L. Alvarez, J. Snchez, R. Deriche, and J. Weickert. Dense disparity map estimation respecting image discontinuities: A pde and scale-space based approach. IAPR Workshop on Machine Vision, No. 28-30:423--427, 2000.  Home/Search   Document Details and Download   Summary   Related Articles   Check

.... schek or aline9 scaley1#kO have beB succey1#HHO9ye4y toreH#9 the risk to ge trappe insome irre50 ant minima [20,4,3] The me4 dpreHM te he isinspire from this kind of variationalframe ork that has also prove nreHk tlyto be veH50HOy1 in manyothe image proceyO#M andcompute vision tasks [25,30,8,1]. We startertykOMBMy1O9O the met dde scribe in [4] and modifyit using ideg similar tothose de es e in [9] to obtain an algorithm that will give the same solution ifapplie be tweO image A and B or b weB image B and A. Contrarilyto [9] we de# with discontinuitie of the flowfie0 andeyHBMkky1OH04 e ....

....1 0 and # 2 1. Thus, we have isotropic beH viour withinrehinyk and atimage boundarie the pro cey smoothe anisotropicallyalongthe ees This bek viour is vekOOky1OH to eBOk0Hy1OBk0O anisotropic di#usion filteion [29,28] and it is alsoclose in spirit tothe modifie meekO4y ature motionconsideH# in [2,1]. At this point, tworeH94H can be made Since # 1 is usuallyunknown,the domain 1 isuse inste5 inthe preHOB0 inteB0MMB The criteHy1 deteHy above iscleB5My1kOO0 mmee5My inthe image I 1 and I 2 so thatthe minimisation of E 1 (h 1 ) and that ofthe similarlyde09y E 2 (h 2 ) will notyieH ....

L Alvarez, R. Deriche, J. Weickert, and J. Sanchez. Dense disparity map estimation respecting image discontinuities: A PDE and scale-space based approach. In IAPR Internatiq Workshop onMachi Vihi Appli atii , Tokyo, Japan, Nov. 2000. The University of Tokyo. A revised version has been accepted for publication in 2002 in Journal ofVi22 Communi atiu and Image Representatiq .

....since minimizing an energy functional is usually NP hard. Recently, however, algorithms have been developed to overcome this drawback. One class of methods formulates the problem in terms of level sets and uses numerical techniques to obtain a local minimum as the solution of a set of PDEs [1]. We follow a different approach, in which the energy functional is discrete, and graph cuts are employed iteratively to successively reduce the energy. Many vision problems have been treated successfully with this kind of energy minimization, including stereo and motion [2, 3, 5, 9] and voxel ....

....that if a 3D point is projected onto a pixel p in one image and a pixel q in another and is visible in both images, then pixels in the neighbourhoods p and q should be similar. Mathematically, we set photo (#) C(p, q) if I, 0 otherwise. The correlation term C(p, q) [0, 1] must be small if differs from q and large if the local pixel neighbourhoods are very similar. We found experimentally that a very good criterion is the statistical measure obtained by computing . The normalized cross correlation between the sets of color values I (C p ) and I (C q ) ....

L. Alvarez, R. Deriche, J. S anchez, and J. Weickert. Dense disparity map estimation respecting image discontinuities: A PDE and scale-space based approach. INRIA Rapport de Recherche, No.3874, Jan. 2000.

....systems [5, 8] hence we will not go into detail at this point. Besides the classical approaches for establishing correspondences between two images, which are feature and area based matching, other techniques such as phase and energy based ones have been developed. An overview can be found in [1]. We propose the use of blockmatching by exploiting the advantages of a similarity accumulator resulting in a very efficient computation scheme for consistent dense disparity maps. 3 D accumulator concepts have been developed previously, e.g. see [15] and [18] Augmented Reality applications using ....

L. Alvarez, R. Deriche, J. Sanchez, and J. Weickert. Dense Disparity Map Estimation Respecting Image Discontinuities: A PDE and Scalespace Based Approach. Technical Report RR-3874, INRIA, January 2000.

....deliver a disparity map whose quality is su#cient for a lot of applications out of the box . Alternatively, the techniques described here can be used as a starting point for implementing more sophisticated algorithms. Many of them aiming at high quality need an initial guess for the disparity map [1], 6] or disparity space [15] The algorithm described in this paper can be used as a fast first stage for those algorithms. The implementation is biased towards speed, however we do not want any restrictions that real time algorithms have, like fixed image size and disparity search range[11] For ....

