R. Szeliski and H.Y. Shum. Motion estimation with quadtree splines. Technical report, DEC Cambridge Research Lab, March 1995.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....we make explicit use of rational B splines to represent 3D surfaces and their projections. Spline curve representations have been used extensively in computer vision in the context of contour tracking and contour pose recovery (e.g. 2, 1] Splines have also been used in motion estimation [14] and image registration [13] By directly modeling surfaces in the scene as splines, this work has the advantage over other methods in that points need not be visible in all views. More specifically, given features points in correspondence, but not necessarily visible in all views, we determine ....

R. Szeliski and H. Shum. Motion estimation with quadtree splines. PAMI, 18(12):1199--1210, 1996.

....we make explicit use of rational B splines to represent 3D surfaces and their projections. Spline curve representations have been used extensively in computer vision in the context of contour tracking and contour pose recovery (e.g. 2, 1] Splines have also been used in motion estimation [14] and image registration [13] By directly modeling surfaces in the scene as splines, this work has the advantage over other methods in that points need not be visible in all views. More specifically, given features points in correspondence, but not necessarily visible in all views, we determine ....

R. Szeliski and H. Shum. Motion estimation with quadtree splines. PAMI, 18(12):1199--1210, 1996.

....of motion estimation [35] and are instrumental for the approach described in Chapters 4 and 5 of this thesis. B spline models were independently used in [36] 2.2.4 Image dependent models It is sometimes useful to adapt the warping model to the images considered. Quadtreebased deformation model [37] is refined only where it is needed. In feature based methods, the basis functions of the warping model can be placed where the features are. The deformation field is interpolated in regions where no information is available. Typical example are radial basis functions such as thin plate splines ....

Richard Szeliski and Heung-Yeung Shum, "Motion estimation with quadtree splines," IEEE Trans. Pattern Anal. Mach. Intell., vol. 18, no. 12, pp. 1199--1207, Dec. 1996.

....of 1 smooth surfaces by using rational B splines to represent 3D surfaces and their projections. Spline curve representations have been used extensively in computer vision in the context of contour tracking and contour pose recovery (e.g. 7, 5] Splines have also been used in motion estimation [24] and image registration [23] Our work is related to [23] where a depth field is computed from spline based image registration. In that approach, the spline was used to find disparity maps from which dense depth maps were then computed. In this work, we instead focus on directly modeling surfaces ....

R. Szeliski and H.Y. Shum. Motion estimation with quadtree splines. PAMI, 18(12):1199--1210, 1996.

....T 2 in the triangulation. This requirement restricts the type of n simplex and the subdivision scheme that can be used for an automatic non uniform cell subdivision. Indeed, di erent mesh re nement techniques were proposed in computer vision but most of them do not ful ll this requirement [32, 31]. Hierarchical triangular decomposition methods are di erentiated on the basis of whether the decomposition is into three (ternary) or four (qua ternary) parts (see Figure 1) Ternary decompositions are formed by taking an internal point of one of the triangles T and joining it to the vertices ....

....triangulation requirement. Using such a mesh for tting a model to given data restricts the authors to use an additional colinearity constraint to avoid the destruction of the triangular tessellation structure. A similar approach is based on the use of Quadtree (adaptive resolution) splines [31] i.e. splines de ned over quadtree domains. Again, this method cannot be used in a FEM scheme since the triangulation is based on a quaternary decomposition and does not ful ll the previous conform triangulation requirement since cracks or rst order discontinuities in the interpolated function ....

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R. Szeliski and H.Y. Shum. Motion estimation with quadtree splines. Technical report, DEC Cambridge Research Lab, March 1995.

....characterize image motion due to the aperture problem, it allows to locate moving points. Indeed, w is high near moving points and becomes null near stationary points. The definition of w gives the theoretical proof of the motion measure D defined by Irani et al. [11] and used by several authors [12, 17] : D(x; y; t) P (x i ;y i )2W jI(x i ; y i ; t 1) Gamma I(x i ; y i ; t)j jrI(x i ; y i ; t)j P (x i ;y i )2W jrI(x i ; y i ; t)j 2 C (7) where W is a small neighborhood and C a constant to avoid numerical instabilities. This motion measure, defined as residual motion, is a ....

