iccv iccv2013 iccv2013-389 knowledge-graph by maker-knowledge-mining
Source: pdf
Author: Petter Strandmark, Johannes Ulén, Fredrik Kahl, Leo Grady
Abstract: This paper describes a method of finding thin, elongated structures in images and volumes. We use shortest paths to minimize very general functionals of higher-order curve properties, such as curvature and torsion. Our globally optimal method uses line graphs and its runtime is polynomial in the size of the discretization, often in the order of seconds on a single computer. To our knowledge, we are the first to perform experiments in three dimensions with curvature and torsion regularization. The largest graphs we process have almost one hundred billion arcs. Experiments on medical images and in multi-view reconstruction show the significance and practical usefulness of regularization based on curvature while torsion is still only tractable for small-scale problems.
Reference: text
sentIndex sentText sentNum sentScore
1 We use shortest paths to minimize very general functionals of higher-order curve properties, such as curvature and torsion. [sent-6, score-0.866]
2 To our knowledge, we are the first to perform experiments in three dimensions with curvature and torsion regularization. [sent-8, score-1.181]
3 Experiments on medical images and in multi-view reconstruction show the significance and practical usefulness of regularization based on curvature while torsion is still only tractable for small-scale problems. [sent-10, score-1.428]
4 Introduction In differential geometry, the fundamental theorem of curves states that any regular curve in three dimensions with non-zero curvature has its shape completely determined by its curvature and torsion [12]. [sent-12, score-1.895]
5 Therefore, for curve recon- struction problems, it makes sense to regularize the solution with curvature and torsion priors. [sent-13, score-1.251]
6 In this paper, we demonstrate that with today’s modern CPUs and clever implementation choices, it is actually possible to solve inverse problems involving both curvature and torsion priors at reasonable running times. [sent-16, score-1.225]
7 In [10], it is shown that Euler’s elastica – the line integral of the squared curvature conforms better to intuitive completion of boundary curves. [sent-18, score-0.703]
8 Other applications where curvature plays an important role include saliency [17], inpainting [9], stereo [21], region-based image segmentation [15] and surface reconstruction [19]. [sent-19, score-0.682]
9 In many applications, the reconstructed – long with high curvature, but have low torsion as they lie approximately in a plane. [sent-21, score-0.587]
10 The coronary arteries are neither short nor have low curvature, but they do have low torsion. [sent-26, score-0.176]
11 We follow a classic approach for computing the global minimum of an active contour model based on shortest paths [2, 3]. [sent-29, score-0.194]
12 Most of × these methods use only weighted length regularization, even though the idea of applying shortest paths to higher-order functionals involving curvature is not new. [sent-31, score-0.921]
13 An extension of the live-wire framework with curvature priors is presented in [20]. [sent-36, score-0.594]
14 Many nice examples of the benefits with curvature are given in both [11] and [20], but no running times are reported. [sent-39, score-0.656]
15 Our contribution is a global method to find a curve of minimal curvature between two points using line graphs. [sent-44, score-0.72]
16 We are the first to demonstrate practical curvature experiments in 3D and our two-dimensional running times are in the order of seconds. [sent-45, score-0.637]
17 Shortest Paths with Curvature and Torsion We are interested in finding a curve γ in two or three dimensions which minimizes an image-dependent functional of its length, curvature and torsion, or more generally: iγn,Lf? [sent-55, score-0.664]
18 (2) Here κ(s) and τ(s) denote the curvature and the torsion, respectively; see Section 2. [sent-68, score-0.594]
19 The scalars ρ, σ and ν are weighting factors of length, curvature and torsion, respectively and can be made image-dependent as well. [sent-70, score-0.594]
20 Figure 2: The same path through a mesh (shown in black) repre- sented in three different ways. [sent-74, score-0.213]
21 The shortest path computation is carried out in a graph, consisting of nodes and arcs. [sent-78, score-0.238]
22 The mesh is stored explicitly in memory and is the same no matter which regularization is used. [sent-81, score-0.267]