Luis Alvarez, Rachid Deriche, Javier Sanchez, Joachim Weickert, Dense Disparity Map Estimation Respecting Image Discontinuities: A Pde and Scale-Space Based Approach, technical report RR-3874, INRIA, January 2000.

....systems [5, 8] hence we will not go into detail at this point. Besides the classical approaches for establishing correspondences between two images, which are feature and area based matching, other techniques such as phase and energy based ones have been developed. An overview can be found in [1]. We propose the use of blockmatching by exploiting the advantages of a similarity accumulator resulting in a very efficient computation scheme for consistent dense disparity maps. 3 D accumulator concepts have been developed previously, e.g. see [15] and [18] Augmented Reality applications ....

L. Alvarez, R. Deriche, J. Sanchez, and J. Weickert. Dense Disparity Map Estimation Respecting Image Discontinuities: A PDE and Scalespace Based Approach. Technical Report RR-3874, INRIA, January 2000.

....the paper. 2. Correspondence search between two images In this section, we discuss the basic method to extract correspondences from a single stereo pair. The method is akin to optical flow extraction. Such PDE based methods have been shown to give good results for correspondence search [5, 12, 11, 9, 6]. They do not require preprocessing PDE = Partial Differential Equation steps (like feature point or line segment extraction) and provide a dense correspondence map. Our point of departure is the method proposed by Proesmans et al. 12] In a recent comparison study [1] it was shown to perform ....

.... ( x 1 ; d 1 ) where the parameter d 1 = Z1 , i.e. a depth related parameter: x 1 ; d 1 ) d 1 H[3]x 1 d 1 t z (4) H[i] is the 3 vector for the i th row of the homography H and similarly for K 2 [i] This parameterisation differs from the one advocated by Alvarez et al. [9], which is less directly coupled to depth. In the following we will use the vector sign to describe nonhomogeneous pixel coordinates x i = x i ; y i ) I 1 I 2 (d 2 ) Figure 1. 3 Stereo disparity relations: l (d k ) are the stereo correspondences eq. 4 3. ....

L.Alvarez, R.Deriche, J.Snchez, and J.Weickert. Dense disparity map estimation respecting image derivatives: a pde and scale-space based approach. Journal of Visual Communication and Image Representation, to appear., 2000.

....We try to deliver a disparity map whose quality is su#cient for a lot of applications out of the box . Alternatively, the techniques described here can be used as starting point for implementing improved algorithms. Many of them aiming at high quality need an initial guess for the disparity map [1], 6] or disparity space [15] The algorithm described in this paper can as well be used as a fast first stage for those algorithms. The implementation is biased towards speed, however we do not want any restrictions that real time algorithms have [11] For an image size of 160120 pixels, 20fps can ....

Luis Alvarez, Rachid Deriche, Javier Sanchez, Joachim Weickert, Dense Disparity Map Estimation Respecting Image Discontinuities: A Pde and Scale-Space Based Approach, technical report RR-3874, INRIA, January 2000.

....the basis of the resulting dense disparity vector fields. The future work will therefore be concentrated on the following two items. The first one is a further improvement of the pixel recursive stage. Here, it might be very interesting to introduce a parameterisation as it has been proposed in [Alvarez00] in the framework of an anisotropic diffusion approach for disparity estimation. A potential advantage of this method is given by the fact that the pixel recursion runs only one parameter along the epipolar line instead of the two independent x and y components which have then again to be ....

L. Alvarez, R. Deriche, J. Sanchez and J. Weickert: "Dense Disparity Map Estimation Respecting Image Discontinuities: A PDE and Scale-Space Based Approach", INRIA Research Report No. 3874, INRIA, Sophia-Antipolis, January 2000.

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Luis Alvarez, Rachid Deriche, Joaquim Weickert, and Javier Sanchez. Dense disparity map estimation respecting image discontinuities: A pde and scale-space based approach. International Journal of Visual Communication and Image Representation, Special Issue on Partial Differential Equations in Image Processing, Computer Vision and Computer Graphics, 2000.

No context found.

L. Alvarez, R. Deriche, J. Weickert, and J. Sanchez. Dense disparity map estimation respecting image discontinuities: A PDE and scale-space based approach. International Journal of Visual Communication and Image Representation, Special Issue on Partial Differential Equations in Image Processing, Computer Vision and Computer Graphics, 2000.

No context found.

L. Alvarez, R. Deriche, J. Weickert, and J. S anchez. Dense disparity map estimation respecting image discontinuities: A PDE and scale-space based approach. International Journal of Visual Communication and Image Representation, Special Issue on Partial Differential Equations in Image Processing, Computer Vision and Computer Graphics, 2000.

