Yuille, A., Snow, D.: Shape and albedo from multiple images using integrability. In: Proc. Conf. Computer Vision and Pattern Recognition. (1997) 158--164  Home/Search   Document Not in Database   Summary   Related Articles   Check

....and intensities are known) Another possibility is to assume that at least six light sources are of equal (or known relative) intensity, or that albedo is uniform (or known up to a global scaler) for at least six normals at a curved surface. Such possibilities were employed and or discussed in [6, 14, 1], and it was shown that such knowledge reduces the ambiguity from the GL(3) group into the group of scaled orthogonal transformations A = #O (O O(3) # 0) Yet another important possibility is given by the integrability constraint that requires the normals recovered by photometric stereo to ....

A. Yuille and D. Snow. Shape and albedo from multiple images using integrability. In Proc. IEEE Conference on Computer Vision and Pattern Recognition, pages 158--164, 1997.

....4 and 5 in Figure 1. However, the image formation model given by Eq. 1 does not account for cast shadows. For the light source direction associated with each extreme ray given by Equation 4, we need to determine which pixels (elements) of x ij will fall in a cast shadow. It has been shown [1, 23] that from multiple images where the light source directions are unknown, one can only recover a Lambertian surface up to a threeparameter family given by the generalized bas relief (GBR) transformation. This family of affine transformations scales the relief (flattens or extrudes) and introduces ....

A. Yuille and D. Snow. Shape and albedo from multiple images using integrability. In Proc. IEEE Conf. on Comp. Vision and Patt. Recog., pages 158--164, 1997.

....wherever the brightness gradient is non zero, or when it is greater than a threshold in the presence of noise, thus avoiding an ill posed formulation of the reconstruction problem. Issues concerning the fusion of shading cues with parallax cues have been discussed in several works, including [1, 29, 17, 32, 19, 7, 3, 28]. To our knowledge, the merging of multi view geometry with shading in a variational framework is novel. Also, the re visitation of the correspondence problem and the de nition of correspondence sets is novel, and so is the fast level set implementation of the stereoscopic shading algorithm that ....

A. Yuille and D. Snow. Shape and albedo from multiple images using integrability. In Proc. of the Intl. Conf. on Comp. Vision and Pattern Recognition, pages 158-164, 1997.

....to reconstruct the surface of the face (see next section) and then use ray tracing techniques. 3 Surface Reconstruction In this section we demonstrate how we can generate an object s surface from B after enforcing the integrability constraint on the surface normal field. It has been shown [4, 31] that from multiple images where the light source directions are unknown, one can only recover a Lambertian surface up to a three parameter family given by the generalized bas relief (GBR) transformation. This family scales the relief (flattens or extrudes) and introduces an additive plane. It has ....

....GBR, the integrability of B must be enforced. Since no method has been developed to enforce integrability during the estimation of B , we enforce it afterwards. That is, given B estimate a matrix A 2 GL(3) such that B A corresponds to an integrable normal field; the development follows [31]. Consider a continuous surface defined as the graph of z(x; y) and let b be the corresponding normal field scaled by an albedo field. The integrability constraint for a surface is z xy = z yx where subscripts denote partial derivatives. In turn, b must satisfy: b 1 b 3 y = b 2 b ....

[Article contains additional citation context not shown here]

A. Yuille and D. Snow. Shape and albedo from multiple images using integrability. In Proc. IEEE Conf. on Comp. Vision and Patt. Recog., pages 158--164, 1997.

....(See the images from Subsets 4 and 5 in Fig. 1) The image formation model (Eq. 1 used to develop the illumination cone does not account for cast shadows. For the light source directions of the extreme rays given by Equation 4, we can predict which pixels will be in cast shadows. It has been shown [1, 17] that from multiple images where the light source directions are unknown, one can only recover a Lambertian surface up to a three parameter family given by the generalized basrelief (GBR) transformation. This family scales the relief (flattens or extrudes) and introduces an additive plane. ....

....normal field. Since no method has been developed to enforce integrability during the estimation of B , we enforce it afterwards. That is, given B computed as described above, we estimate a matrix A 2 GL(3) such that B A corresponds to an integrable normal field; the development follows [17]. Consider a continuous surface defined as the graph of a function z(x; y) and let b be the corresponding normal field scaled by an albedo (scalar) field. The integrability constraint for a surface is z xy = z yx where subscripts denote partial derivatives. In turn, b must satisfy: b 1 b 3 ....

[Article contains additional citation context not shown here]

A. Yuille and D. Snow. Shape and albedo from multiple images using integrability. In Proc. IEEE Conf. on Comp. Vision and Patt. Recog., pages 158--164, 1997.

No context found.

A. Yuille and D. Snow. Shape and albedo from multiple images using integrability. In Proc. IEEE Conf. on Comp. Vision and Patt. Recog., pages 158--164, 1997.

....a GBR ambiguity. Thus, if we have at least three images each acquired under different light source directions of a Lambertian surface f(x; y) then by imposing the integrability constraint in Eq. 6, we can recover the surface f(x; y) up to a GBR transformation f(x; y) f(x; y) x y: See [30] for a method to estimate an integrable b from image data. Note that no information given in the image shadows can resolve this ambiguity, as Section 2 showed that the set of all possible images of a surface f(x; y) is invariant under the GBR transformation. It should be noted that Fan and Wolff ....

A. Yuille and D. Snow. Shape and albedo from multiple images using integrability. In Proc. IEEE Conf. on Comp. Vision and Patt. Recog., pages 158--164, 1997. 19

....the signs of the surface curvatures. Their results can be re interpreted in light of the generalized bas relief (GBR) ambiguity, see section (3) which clarifies precisely which properties of the surface can be estimated. Some of the work described in this paper has appeared in conference articles [5, 6, 43, 3] and more details are available in PhD theses [14, 7] Recent work on bilinear models [10] has applied SVD to a variety of vision problems including estimating shape and lighting. Other recent work includes [29] In section (2) we describe, extend and analyze the SVD approach. We demonstrate in ....

.... of this work [6] these constraints are powerful enough, theoretically, to determine the surface and albedo up to a generalized bas relief transformation (GBR) see [3] for a full treatment of the GBR) In this section we will introduce GBR and demonstrate a method, which we first presented in [43], for using it to solve for the shape and albedo up to a GBR. Additional assumptions can then be used to determine the full solution. The integrability constraints are usually expressed in terms of the surface normals but, as shown in [6] they can be generalized to apply to the b(x) vectors. The ....

[Article contains additional citation context not shown here]

A.L. Yuille and D. Snow. "Shape and Albedo from Multiple Images using Integrability." In Proceedings of Computer Vision and Pattern Recognition (CVPR'97). Puerto-Rico. 1997. 35

No context found.

Yuille, A., Snow, D.: Shape and albedo from multiple images using integrability. In: Proc. Conf. Computer Vision and Pattern Recognition. (1997) 158--164

No context found.

A.L. Yuille, D. Snow, Shape and albedo from multiple images using integrability, IEEE Conf. Comput. Vision Pattern Recognition (1997).

No context found.

Alan Yuille and Daniel Snow. Shape and albedo from multiple images using integrability. In Proc. of Computer Vision and Pattern Recognition, 1997. 16

Online articles have much greater impact   More about CiteSeer.IST   Add search form to your site   Submit documents   Feedback  

CiteSeer.IST - Copyright Penn State and NEC