23 The simplest case is length regularization (σ = ν = 0), for which the graph is identical to the mesh. [sent-84, score-0.284]
24 It follows that we need to consider at least three points to determine the curvature cost. [sent-89, score-0.631]
25 To achieve this, a line graph is constructed in which each node corresponds to an edge in the mesh. [sent-90, score-0.171]
26 In this manner we can compute the curvature cost of any path through the original mesh. [sent-92, score-0.699]
27 Because three points always lie in the same plane, at least four points are needed to determine the torsion cost. [sent-95, score-0.661]
28 Figure 2c shows the same path as before, with each node in the graph corresponding to an edge pair in the mesh. [sent-97, score-0.253]
29 The graph grows very rapidly in size, but we never construct it explicitly; only the mesh is explicitly created and stored. [sent-98, score-0.176]
30 squared curvature as well as the length element ds = ? [sent-114, score-0.749]
31 Figure 3 graphs an example curve (a helix), for which the exact curvature and torsion are well known: they are both = det ? [sent-131, score-1.278]
32 Figure 4 shows the error when approximating the curvature and torsion using three and four points, respectively. [sent-142, score-1.181]
33 Figure 4: Error when computing the curvature and torsion using the middle point of a spline fit to two or three edges on the curve in Figure 3. [sent-144, score-1.319]
34 Our Implementation Dijkstra’s algorithm for computing the shortest path is well known. [sent-147, score-0.197]
35 (ii) An oracle that given a node returns its neighbors and arc weights. [sent-150, score-0.167]
36 Each edge and edge pair in the mesh then require 8 and 12 bytes, respectively. [sent-172, score-0.302]
37 The array of edges is sorted after the mesh is created, which makes it possible to find the index of a given edge in logarithmic time. [sent-173, score-0.299]
38 Then it looks up the edge index for each pair of points in the sorted edge array. [sent-176, score-0.207]
39 Instead, the neighbors of an edge pair are computed via the edge neighbors of its last edge as above. [sent-180, score-0.335]
40 For example, the curvature cost between two edges is the same even if both edges are translated by the same amount. [sent-182, score-0.706]
41 Thus, the integrated curvature needs only • – be computed once for each configuration. [sent-183, score-0.612]
42 The cache has to be fast, since when working with torsion there are millions of different configurations of two edge pairs. [sent-184, score-0.722]
43 Computing the shortest path between two nodes efficiently in parallel is not a trivial task. [sent-189, score-0.238]
44 The curvature or torsion cache is filled before the computation starts. [sent-193, score-1.241]
45 First, we would like to demonstrate the differences between length, curvature, and torsion with a couple of synthetic experiments. [sent-197, score-0.587]
46 54 s) Table 1: Number of nodes visited using Dijkstra’s (first row) and A* (second row) for the curvature experiments in Figure 6. [sent-214, score-0.658]
47 Naturally, the heuristic works best for low curvature regularization. [sent-215, score-0.614]
48 All of our 2D (3D) experiments are performed with a mesh whose points are arranged in a square (cubic) lattice. [sent-223, score-0.169]
49 We manually sampled the river image in Figure 6 at different locations and calculated the data cost for every pixel as the shortest (Euclidean) distance in L*a*b* space to any of the color samples of the river delta. [sent-230, score-0.226]
50 Curvature regularization yields a long path which does not turn much. [sent-233, score-0.216]
51 No amount of length regularization is able to find that path as indicated by Figure 6a. [sent-234, score-0.341]
52 Figure 7 shows an experiment where some edges have been removed around the start and end sets in such a way that the optimal analytical solution is a circle of maximum radius. [sent-236, score-0.172]
53 This experiment shows that low regularization radii introduce significant bias when minimizing the squared curvature. [sent-237, score-0.19]
54 The underlying mesh has 220,443 points (373 591) and 3,509,756 edges (16-connected). [sent-246, score-0.236]
55 Figures (c) and (d) show the order in which the nodes were visited for medium curvature with and without A*, from blue (early) to red (late). [sent-249, score-0.677]
56 ference between a curve with curvature regularization and torsion regularization is given. [sent-251, score-1.521]
57 High torsion regularization forces the curve to stay within a plane, but within the plane, the curve may have high length and curvature. [sent-252, score-0.967]