.... possible applications including various computer vision tasks, such as color image restoration [7, 26, 52, 54, 55, 61, 68] and segmentation [11, 31, 40, 49, 50] regularization of optical ows and direction elds [6, 12, 27, 36, 41, 58, 63, 66] image in painting [5, 13, 14] scale space analysis [2, 69], etc. A PDE ow on multi valued data is not a straightforward generalization of its scalar counterpart, since it must explicitly take the coupling between vector components as well as the local vector geometry into account. Indeed, the vector data may lie on a constrained and non at manifold, ....

L. Alvarez, R. Deriche, J. Weickert, and J. Sanchez. Dense disparity map estimation respecting image discontinuities: A PDE and scale-space based approach. International Journal of Visual Communication and Image Representation, Special Issue on PDE in Image Processing, Computer Vision and Computer Graphics, Vol. 13, No. 1/2, March 2002 p. 3-21

....(applications in medical images analysis) Here, a vector field models the pixels motion between the two images and a PDE is used to describe its evolution until it converges to the expected image transformation (Fig.1. 7) Interesting survey and references on this subject can be found in [5, 3, 6, 11, 13, 15, 17, 18, 49, 56, 67, 74, 94, 98, 109, 117, 124, 151, 172, 183, 192]. a) Direct superposing of two MRI images of the brain (b) Superposing after image registration [49] Figure 1.7: Image registration, treated as the evolution of a displacement field. Shape from Shading : This new and challenging problem consists in reconstructing a 3D representation of an ....

....can easily compute the term # trace (AH) of the different diffusion contributions in the PDE velocity #, using simple matrix multiplications. Experimentally, we noticed that this scheme gives very similar results as the classical 0. 5 centered schemes for divergence discretization, as proposed in [5, 12]. 3.5.3 Using local filtering considerations Another method to estimate a term such as trace (TH i ) at a certain time t, is to follow the geometric interpretation in term of local filtering, as described in section (3.2.1) We quickly remind the idea. If T is a constant diffusion tensor, we ....

[Article contains additional citation context not shown here]

L. Alvarez, R. Deriche, J. Weickert, and J. Sanchez. Dense disparity map estimation respecting image discontinuities: A PDE and scale-space based approach. International Journal of Visual Communication and Image Representation, Special Issue on Partial Differential Equations in Image Processing, Computer Vision and Computer Graphics, 2000.

....to smooth grey valued images while preserving the edges, overcoming the restrictions imposed by linear ltering techniques. Since then, many authors have proposed and studied well posedness PDE s that tackle the problem of scalar image regularization. We can cite for instance papers from Alvarez [2, 1], Aubert [10] Chambolle Lions [7] Chan [5] Cohen [13] Cottet Germain [14] Hamza Krim [18] Kornprobst Deriche [22, 23, 24] Malladi Sethian [27] Mumford Shah [29, 46] Morel [28] Nordstr om [30] Osher Rudin [39] Perona Malik [34] Polyak [35] Proesman [38] Sapiro [6, ....

.... of possible applications, including various computer vision tasks : color image restoration, 5, 20, 45, 48, 53, 58] regularization of optical ows and direction elds [8, 21, 33, 50, 49, 55] image inpainting [4, 9] regularization of di usion MRI, 15, 12, 36, 54, 57] scale space analysis [1, 62]. Proposed algorithms rely on various frameworks, such as image variation minimization [3, 5, 46] local geometrybased di usion [45, 53] ow of manifolds embedded in higher dimensional space minimizing Polyakov actions [47] or di usion of chemical concentrations [58] In this paper, we are rst ....

L. Alvarez, R. Deriche, J. Weickert, and J. Sanchez. Dense disparity map estimation respecting image discontinuities: A PDE and scale-space based approach. International Journal of Visual Communication and Image Representation, Special Issue on Partial Dierential Equations in Image Processing, Computer Vision and Computer Graphics, vol.13, p.3-21, 2002.

....has been heavily studied in the computer vision community. The variational framework, based on functional minimizations via diffusion PDE s evolutions has proved its efficiency for scalar data regularization (in particular, within the functions theory) We can cite for instance, Alvarez et al. [1, 2], Aubert et al. 10] Chambolle Lions [7] Chan [5] Cohen [11] Kornprobst Deriche [15, 16, 17] Malladi Sethian [18] Mumford Shah [20, 31] Morel [19] Nordstrom [21] Osher Rudin [26] Perona Malik [23] Proesman et al. 25] Sapiro [6, 28, 29, 30] Weickert [38, 39] You [41] ....

