cvpr cvpr2013 cvpr2013-316 knowledge-graph by maker-knowledge-mining
Source: pdf
Author: Wenbin Li, Darren Cosker, Matthew Brown, Rui Tang
Abstract: In this paper we present a novel non-rigid optical flow algorithm for dense image correspondence and non-rigid registration. The algorithm uses a unique Laplacian Mesh Energy term to encourage local smoothness whilst simultaneously preserving non-rigid deformation. Laplacian deformation approaches have become popular in graphics research as they enable mesh deformations to preserve local surface shape. In this work we propose a novel Laplacian Mesh Energy formula to ensure such sensible local deformations between image pairs. We express this wholly within the optical flow optimization, and show its application in a novel coarse-to-fine pyramidal approach. Our algorithm achieves the state-of-the-art performance in all trials on the Garg et al. dataset, and top tier performance on the Middlebury evaluation.
Reference: text
sentIndex sentText sentNum sentScore
1 uk i Abstract In this paper we present a novel non-rigid optical flow algorithm for dense image correspondence and non-rigid registration. [sent-8, score-0.407]
2 The algorithm uses a unique Laplacian Mesh Energy term to encourage local smoothness whilst simultaneously preserving non-rigid deformation. [sent-9, score-0.144]
3 Laplacian deformation approaches have become popular in graphics research as they enable mesh deformations to preserve local surface shape. [sent-10, score-0.951]
4 In this work we propose a novel Laplacian Mesh Energy formula to ensure such sensible local deformations between image pairs. [sent-11, score-0.117]
5 We express this wholly within the optical flow optimization, and show its application in a novel coarse-to-fine pyramidal approach. [sent-12, score-0.524]
6 dataset, and top tier performance on the Middlebury evaluation. [sent-14, score-0.07]
7 Introduction Optical flow estimation is an important area of computer vision research. [sent-16, score-0.221]
8 Current algorithms can broadly be clas- sified into two categories variational methods and discrete optimization methods. [sent-17, score-0.076]
9 The former is a continuous approach [5, 6, 18] to estimate optical flow based on modifications of Horn and Schunck’s framework proposed in [9]. [sent-18, score-0.379]
10 Such approaches can provide high subpixel accuracy but may be limited by minimization of the non-convex energy function. [sent-19, score-0.154]
11 The latter [4, 14] is based on combinatorial optimization algorithms such as min-cut and max-flow, which can recover non-convex energy functions and multiple local minima but may suffer from discretization artifacts, e. [sent-20, score-0.154]
12 the optical flow field boundary is aligned with the coordinate axes. [sent-22, score-0.408]
13 One desirable property of optical flow techniques is to preserve local image detail and also handle non-rigid image deformations. [sent-23, score-0.433]
14 Under such deformations, the preservation of local detail is particularly important. [sent-24, score-0.041]
15 [7] impose this by maintaining correlations between 2D trajectories of different points on a non-rigid surface using a variational framework. [sent-26, score-0.134]
16 [12] propose a feature matching approach based on local surface smoothness, and also show particular application to non-rigidly deforming objects. [sent-28, score-0.031]
17 In computer graphics research, a common requirement is that surface meshes are globally editable, but capable of maintaining local details under mesh deformations. [sent-29, score-0.863]
18 In order to provide a flexible representation to allow computation and preservation of such details, Laplacian mesh structures have previously been described [13, 11]. [sent-30, score-0.753]
19 Such schemes impose constraints in differential Laplacian coordinates calculated upon groups of triangles associated with each vertex. [sent-31, score-0.087]
20 Meshes have previously been used in optical flow estima– tion [8]. [sent-32, score-0.379]
21 However, this is to reduce processing complexity as opposed to specifically imposing smoothness. [sent-33, score-0.026]
22 In this paper we present an variational optical flow model which introduces a novel discrete energy based on Laplacian Mesh Deformation. [sent-34, score-0.609]
23 Such deformation approaches are widely applied in graphics research, particularly for preserving local details [13, 11]. [sent-35, score-0.11]
24 that of an underlying mesh which penalizes local movements and preserves smooth global ones, can be of great use for optical flow and tracking. [sent-38, score-1.13]
25 Constraints on the local deformations expressed in Laplacian coordinates encourage local regularity of the mesh whilst allowing global non-rigidity. [sent-39, score-0.88]
26 Our algorithm applies a mesh to an image with a resolution up to one vertex per pixel. [sent-40, score-0.829]