58 The graph used for the torsion regularization had about 75 billion arcs. [sent-253, score-0.791]
59 2D Retinal Images Automated segmentation of vessels in retinal images is an important problem in medical image analysis, which, for example, can be used when screening for diabetic retinopathy. [sent-257, score-0.256]
60 We have investigated whether curvature regularization is useful for this task on a publicly available dataset [18]. [sent-258, score-0.729]
61 We iteratively computed shortest paths from a user-provided start point to any point on the image boundary. [sent-260, score-0.221]
62 A curve could start anywhere along the previously found curves, but not end close to a previous end point. [sent-261, score-0.2]
63 We performed experiments with different amounts of length regularization (Figures 8b–8e). [sent-262, score-0.24]
64 No or low length regularization resulted in noisy, wiggling paths. [sent-263, score-0.24]
65 This problem expectedly disappeared for medium regularization, but sharp turns were still present in the solution (sharp turns usually change direction in the vessel tree). [sent-264, score-0.302]
66 When using too high regularization (Figure 8e), the solution almost ignores the data term and prefers paths along the image boundary. [sent-265, score-0.194]
67 Art laln pdo ienntds points have been chosen in such a way that the analytical solution when minimizing the integrated squared curvature is a circle with cost π/10. [sent-270, score-0.753]
68 In contrast, curvature regularization is able to more cor- rectly capture the vessel tree. [sent-271, score-0.938]
69 3D Coronary Artery Centerline Extraction Finding the centerlines of coronary arteries is of high clinical importance [14], but is very time consuming when performed manually. [sent-275, score-0.176]
70 Each segmentation is initialized by manually specifying the start and end of each vessel information which is included in the dataset. [sent-278, score-0.329]
71 To model the vessel we adopt the speed image S from [5], which combines the probability of a voxel being a vessel, measured by “vesselness” [13] and a soft threshold of the image. [sent-280, score-0.231]
72 Figure 8: Segmenting a vessel tree with 8 leaves in a 2D retinal image from the DRIVE [18] database. [sent-300, score-0.271]
73 The underlying mesh has 329,960 points (584 565) and 10,496,766 edges (32-connected). [sent-302, score-0.236]
74 oAnlnl length regularizations (b-d) have various issues and curvature regularization (e) finds a reasonable tree. [sent-305, score-0.864]
75 ble 2 presents quantitative result on the training data of [14] and compares length to curvature regularization. [sent-306, score-0.699]
76 A example where curvature regularization outperforms length is given in Figure 9. [sent-307, score-0.834]
77 We reconstructed a tree iteratively in the same way as in Figure 8 and, as expected, length regularization introduces similar artifacts. [sent-313, score-0.259]
78 Integrating the image along the projected 3D edge gives the edge cost for a single view. [sent-314, score-0.174]
79 2 · (3 · 10−4) 10 Table 2: Length and curvature regularization for coronary vessel segmentation. [sent-319, score-1.075]
80 We segmented each vessel in the training set of [14] with length and curvature regularization. [sent-320, score-0.927]
81 For both length and curvature we choose the strength giving the best result and applied it to all vessels. [sent-322, score-0.699]
82 The second column reports the number of vessels for which length and curvature performed best, respectively, not counting any vessel with less than 50% overlap (6 out of 28 vessels) or ties (5 vessels). [sent-323, score-1.014]
83 Figure 9: Example of coronary artery segmentation in 3D using length (left) and curvature (right). [sent-331, score-0.938]
84 The mesh has 841,662 points (114 107 69) and s60ol,u2t7io1,n57 (848 edges. [sent-339, score-0.169]
85 We run the segmentation with either very high curvature (yellow) or very high torsion regularization (red). [sent-349, score-1.359]
86 The underlying mesh has 32,560 points (22 74 20), 4,118,200 edges (146connected) a2n,5d6 053 p8o,i7n1t7s,7 (2922 edge pairs. [sent-350, score-0.311]
87 6 s for torsion (harder problems will take longer time to solve). [sent-353, score-0.587]
88 Using length regularization gives similar artifacts (sharp turns) as in Figure 8. [sent-355, score-0.24]
89 The underlying mesh has 125,000 points and 24,899,888 edges (218-connectivity). [sent-356, score-0.236]
