S. Li, "Invariant surface segmentation through energy minimization with discontinuities", submitted to Intl. J. of Computer Vision, 1989.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....manner. Furthermore, MRF theory provides a foundation for multi resolution computation [49] For the above reasons, MRFs have been widely employed to solve image analysis problems at all levels. Most of the MRF models are for lowlevel processing. These include image restoration and segmentation [61,56,23,36,46,21,27,85,89,92], surface reconstruction [8,53,98,17,99,24,43] edge detection [103,131,44] texture analysis [23,30,40,34,35] optical ow [64,63,78,118,60] shape from X [9,68] active contours [74,3,123] deformable templates [97,95,70] data fusion [26] visual integration, and perceptual organization [2,125] ....

....(LS) tting. Nowadays, optimization is pervasive in all aspects of image analysis, including image restoration and reconstruction [53,127,46,82,67,93] shape from shading [68] stereo, motion and optical ow [132,64,63,105,7] texture [61,73,30] edge detection [131,126] image segmentation [119,85], perceptual grouping [94,101,62] interpretation of line drawings [83] object matching and recognition [41,32,117,16,10,100,106,134,42,86,87] and pose estimation [58] In all of the above cited examples, the solution is explicitly de ned as an optimum of an objective function by which the ....

S. Z. Li. \Invariant surface segmentation through energy minimization with discontinuities". International Journal of Computer Vision, 5(2):161-194, 1990.

....the use of minimum energy or minimum entropy criteria. An example of such a computation is provided by a Hopfield net [Hopfield 82] The idea is to minimize some sort of energy function that expresses quantitatively by how much each available measurement and each imposed constraint are violated [Li 89] This idea is related to regularization techniques for surface reconstruction employed by Terzopoulos [Terzopoulos 86] The implementation of regularization algorithms using massively parallel neural nets has been discussed by Marroquin, Koch et al. Koch et al. 85] Poggio and Koch [Koch Poggio ....

S. Li, "Invariant surface segmentation through energy minimization with discontinuities", submitted to Intl. J. of Computer Vision, 1989.

....Newman et al. 1993 concentrate on the model based surface classification. In the context of building extraction, integrated approaches for segmentation and classification seem to be of more interest, as roofs mainly consist of tilted planes, thus reducing the problem almost to mere segmentation (Li 1990). Up to now, the user has to define which models should be applied for the entire data set, either parametric or prismatic models. In areas where simple and complex models are included, this is not acceptable, because of two facts. March 27, 1996 Building Extraction from Digital Elevation Models ....

Li, S. Z. (1990): Invariant Surface Segmentation Through Energy Minimization with Discontinuities. IJCV, 5(2):161--194, 1990.

....descent, a random weight is applied between the two terms in every updating for every i and n. It is more ecient than random sampling methods such as Metropolis algorithm [13] and Gibbs sampler [1] because the acceptance probability of any update is always one. A randomized neighborhood system [14] also works well in avoiding local minima. III. Experimental Results Range images are used because in such data there are geometrically well de ned roof and step edges. The 8 adjacency is used for de ning the MRF neighborhood system. The surfaces are assumed to be of the form z(x i ; y i ) a i ....

S. Z. Li, \Invariant surface segmentation through energy minimization with discontinuities", International Journal of Computer Vision, vol. 5, no. 2, pp. 161-194, 1990.

....manner. Furthermore, MRF theory provides a foundation for multi resolution computation [49] For the above reasons, MRFs have been widely employed to solve image analysis problems at all levels. Most of the MRF models are for low level processing. These include image restoration and segmentation [61,56,23,36,46,21,27,85,89,92], surface reconstruction [8,53,98,17,99,24,43] edge detection [103,131,44] texture analysis [23,30,40,34,35] optical ow [64,63,78,118,60] shape from X [9,68] active contours [74,3,123] deformable templates [97,95,70] data fusion [26] visual integration, and perceptual organization [2,125] ....

....(LS) tting. Nowadays, optimization is pervasive in all aspects of image analysis, including image restoration and reconstruction [53,127,46,82,67,93] shape from shading [68] stereo, motion and optical ow [132,64,63,105,7] texture [61,73,30] edge detection [131,126] image segmentation [119,85], perceptual grouping [94,101,62] interpretation of line drawings [83] object matching and recognition [41,32,117,16,10,100,106,134,42,86,87] and pose estimation [58] In all of the above cited examples, the solution is explicitly de ned as an optimum of an objective function by which the ....

S. Z. Li. \Invariant surface segmentation through energy minimization with discontinuities". International Journal of Computer Vision, 5(2):161-194, 1990.

....of the sign of mean curvature and the sign of Gaussian curvature of surface points yields eight possible surface types [6] The signs of the surface curvatures are, therefore, symbolic invariants. In practice, however, a curvature sign is always with respect to a scale relative threshold [7]. So it is safer not to use it as a scale invariant unless a scale adaptive threshold can be computed. The Euclidean distance between two points is an invariant binary relation under TE . Let p 1 and p 2 are transformed from P 1 and P 2 , respectively. The distance (p 1 Gamma p 2 ) T (p 1 ....

S. Z. Li. "Invariant surface segmentation through energy minimization with discontinuities". International Journal of Computer Vision, 5(2):161--194, 1990.

....level. At the bottom are the refined maps by the intermediate level. Significant improvement on the coherence of the segmentation can be seen in the transition from the coarse maps to the refined maps. For more segmentation results from images of various complexity, readers are referred to [62]. The refined HK map identifies up to eight different surface types which are independent of rotations, translations and scale changes. From this, an attributed adjacency graph (ARG) can be built to give an invariant description of the scene in the image. Model objects are also represented in the ....

....can be compensated by the intermediate level (see the next subsection) which significantly improves the coherence of the segmentation. False or missing detection of some of the discontinuities will not cause the failure of the whole process. Therefore we have used a simple scheme in determining ff [62]. However, better detection of discontinuities is always desired. Some algorithms by other researchers may lead to improvements of the quality of the derivative estimation, such as BlakeZisserman s GNC algorithm [13] and an algorithm of generalized smoothing networks by Harris CVGIP: Image ....

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S. Z. Li. "Invariant surface segmentation through energy minimization with discontinuities". International Journal of Computer Vision, 5(2):161--194, 1990.

....definition of the sign of a quantity in theory. Clearly, this definition can not be used in noisy situations, sometimes even not in noise free situations. What people do in practice is to classify surfaces as (1) very positively curved, 2) very negatively curved or (3) flat and slightly curved [15, 16, 17]. The signs Image and Vision Computing, 10(8) 566 576, October 1992 5 are practically defined with respect to a small positive number, i.e. a threshold. Nonetheless, the difference between highly curved surfaces and slightly curved surfaces still remains fuzzy because that the threshold ....

S. Z. Li. "Invariant surface segmentation through energy minimization with discontinuities". International Journal of Computer Vision, 5(2):161--194, 1990.

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S. Li, "Invariant surface segmentation through energy minimization with discontinuities", submitted to Intl. J. of Computer Vision, 1989.

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S. Li, "Invariant surface segmentation through energy minimization with discontinuities", submitted to Intl. J. of Computer Vision, 1989.

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