27 The Laplacian Mesh Energy is described as an additional term for the energy function, and can be applied in a straightforward manner using our proposed minimization strategy. [sent-41, score-0.185]
28 In addition, a novel coarse-to-fine approach is described for overcoming the loss of small optical flow details during its propagation between adjacent pyramid levels. [sent-42, score-0.471]
29 Our approach provides excellent performance ranked in the top tier of the Middlebury evaluation1 , and either outperforms or shows comparable accuracy against the leading publicly available non-rigid approaches when evaluated on the non-rigid data set of Garg et al. [sent-45, score-0.07]
30 Hybrid Energy In this section, we introduce our novel hybrid energy formula in which our algorithm considers a pair of consecutive frames in an image sequence. [sent-50, score-0.244]
31 We define the optical flow displacement between I1(X) and I2 (X) as w = (u, v)T. [sent-52, score-0.418]
32 Similar to [5, 9], a smoothness term is introduced into the formula, which controls global flow smoothness. [sent-54, score-0.297]
33 Continuous Intensity Energy Following the standard optical flow assumption regarding Intensity Constancy, we assume that the gray value of a pixel is not varied by its displacement through the entire image sequence. [sent-61, score-0.418]
34 In addition, we also make a Gradient Constancy assumption which is engaged to provide additional stability in case the first assumption (Intensity Constancy) is violated by changes in illumination. [sent-62, score-0.026]
35 The data term of energy function encoding these assumptions is therefore formulated as: EData(w) =? [sent-63, score-0.185]
36 The term = (∂xx, ∂yy)T is the spatial gradient and θ ∈ [0, 1] dteernmot ∇es a weight that can bthee manually assigned dw θith ∈ ∈di [f0f,e1r-] ent values. [sent-72, score-0.062]
37 Furthermore, the smoothness term of our algorithm is a dense pixel based regularizer that penalizes global variation. [sent-73, score-0.115]
38 The objective is to produce a globally smooth optical flow field: ∇ ESmooth(w) =? [sent-74, score-0.379]
39 Discrete Laplacian Mesh Energy In order to improve optical flow estimation against the local complexity of non-rigid motion, a novel Laplacian Mesh Energy concept is proposed in this section. [sent-82, score-0.419]
40 The aim of this energy is to account for non-rigid motion in scene deformation. [sent-83, score-0.186]
41 This concept is inspired by Laplacian Mesh Deformation research in graphics, which aims to preserve local mesh smoothness under non-linear transformation [13]. [sent-84, score-0.851]
42 The usage of this concept in computer vision research for optical flow estimation is introduced for the first time here. [sent-85, score-0.419]
43 Although non-rigid motion is highly nonlinear, the movement of pixels in such deformations still often exhibits strong correlations in local regions. [sent-86, score-0.128]
44 Let M = (V, E, F) be a triangular mesh where mV =tio n{v. [sent-90, score-0.751]
45 , =vn} ( Vd,eEsc,rFib)e sb geometric positions wofh tehree Vver =tice {sv in absolute c}art deessicarnib bceoso gredoinmateetsr,i cE p doesintoiotenss t ohef tsheet of edges, and F the set of faces. [sent-94, score-0.07]
46 Considering a small mesh region, each vertex vi has a neighborhood ring denoted by Ni = {j | (i, j) ∈ E} which is the set of adjacent vertices oNf v=erte {xj vi. [sent-95, score-0.999]
47 T,jh)e degree hdii ohf vi hise th seet n oufm abdejarc eofn tel veemrteicnetss in Ni. [sent-96, score-0.14]
48 Here the mesh geometric motion is described by diifnfe Nrentials instead of absolute Cartesian coordinates. [sent-97, score-0.744]
49 We define the differentials set as L = {δ1 , δ2 , . [sent-98, score-0.029]
50 δn} where tdheef ncoeo trhdein daitfef rise presented as Lthe = di {ffδerence betw}ee wnh tehree vertex vi and the geometric average of its neighbors, i. [sent-101, score-0.271]
51 (4) These uniform weights are found sufficient for the 2D mesh in our evaluation. [sent-106, score-0.712]
52 Next, we have the mesh energy in Laplacian coordinates as follows: ? [sent-107, score-0.897]
53 1 Where wi denotes the motion of the vertices vi. [sent-113, score-0.081]
54 This term of the energy function penalizes the shape variance after vertex motion. [sent-114, score-0.341]
55 The rationale of using this energy is that the Laplacian coordinates L encode relative information between vertices and can therefore be used to preserve shape under mesh deformation. [sent-115, score-1.042]
56 Optical Flow Framework Table 1 outlines our overall optical flow framework. [sent-117, score-0.379]
57 In order to utilize the Laplacian Mesh Energy it is required to create a mesh over the initial image I1. [sent-118, score-0.738]
58 Ideally, we desire that the triangles of this mesh do not overlap boundaries in the scene as this may lead to distortions given parallax motion between objects at different depths. [sent-119, score-0.889]
59 We also present a novel coarse-to-fine pyramidal framework [5] to utilize our Laplacian Mesh Energy in a variational model. [sent-122, score-0.194]