90 Conclusions This paper has demonstrated the possibility of incorporating curvature and torsion to shortest path problems. [sent-362, score-1.378]
91 Although all of our methods find the global optimum in polynomial time, using torsion can not be considered feasible, as we have only used it for quite small problems. [sent-365, score-0.587]
92 On the other hand, using curvature is not that expensive for many problems and we believe we have demonstrated its usefulness for medical imaging problems, both in 2D (Figure 8) and in 3D (Figure 9). [sent-366, score-0.684]
93 The “vesselness” measures [4, 13] commonly used for blood vessel segmentation use the eigenvalues of the Hessian. [sent-372, score-0.284]
94 An interesting avenue for future research is to include the eigenvectors with anisotropic curvature, resulting in a direction-aware curvature regularization. [sent-373, score-0.594]
95 A review of 3d vessel lumen segmentation techniques: models, features and extraction schemes. [sent-430, score-0.275]
96 Three-dimensional multi-scale line filter for segmentation and visualization of curvilinear structures in medical images. [sent-456, score-0.172]
97 Standardized evaluation methodology and reference database for evaluating coronary artery centerline extraction algorithms. [sent-460, score-0.267]
98 A linear framework for region-based image segmentation and inpainting involving curvature penalization. [sent-467, score-0.68]
99 The elastic ratio: Introducing curvature into ratio-based globally optimal image segmentation. [sent-474, score-0.636]
100 Ridge based vessel segmentation in color images of the retina. [sent-490, score-0.252]
wordName wordTfidf (topN-words)
[('curvature', 0.594), ('torsion', 0.587), ('vessel', 0.209), ('coronary', 0.137), ('regularization', 0.135), ('mesh', 0.132), ('shortest', 0.116), ('length', 0.105), ('dijkstra', 0.097), ('medical', 0.09), ('path', 0.081), ('vessels', 0.08), ('edge', 0.075), ('curve', 0.07), ('cache', 0.06), ('paths', 0.059), ('artery', 0.059), ('arc', 0.055), ('centerline', 0.048), ('array', 0.048), ('start', 0.046), ('neighbors', 0.045), ('edges', 0.044), ('graph', 0.044), ('retinal', 0.043), ('std', 0.043), ('river', 0.043), ('segmentation', 0.043), ('nodes', 0.041), ('arteries', 0.039), ('elastica', 0.039), ('estart', 0.039), ('vesselness', 0.039), ('points', 0.037), ('cubic', 0.037), ('masnou', 0.035), ('schoenemann', 0.035), ('oracle', 0.034), ('node', 0.033), ('blood', 0.032), ('sweden', 0.032), ('curves', 0.032), ('end', 0.031), ('circle', 0.031), ('regularizations', 0.03), ('swedish', 0.029), ('squared', 0.029), ('storing', 0.029), ('sharp', 0.028), ('discretization', 0.028), ('graphs', 0.027), ('functionals', 0.027), ('wins', 0.027), ('dots', 0.026), ('kahl', 0.026), ('radii', 0.026), ('overlap', 0.026), ('strengths', 0.026), ('parallelization', 0.025), ('miccai', 0.025), ('billion', 0.025), ('cost', 0.024), ('running', 0.024), ('spline', 0.024), ('turns', 0.023), ('inpainting', 0.023), ('usa', 0.023), ('figures', 0.023), ('underlying', 0.023), ('visited', 0.023), ('extraction', 0.023), ('previously', 0.022), ('reconstruction', 0.022), ('voxel', 0.022), ('globally', 0.022), ('integral', 0.022), ('analytically', 0.021), ('ds', 0.021), ('penalizing', 0.02), ('indicated', 0.02), ('heuristic', 0.02), ('involving', 0.02), ('pair', 0.02), ('structures', 0.02), ('orange', 0.02), ('elastic', 0.02), ('analytical', 0.02), ('segmented', 0.019), ('line', 0.019), ('nice', 0.019), ('medium', 0.019), ('contour', 0.019), ('cos', 0.019), ('times', 0.019), ('tree', 0.019), ('connectivity', 0.019), ('integrated', 0.018), ('differential', 0.018), ('keriven', 0.017), ('tast', 0.017)]
simIndex simValue paperId paperTitle
same-paper 1 0.99999893 389 iccv-2013-Shortest Paths with Curvature and Torsion
Author: Petter Strandmark, Johannes Ulén, Fredrik Kahl, Leo Grady
Abstract: This paper describes a method of finding thin, elongated structures in images and volumes. We use shortest paths to minimize very general functionals of higher-order curve properties, such as curvature and torsion. Our globally optimal method uses line graphs and its runtime is polynomial in the size of the discretization, often in the order of seconds on a single computer. To our knowledge, we are the first to perform experiments in three dimensions with curvature and torsion regularization. The largest graphs we process have almost one hundred billion arcs. Experiments on medical images and in multi-view reconstruction show the significance and practical usefulness of regularization based on curvature while torsion is still only tractable for small-scale problems.