R. Szeliski and H.Y. Shum. Motion estimation with quadtree splines. Technical report, DEC Cambridge Research Lab, March 1995.

....project to points that can be matched across views. Unfortunately, this assumption cannot be used as a basis for designing approximate shape recovery algorithms because it breaks down in that case. Hence, even though recent particle and mesh based stereo techniques allow level of detail control [9, 11, 19, 20], their reliance on regularization criteria that enforce this assumption makes it impossible to analyze their behavior during approximate reconstruction (e.g. existence of local minima, convergence properties, shape determinism) Fourth, existing attempts to recover approximate shapes from ....

R. Szeliski and H.-Y. Shum, "Motion estimation with quadtree splines," IEEE Trans. Pattern Anal. Machine Intell., vol. 18, no. 12, pp. 1199--1210, 1996.

....the prior distribution and makes the estimation well posed regardless of the dimensionality of the parameter vector ff. In general, the solution obtained by solving equation 10 will be different from one obtained by simply assuming the flow field is parameterized by a spline basis set (e.g. [17]) Finally, note that the reduced rank of the system is obtained by using only a subset of the basis fields, not by using a subset of the gradient constraints. The solution of the system gives the flow field spanned by the reduced basis set that best satisfies the gradient constraints at all ....

R. Szeliski and H.-Y. Shum. Motion estimation with quadtree splines. In Proc. Int'l Conf. Comput. Vision, pages 757--762, 1995.

....Phase Portrait Models: Environmental Applications13 fitting a model to given data restricts the authors to use an additional colinearity constraint to avoid the destruction of the triangular tessellation structure. A similar approach is based on the use of Quadtree (adaptive resolution) splines [26] i.e. splines defined over quadtree domains. Again, this method cannot be used in a FEM scheme since the triangulation is based on a quaternary decomposition and does not fulfill the previous conform triangulation requirement and furthermore cracks or first order discontinuities in the ....

....equation (19) cannot characterize image motion) it allows to locate moving points. Indeed, w is high near moving points and becomes null near stationary points. The definition of w gives the theoretical proof of the motion measure D, defined by Irani et al. [13] and used by several authors [26, 17] : D(x; y; t) X (x i ;y i )2W jI(x i ; y i ; t 1) Gamma I(x i ; y i ; t)j jrI(x i ; y i ; t)j X (x i ;y i )2W jrI(x i ; y i ; t)j 2 C (20) where W is a small neighborhood and C a constant used to avoid numerical instabilities. This motion measure, defined as residual motion, is a ....

[Article contains additional citation context not shown here]

R. Szeliski and H.Y. Shum. Motion estimation with quadtree splines. Technical report, DEC Cambridge Research Lab, March 1995.

....1 for the variation of the flow within it. Finding these boundaries is a hard optimization problem; Schnorr [14] assumes some prior knowledge of the location of these and deforms the boundaries to minimize an error functional, but this is not suitable for general purpose optical flow. Szeliski [15] uses a quad tree technique to decompose the image into square domains. In each domain an a#ne model is applied and if the residual error is high this domain is subdivided into four until the model fits the data within a su#cient degree of accuracy. 3 Optimal Optical Flow Estimation in a narrow ....

Richard Szeliski and Shum. Heung-Yeung. Motion estimation with quadtree splines. In Proc. Int. Conf. on Computer Vision, pages 757--763, 1995. 14

....methods suffer from such problems [4] 5] This paper proposes a motion estimation algorithm robust to motion discontinuity and noise. Because of ill posedness, it is difficult to find a solution in all cases [6] Generally, such a problem has been solved by using additional constraints [7] [8], 9] 10] To obtain a solution having a physical meaning, conventional approaches based on regularization or maximum a posteriori MAP scheme [11] were presented. Although these two approaches were derived from different points of view, they used a similar framework for data fusion. ....

# E. Szeliski and H.Y. Shum, "Motion Estimation With Quadtree Splines," Proc. Fifth Int'l Conf. Computer Vision, pp. 757-763, Boston, June 1995.