60 In our framework we overcome a previous limitation of such pyramidal approaches, i. [sent-123, score-0.145]
61 the loss of small flow details when propagating flow field from coarse to finer pyramidal levels. [sent-125, score-0.714]
62 In such cases, small image details at a finer level of the pyramid are lost due to flow computation being initially performed on a coarsely sampled version of the image. [sent-126, score-0.342]
63 As such, the flow for these detailed regions is not remained and propagated to the finer level. [sent-127, score-0.295]
64 3) is proposed to minimize the discrete Laplacian Mesh Energy on every level of the pyramidal framework. [sent-130, score-0.172]
65 Edge-Aware Mesh Initialization The proposed algorithm is input by an image pair and a mesh with triangle edges that follow object boundaries in one of the images as closely as possible. [sent-134, score-0.821]
66 We will discuss the implications of mesh design and its affect on our algorithms behavior in the evaluation. [sent-135, score-0.712]
67 The underlying mesh is an essential part of Laplacian Mesh Energy computation. [sent-136, score-0.712]
68 Using a uniform mesh with equal distances between vertices along its horizontal and vertical adjacent neighbors is one strategy that can be employed in our approach. [sent-137, score-0.8]
69 However, in such a case the grid elements within the mesh will typically overlap the boundaries of objects scene, which results in unexpected errors in our energy minimization. [sent-138, score-0.914]
70 This is because triangles within the mesh will be skewed given parallax motion between different objects at different image depths, resulting in a noisier flow field in these areas. [sent-139, score-1.142]
71 In order to address this issue, we propose an edge-aware meshing scheme which operates as follows: First, we create two edge maps on the input image using SLIC Superpixels [1] and Sobel Kernel edge detection respectively. [sent-140, score-0.109]
72 We then apply a binary AND Operation on the two edge maps in order to deduce uncommon edges, and remove noise using a Gaussian filter. [sent-141, score-0.053]
73 The rationale behind this approach is that the Sobel kernel returns a large number of candidate edges, but also multiple false-positive noise like edges relating to image detail as opposed to object boundaries. [sent-142, score-0.132]
74 The SLIC Superpixels on the other hand is less likely to create boundaries relating to image detail. [sent-143, score-0.108]
75 Performing an AND operation eliminates a great deal of the noisy edge boundaries and retains a large proportion of reliable ones. [sent-144, score-0.075]
76 Finally, we construct a triangular mesh M1 using Delaunay triangulation on tthe a remaining edge points. [sent-145, score-0.778]
77 Given the input mesh M1, an n-level image pyramid is buiGlt i(vTeanbl the e1) i. [sent-146, score-0.74]
78 n Tpuhet input images I1, I2 along with the mesh M1 are resized with the same sampling rate on each level, denoted by I1k, I2k and M1k, where k = 1, 2, . [sent-147, score-0.712]
79 3, the aim of this step is to preserve small flow details which may be lost when propagated from the adjacent coarser level. [sent-155, score-0.401]
80 First, we estimate a mesh M2k by propagating the mesh M1k from I1k eonsttiom Ia2kte. [sent-156, score-1.457]
81 aN mexets, we bubildy a labelling gm thoede ml using vertex displacement vectors and solve it to retain small flow details. [sent-157, score-0.408]
82 The iterative refinement algorithm for tracked mesh M2k Tesatbilmea 2ti. [sent-179, score-0.739]
83 h In order to propagate the mesh from M1k to M2k at pyramidIn nle ovrdeel kr ,t we employ an m Aneschho frro Pmat Mch batose Md technique and Laplacian Mesh Deformation, which utilizes I1k, I2k and M1k. [sent-181, score-0.743]
84 We follow the Anchor Patch process outlined in [10] tMo achieve this mesh propagation: SIFT features are initially detected and matched between images I1k and I2k given a corresponding set of features between each image. [sent-182, score-0.712]
85 We then 222444333755 – go through every vertex v of M1k and search for the three gnoea rthesrot uSgIhFT e vfeeraytu vreesr ef∗x w vi tohfin M a 9 9 search window centered on the vertex v in Iw1ki. [sent-183, score-0.316]
86 t Tinh ea corresponding ifnedaotuwre cse ninI2k and Barycentric Coordinate Mappings defined by the triangle formed by the 3 SIFT features are used to calculate a corresponding vertex v? [sent-184, score-0.173]
87 ) from [3, N1e0]x on waell taphep newly crrreoarte fdu nvcetirtoenx correspondences between I1k and I2k. [sent-187, score-0.031]
88 This is carried out in order to select the most reliable vertex matches between the two images. [sent-188, score-0.117]
89 sTmhael lve rretgeixo nmsa (tc3h ×es 3w)i tche nlotewre errors are dsel vected as sets of control points defined here as Vc, V? [sent-191, score-0.052]
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