2 0.4370375 309 iccv-2013-Partial Enumeration and Curvature Regularization
Author: Carl Olsson, Johannes Ulén, Yuri Boykov, Vladimir Kolmogorov
Abstract: Energies with high-order non-submodular interactions have been shown to be very useful in vision due to their high modeling power. Optimization of such energies, however, is generally NP-hard. A naive approach that works for small problem instances is exhaustive search, that is, enumeration of all possible labelings of the underlying graph. We propose a general minimization approach for large graphs based on enumeration of labelings of certain small patches. This partial enumeration technique reduces complex highorder energy formulations to pairwise Constraint Satisfaction Problems with unary costs (uCSP), which can be efficiently solved using standard methods like TRW-S. Our approach outperforms a number of existing state-of-the-art algorithms on well known difficult problems (e.g. curvature regularization, stereo, deconvolution); it gives near global minimum and better speed. Our main application of interest is curvature regularization. In the context of segmentation, our partial enumeration technique allows to evaluate curvature directly on small patches using a novel integral geometry approach. 1
3 0.37967208 296 iccv-2013-On the Mean Curvature Flow on Graphs with Applications in Image and Manifold Processing
Author: Abdallah El_Chakik, Abderrahim Elmoataz, Ahcene Sadi
Abstract: In this paper, we propose an adaptation and transcription of the mean curvature level set equation on a general discrete domain (weighted graphs with arbitrary topology). We introduce the perimeters on graph using difference operators and define the curvature as the first variation of these perimeters. Our proposed approach of mean curvature unifies both local and non local notions of mean curvature on Euclidean domains. Furthermore, it allows the extension to the processing of manifolds and data which can be represented by graphs.
4 0.20093402 429 iccv-2013-Tree Shape Priors with Connectivity Constraints Using Convex Relaxation on General Graphs
Author: Jan Stühmer, Peter Schröder, Daniel Cremers
Abstract: We propose a novel method to include a connectivity prior into image segmentation that is based on a binary labeling of a directed graph, in this case a geodesic shortest path tree. Specifically we make two contributions: First, we construct a geodesic shortest path tree with a distance measure that is related to the image data and the bending energy of each path in the tree. Second, we include a connectivity prior in our segmentation model, that allows to segment not only a single elongated structure, but instead a whole connected branching tree. Because both our segmentation model and the connectivity constraint are convex, a global optimal solution can be found. To this end, we generalize a recent primal-dual algorithm for continuous convex optimization to an arbitrary graph structure. To validate our method we present results on data from medical imaging in angiography and retinal blood vessel segmentation.
5 0.19977081 100 iccv-2013-Curvature-Aware Regularization on Riemannian Submanifolds
Author: Kwang In Kim, James Tompkin, Christian Theobalt
Abstract: One fundamental assumption in object recognition as well as in other computer vision and pattern recognition problems is that the data generation process lies on a manifold and that it respects the intrinsic geometry of the manifold. This assumption is held in several successful algorithms for diffusion and regularization, in particular, in graph-Laplacian-based algorithms. We claim that the performance of existing algorithms can be improved if we additionally account for how the manifold is embedded within the ambient space, i.e., if we consider the extrinsic geometry of the manifold. We present a procedure for characterizing the extrinsic (as well as intrinsic) curvature of a manifold M which is described by a sampled point cloud in a high-dimensional Euclidean space. Once estimated, we use this characterization in general diffusion and regularization on M, and form a new regularizer on a point cloud. The resulting re-weighted graph Laplacian demonstrates superior performance over classical graph Laplacian in semisupervised learning and spectral clustering.
6 0.11391178 284 iccv-2013-Multiview Photometric Stereo Using Planar Mesh Parameterization
7 0.081451327 441 iccv-2013-Video Motion for Every Visible Point
8 0.070440605 448 iccv-2013-Weakly Supervised Learning of Image Partitioning Using Decision Trees with Structured Split Criteria
9 0.068458989 165 iccv-2013-Find the Best Path: An Efficient and Accurate Classifier for Image Hierarchies
10 0.066261172 65 iccv-2013-Breaking the Chain: Liberation from the Temporal Markov Assumption for Tracking Human Poses
11 0.062784865 238 iccv-2013-Learning Graphs to Match
12 0.056961007 153 iccv-2013-Face Recognition Using Face Patch Networks
13 0.053779837 404 iccv-2013-Structured Forests for Fast Edge Detection
14 0.049856581 140 iccv-2013-Elastic Net Constraints for Shape Matching
15 0.049587116 11 iccv-2013-A Fully Hierarchical Approach for Finding Correspondences in Non-rigid Shapes
16 0.048711207 120 iccv-2013-Discriminative Label Propagation for Multi-object Tracking with Sporadic Appearance Features