.... area, due to the large number of possible applications, including various computer vision tasks : multivalued image restoration (in particular color images) 5, 14, 30, 32, 36, 37, 38] regularization of optical flows and direction fields [8, 22, 33] image inpainting [3, 9] scale space analysis [2, 40], The introduction of minimization on constrained manifolds has also permitted to regularize more complex and specific data, using the knowledge of the solution space. We can mention for instance the case of vector directions and chromaticity diffusion, based on the harmonic map framework ....

[Article contains additional citation context not shown here]

Luis Alvarez, Rachid Deriche, Joaquim Weickert, and Javier Sanchez. Dense disparity map estimation respecting image discontinuities: A pde and scale-space based approach. International Journal of Visual Communication and Image Representation, Special Issue on Partial Differential Equations in Image Processing, Computer Vision and Computer Graphics,

....to a mathematically correct concept and we have proven the existence and uniqueness of the solution of the parabolic equation which governs our method. Finally, our approach has been validated on a large set of synthetic and real stereo data. All these results are presented in a previous work [1]. 2 Formalism of the matching process 2.1 Notation and Background In this paper we use a projective camera model. This model maps a 3D point M = X; Y; Z] t to a 2D image point m = x; y] t through a 3 Theta 4 projection matrix P via s m = P M, where s is a nonzero scale factor and the ....

L. Alvarez, R. Deriche, J. S#nchez, and J. Weickert, Dense Disparity Map Estimation Respecting Image Discontinuities: a PDE and ScaleSpace Based Approach, Technical Report INRIA 3874, SophiaAntipolis, France, 2000.

....estimation of the depth where the interesting objects are located. Another possibility is to use the result of a simple classic method for estimating the disparity, for instance a correlation technique. DENSE DISPARITY MAP ESTIMATION 9 Equation (24) leads to a mathematically correct concept: in [1] we have shown that if I l , I r and the initial data 0 belong to L 2 (R 2 ) then there exists a unique generalized solution (t) 2 C [0; 1) L 2 (R 2 ) 2.6. Invariance Under Linear Grey Value Transformations A remaining shortcoming of the modi ed model is that the energy ....

L. Alvarez, R. Deriche, J. Sanchez, and J. Weickert, Dense Disparity Map Estimation Respecting Image Discontinuities: a PDE and Scale-Space Based Approach, Technical Report INRIA 3874, Sophia{Antipolis, France, 2000.

No context found.

L. Alvarez, J. Snchez, R. Deriche, and J. Weickert. Dense disparity map estimation respecting image discontinuities: A pde and scale-space based approach. IAPR Workshop on Machine Vision, No. 28-30:423--427, 2000.

No context found.

L. Alvarez, R. Deriche, J. Sanchez, and J. Weickert, "Dense disparity map estimation respecting image discontinuities: APDE and scale-space based approach," J. Vis. Commun. Image, vol. 13, no. 1--2, pp. 3--21, 2002.

No context found.

L. Alvarez, R. Deriche, J. Sanchez, and J. Weickert. Dense disparity map estimation respecting image discontinuities: A pde and scale-space based approach. Technical Report 3874, INRIA, 2000.

No context found.

L. Alvarez, R. Deriche, J. Sanchez and J. Weickert, "Dense disparity map estimation respecting image discontinuities: A PDE and scale-space based approach", J. Vision Commun. Image, vol.13(1-2), pp.3-21, 2002.

No context found.

L. Alvarez, R. Deriche, J. Sanchez and J. Weickert, "Dense Disparity Map Estimation Respecting Image Discontinuities: a PDE and Scale-Space Based Approach ", Technical Report RR-3874, INRIA, 2000.

No context found.

L. Alvarez, R.Deriche, J.Weickert, and X. Sanchez. Dense disparity map estimation respecting image discontinuities: A pde and scale-space based approach . Research Report 3874, INRIA, January 2000.

No context found.

L. Alvarez, R. Deriche, J. Sanchez, and J. Weickert. Dense disparity map estimation respecting image derivatives: a pde and scale-space based approach. Journal of Visual Communication and Image Representation, 13(1/2):3--21, 2002.

No context found.

L. Alvarez, R.Deriche, J.Weickert, and X. Sanchez. Dense disparity map estimation respecting image discontinuities: A pde and scale-space based approach . Research Report 3874, INRIA, January 2000.

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