.... displacement vector for each pixel in the image can be determined using various approaches: correlation [2] gradient [35, 42] spatio temporal filtering [26] or regularization [35, 54] For large image motion, multiresolution approaches are used to prevent local minima in the matching process [7, 62, 68]. Adaptive window sizes [51] and quadtree splines [62] are used to treat different parts of the image with varying resolution. Affine flow or quadratic flow assumptions can be used to represent optical flow parametrically [7] Recovering the camera relationships for 2 frames can be solved using ....

.... using various approaches: correlation [2] gradient [35, 42] spatio temporal filtering [26] or regularization [35, 54] For large image motion, multiresolution approaches are used to prevent local minima in the matching process [7, 62, 68] Adaptive window sizes [51] and quadtree splines [62] are used to treat different parts of the image with varying resolution. Affine flow or quadratic flow assumptions can be used to represent optical flow parametrically [7] Recovering the camera relationships for 2 frames can be solved using methods such as the eight point algorithm [41] An ....

R. Szeliski and H. Y. Shum. Motion estimation with quadtree splines. IEEE Transactions on Pattern Analysis and Machine Intelligence, 18(12):1199--1210, December 1996.

....the prior distribution and makes the estimation well posed regardless of the dimensionality of the parameter vector ff. In general, the solution obtained by solving equation 4. 10 will be different from one obtained by simply assuming the flow field is parameterized by a spline basis set (e.g. (Szeliski and Shum, 1995)) Finally, note that the reduced rank of the system is obtained by using only a subset of the basis fields, not by using a subset of the gradient constraints. The solution of the system gives the flow field spanned by the reduced basis set that best satisfies the gradient constraints at all ....

Szeliski, R. and Shum, H.-Y. (1995). Motion estimation with quadtree splines. In Proc. Int'l Conf. Comput. Vision, pages 757--762.

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R. Szeliski and H.Y. Shum. Motion estimation with quadtree splines. Technical report, DEC Cambridge Research Lab, March 1995.

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R. Szeliski and H.Y. Shum. Motion estimation with quadtree splines. Technical report, DEC Cambridge Research Lab, March 1995.

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R. Szeliski and H.Y. Shum. Motion estimation with quadtree splines. PAMI, 18(12):1199--1210, 1996.

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R. Szeliski and H. Shum. Motion estimation with quadtree splines. IEEE Transactions on Pattern Analysis and Machine Intelligence, 18(12):1199--1211, 1996.

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Richard Szeliski and Heung-Yeung Shum. Motion estimation with quadtree splines. IEEE Transactions on Pattern Analysis and Machine Intelligence, 18(12):1199--1210, 1996.

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R. Szeliski and H.-Y. Shum. Motion estimation with quadtree splines. IEEE Transactions on Pattern Analysis and Machine Intelligence, 18(12):1199--1210, December 1996. 186

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R. Szeliski and H.-Y. Shum. Motion estimation with quadtree splines. In Fifth International Conference on Computer Vision (ICCV'95), pages 757--763, Cambridge, Massachusetts, June 1995.

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R. Szeliski and H.Y. Shum. Motion estimation with quadtree splines. In Proceedings of the 5th International Conference on Computer Vision, Cambridge, Massachusetts, USA, pages 757-763. ieee Computer Society Press, June 1995.

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Richard Szeliski and Heung-Yeung Shum. Motion estimation with quadtree splines. Technical report, DEC Cambridge Research Lab, 1995.

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R. Szeliski and H.-Y. Shum. Motion estimation with quadtree splines. IEEE Transactions on Pattern Analysis and Machine Intelligence, vol.18, no.12 pages 1199-210, 1997

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Szeliski, R., Shum, H.Y.: Motion estimation with quadtree splines. IEEE Transactions on Pattern Analysis and Machine Intelligence 18 (1996) 1199--1210

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R. Szeliski, H.-Y. Shum, "Motion estimation with quadtree splines", IEEE Trans. on PAMI, vol. 18, no. 12, pp. 11991.

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