17 0.048072476 186 iccv-2013-GrabCut in One Cut
18 0.045906004 408 iccv-2013-Super-resolution via Transform-Invariant Group-Sparse Regularization
19 0.045474671 183 iccv-2013-Geometric Registration Based on Distortion Estimation
20 0.045443092 112 iccv-2013-Detecting Irregular Curvilinear Structures in Gray Scale and Color Imagery Using Multi-directional Oriented Flux
topicId topicWeight
[(0, 0.124), (1, -0.073), (2, -0.009), (3, -0.015), (4, -0.013), (5, 0.061), (6, -0.039), (7, -0.013), (8, 0.058), (9, -0.125), (10, -0.085), (11, 0.035), (12, -0.018), (13, 0.112), (14, 0.166), (15, 0.14), (16, 0.01), (17, -0.066), (18, -0.034), (19, -0.028), (20, 0.072), (21, 0.095), (22, 0.066), (23, -0.114), (24, -0.026), (25, 0.152), (26, -0.167), (27, -0.161), (28, 0.211), (29, -0.005), (30, -0.336), (31, -0.092), (32, -0.016), (33, 0.011), (34, -0.114), (35, -0.206), (36, -0.026), (37, 0.038), (38, -0.05), (39, 0.089), (40, -0.109), (41, 0.008), (42, -0.102), (43, 0.033), (44, -0.057), (45, -0.046), (46, -0.065), (47, 0.076), (48, -0.036), (49, 0.093)]
simIndex simValue paperId paperTitle
same-paper 1 0.95665205 389 iccv-2013-Shortest Paths with Curvature and Torsion
Author: Petter Strandmark, Johannes Ulén, Fredrik Kahl, Leo Grady
Abstract: This paper describes a method of finding thin, elongated structures in images and volumes. We use shortest paths to minimize very general functionals of higher-order curve properties, such as curvature and torsion. Our globally optimal method uses line graphs and its runtime is polynomial in the size of the discretization, often in the order of seconds on a single computer. To our knowledge, we are the first to perform experiments in three dimensions with curvature and torsion regularization. The largest graphs we process have almost one hundred billion arcs. Experiments on medical images and in multi-view reconstruction show the significance and practical usefulness of regularization based on curvature while torsion is still only tractable for small-scale problems.
2 0.90688181 296 iccv-2013-On the Mean Curvature Flow on Graphs with Applications in Image and Manifold Processing
Author: Abdallah El_Chakik, Abderrahim Elmoataz, Ahcene Sadi
Abstract: In this paper, we propose an adaptation and transcription of the mean curvature level set equation on a general discrete domain (weighted graphs with arbitrary topology). We introduce the perimeters on graph using difference operators and define the curvature as the first variation of these perimeters. Our proposed approach of mean curvature unifies both local and non local notions of mean curvature on Euclidean domains. Furthermore, it allows the extension to the processing of manifolds and data which can be represented by graphs.
3 0.88622075 309 iccv-2013-Partial Enumeration and Curvature Regularization
Author: Carl Olsson, Johannes Ulén, Yuri Boykov, Vladimir Kolmogorov
Abstract: Energies with high-order non-submodular interactions have been shown to be very useful in vision due to their high modeling power. Optimization of such energies, however, is generally NP-hard. A naive approach that works for small problem instances is exhaustive search, that is, enumeration of all possible labelings of the underlying graph. We propose a general minimization approach for large graphs based on enumeration of labelings of certain small patches. This partial enumeration technique reduces complex highorder energy formulations to pairwise Constraint Satisfaction Problems with unary costs (uCSP), which can be efficiently solved using standard methods like TRW-S. Our approach outperforms a number of existing state-of-the-art algorithms on well known difficult problems (e.g. curvature regularization, stereo, deconvolution); it gives near global minimum and better speed. Our main application of interest is curvature regularization. In the context of segmentation, our partial enumeration technique allows to evaluate curvature directly on small patches using a novel integral geometry approach. 1
4 0.70081097 100 iccv-2013-Curvature-Aware Regularization on Riemannian Submanifolds
Author: Kwang In Kim, James Tompkin, Christian Theobalt
Abstract: One fundamental assumption in object recognition as well as in other computer vision and pattern recognition problems is that the data generation process lies on a manifold and that it respects the intrinsic geometry of the manifold. This assumption is held in several successful algorithms for diffusion and regularization, in particular, in graph-Laplacian-based algorithms. We claim that the performance of existing algorithms can be improved if we additionally account for how the manifold is embedded within the ambient space, i.e., if we consider the extrinsic geometry of the manifold. We present a procedure for characterizing the extrinsic (as well as intrinsic) curvature of a manifold M which is described by a sampled point cloud in a high-dimensional Euclidean space. Once estimated, we use this characterization in general diffusion and regularization on M, and form a new regularizer on a point cloud. The resulting re-weighted graph Laplacian demonstrates superior performance over classical graph Laplacian in semisupervised learning and spectral clustering.
