image. Additional constraints have been used to ....

J. Oliensis, "Uniqueness in Shape from Shading", International Journal of Computer Vision 6, 75-104 (1991).

....and saddle like surfaces that appear the same from certain viewpoints 2 . 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 ....

.... Gamma y 2 all appear the same. Journal of Mathematical Imaging and Vision 4(2) 119 138, April 1994 3 2 Geometrical properties of surfaces near global shading maxima: Many shape from shading algorithms need, or can take advantage of, information on the shape near shading singularities (e.g. [13, 22]) A qualitative analysis of shading extrema was suggested by Koenderink van Doorn [17] showing that these singularities often cling to parabolic points. In this section, a qualitative classification of the shape of surfaces near global shading maxima is obtained from the change in the ....

J. Oliensis. Uniqueness in shape from shading. International Journal of Computer Vision, 1990. in press.

....used below. Our results can be extended to essentially any image irradiance equation that can be so written. Singular points those image points where the intensity achieves its maximal brightness I( Delta) 1 play a critical role in constraining the surface corresponding to a shaded image [8,11,16,2]. Only at these points is the local surface orientation determined from the intensity alone. Let S denote the set of singular points in the image. It is easy to see that rf = 0 on S, so that S includes all local maxima and minima of f(x; y) We will focus on those singular points corresponding ....

J. Oliensis, "Uniqueness in Shape From Shading," The International Journal of Computer Vision, Vol. 6 no. 2, pp. 75-104, 1991.

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J. Oliensis, "Uniqueness in Shape From Shading," in the Int. Journal of Computer Vision, Vol. 6(2), pp. 75-- 104, 1991.

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J. Oliensis. Uniqueness in shape from shading. Int. Journal of Computer Vision, 6(2):75--104, 1991.

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J. Oliensis. Uniqueness in shape from shading. Int. Journal of Computer Vision, 6(2):75--104, 1991.

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J. Oliensis. Uniqueness in shape from shading. Int. Journal of Computer Vision, 6(2):75--104, 1991.

No context found.

J. Oliensis. Uniqueness in shape from shading. Int. Journal of Computer Vision, 6(2):75--104, 1991.

No context found.

J. Oliensis. Uniqueness in shape from shading. Int. J. Comput. Vision, 6:75-104, 1991.

No context found.

J. Oliensis. Uniqueness in shape from shading. Int. J. Computer Vision, 6(2):75--104, June 1991.

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J. Oliensis. Uniqueness in shape from shading. IJCV, 2(6):75--104, 1991.

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J. Oliensis, "Uniqueness in Shape From Shading," in the Int. Journal of Computer Vision, Vol. 6(2), pp. 75-- 104, 1991.

No context found.

Oliensis, J. 1991. Uniqueness in Shape from Shading. Int. Journal of Computer Vision, Vol. 6, pp. 75-104.

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