5 0.4942275 429 iccv-2013-Tree Shape Priors with Connectivity Constraints Using Convex Relaxation on General Graphs
Author: Jan Stühmer, Peter Schröder, Daniel Cremers
Abstract: We propose a novel method to include a connectivity prior into image segmentation that is based on a binary labeling of a directed graph, in this case a geodesic shortest path tree. Specifically we make two contributions: First, we construct a geodesic shortest path tree with a distance measure that is related to the image data and the bending energy of each path in the tree. Second, we include a connectivity prior in our segmentation model, that allows to segment not only a single elongated structure, but instead a whole connected branching tree. Because both our segmentation model and the connectivity constraint are convex, a global optimal solution can be found. To this end, we generalize a recent primal-dual algorithm for continuous convex optimization to an arbitrary graph structure. To validate our method we present results on data from medical imaging in angiography and retinal blood vessel segmentation.
6 0.31027141 324 iccv-2013-Potts Model, Parametric Maxflow and K-Submodular Functions
7 0.25973997 215 iccv-2013-Incorporating Cloud Distribution in Sky Representation
8 0.25956306 84 iccv-2013-Complex 3D General Object Reconstruction from Line Drawings
9 0.2591157 408 iccv-2013-Super-resolution via Transform-Invariant Group-Sparse Regularization
10 0.25082913 421 iccv-2013-Total Variation Regularization for Functions with Values in a Manifold
11 0.24410769 112 iccv-2013-Detecting Irregular Curvilinear Structures in Gray Scale and Color Imagery Using Multi-directional Oriented Flux
12 0.24168047 448 iccv-2013-Weakly Supervised Learning of Image Partitioning Using Decision Trees with Structured Split Criteria
13 0.23301524 120 iccv-2013-Discriminative Label Propagation for Multi-object Tracking with Sporadic Appearance Features
15 0.22192746 312 iccv-2013-Perceptual Fidelity Aware Mean Squared Error
16 0.22024202 250 iccv-2013-Lifting 3D Manhattan Lines from a Single Image
17 0.21597485 186 iccv-2013-GrabCut in One Cut
18 0.21461628 171 iccv-2013-Fix Structured Learning of 2013 ICCV paper k2opt.pdf
19 0.21400322 284 iccv-2013-Multiview Photometric Stereo Using Planar Mesh Parameterization
20 0.20933586 90 iccv-2013-Content-Aware Rotation
topicId topicWeight
[(2, 0.062), (7, 0.036), (12, 0.016), (13, 0.048), (26, 0.075), (31, 0.052), (34, 0.01), (35, 0.019), (40, 0.012), (42, 0.072), (48, 0.015), (54, 0.225), (64, 0.052), (73, 0.038), (89, 0.154), (98, 0.02)]
simIndex simValue paperId paperTitle
same-paper 1 0.80103439 389 iccv-2013-Shortest Paths with Curvature and Torsion
Author: Petter Strandmark, Johannes Ulén, Fredrik Kahl, Leo Grady
Abstract: This paper describes a method of finding thin, elongated structures in images and volumes. We use shortest paths to minimize very general functionals of higher-order curve properties, such as curvature and torsion. Our globally optimal method uses line graphs and its runtime is polynomial in the size of the discretization, often in the order of seconds on a single computer. To our knowledge, we are the first to perform experiments in three dimensions with curvature and torsion regularization. The largest graphs we process have almost one hundred billion arcs. Experiments on medical images and in multi-view reconstruction show the significance and practical usefulness of regularization based on curvature while torsion is still only tractable for small-scale problems.
2 0.75749618 407 iccv-2013-Subpixel Scanning Invariant to Indirect Lighting Using Quadratic Code Length
Author: Nicolas Martin, Vincent Couture, Sébastien Roy
Abstract: We present a scanning method that recovers dense subpixel camera-projector correspondence without requiring any photometric calibration nor preliminary knowledge of their relative geometry. Subpixel accuracy is achieved by considering several zero-crossings defined by the difference between pairs of unstructured patterns. We use gray-level band-pass white noise patterns that increase robustness to indirect lighting and scene discontinuities. Simulated and experimental results show that our method recovers scene geometry with high subpixel precision, and that it can handle many challenges of active reconstruction systems. We compare our results to state of the art methods such as micro phase shifting and modulated phase shifting.
3 0.75282669 68 iccv-2013-Camera Alignment Using Trajectory Intersections in Unsynchronized Videos
Author: Thomas Kuo, Santhoshkumar Sunderrajan, B.S. Manjunath
Abstract: This paper addresses the novel and challenging problem of aligning camera views that are unsynchronized by low and/or variable frame rates using object trajectories. Unlike existing trajectory-based alignment methods, our method does not require frame-to-frame synchronization. Instead, we propose using the intersections of corresponding object trajectories to match views. To find these intersections, we introduce a novel trajectory matching algorithm based on matching Spatio-Temporal Context Graphs (STCGs). These graphs represent the distances between trajectories in time and space within a view, and are matched to an STCG from another view to find the corresponding trajectories. To the best of our knowledge, this is one of the first attempts to align views that are unsynchronized with variable frame rates. The results on simulated and real-world datasets show trajectory intersections area viablefeatureforcamera alignment, and that the trajectory matching method performs well in real-world scenarios.
4 0.72866023 293 iccv-2013-Nonparametric Blind Super-resolution
Author: Tomer Michaeli, Michal Irani
Abstract: Super resolution (SR) algorithms typically assume that the blur kernel is known (either the Point Spread Function ‘PSF’ of the camera, or some default low-pass filter, e.g. a Gaussian). However, the performance of SR methods significantly deteriorates when the assumed blur kernel deviates from the true one. We propose a general framework for “blind” super resolution. In particular, we show that: (i) Unlike the common belief, the PSF of the camera is the wrong blur kernel to use in SR algorithms. (ii) We show how the correct SR blur kernel can be recovered directly from the low-resolution image. This is done by exploiting the inherent recurrence property of small natural image patches (either internally within the same image, or externally in a collection of other natural images). In particular, we show that recurrence of small patches across scales of the low-res image (which forms the basis for single-image SR), can also be used for estimating the optimal blur kernel. This leads to significant improvement in SR results.
5 0.6921382 147 iccv-2013-Event Recognition in Photo Collections with a Stopwatch HMM
Author: Lukas Bossard, Matthieu Guillaumin, Luc Van_Gool
Abstract: The task of recognizing events in photo collections is central for automatically organizing images. It is also very challenging, because of the ambiguity of photos across different event classes and because many photos do not convey enough relevant information. Unfortunately, the field still lacks standard evaluation data sets to allow comparison of different approaches. In this paper, we introduce and release a novel data set of personal photo collections containing more than 61,000 images in 807 collections, annotated with 14 diverse social event classes. Casting collections as sequential data, we build upon recent and state-of-the-art work in event recognition in videos to propose a latent sub-event approach for event recognition in photo collections. However, photos in collections are sparsely sampled over time and come in bursts from which transpires the importance of specific moments for the photographers. Thus, we adapt a discriminative hidden Markov model to allow the transitions between states to be a function of the time gap between consecutive images, which we coin as Stopwatch Hidden Markov model (SHMM). In our experiments, we show that our proposed model outperforms approaches based only on feature pooling or a classical hidden Markov model. With an average accuracy of 56%, we also highlight the difficulty of the data set and the need for future advances in event recognition in photo collections.
6 0.66912264 376 iccv-2013-Scene Text Localization and Recognition with Oriented Stroke Detection
7 0.66715831 429 iccv-2013-Tree Shape Priors with Connectivity Constraints Using Convex Relaxation on General Graphs
8 0.66602921 349 iccv-2013-Regionlets for Generic Object Detection
9 0.66504478 145 iccv-2013-Estimating the Material Properties of Fabric from Video
10 0.6646049 273 iccv-2013-Monocular Image 3D Human Pose Estimation under Self-Occlusion
12 0.66264021 137 iccv-2013-Efficient Salient Region Detection with Soft Image Abstraction
13 0.66142702 414 iccv-2013-Temporally Consistent Superpixels
14 0.66128159 377 iccv-2013-Segmentation Driven Object Detection with Fisher Vectors
15 0.66121054 420 iccv-2013-Topology-Constrained Layered Tracking with Latent Flow
16 0.66118228 204 iccv-2013-Human Attribute Recognition by Rich Appearance Dictionary
17 0.66114295 340 iccv-2013-Real-Time Articulated Hand Pose Estimation Using Semi-supervised Transductive Regression Forests
18 0.66076273 426 iccv-2013-Training Deformable Part Models with Decorrelated Features
19 0.66000205 22 iccv-2013-A New Adaptive Segmental Matching Measure for Human Activity Recognition
20 0.65998328 315 iccv-2013-PhotoOCR: Reading Text in Uncontrolled Conditions