iccv iccv2013 iccv2013-358 knowledge-graph by maker-knowledge-mining
Source: pdf
Author: Wen-Yan Lin, Ming-Ming Cheng, Shuai Zheng, Jiangbo Lu, Nigel Crook
Abstract: We propose a generic method for obtaining nonparametric image warps from noisy point correspondences. Our formulation integrates a huber function into a motion coherence framework. This makes our fitting function especially robust to piecewise correspondence noise (where an image section is consistently mismatched). By utilizing over parameterized curves, we can generate realistic nonparametric image warps from very noisy correspondence. We also demonstrate how our algorithm can be used to help stitch images taken from a panning camera by warping the images onto a virtual push-broom camera imaging plane.
Reference: text
sentIndex sentText sentNum sentScore
1 Our formulation integrates a huber function into a motion coherence framework. [sent-2, score-0.489]
2 This makes our fitting function especially robust to piecewise correspondence noise (where an image section is consistently mismatched). [sent-3, score-0.87]
3 By utilizing over parameterized curves, we can generate realistic nonparametric image warps from very noisy correspondence. [sent-4, score-0.455]
4 We also demonstrate how our algorithm can be used to help stitch images taken from a panning camera by warping the images onto a virtual push-broom camera imaging plane. [sent-5, score-0.468]
5 Introduction Fitting a warp or transformation field onto an image section is a long standing computer vision and graphics problem and lies at the heart of many novel image synthesis algorithms. [sent-7, score-0.192]
6 While there are many techniques for establishing correspondence between images [24, 23, 13], converting them into a coherent warp remains a significant problem. [sent-8, score-0.451]
7 For specific applications or correspondence types, there have been many proposals regarding how outlying correspondence can be removed [3 1] or correspondence jointly estimated with the warp [21]. [sent-9, score-0.86]
8 What is lacking is a generic, computationally simple method to robustly establish a nonparametric warp from noisy correspondence. [sent-10, score-0.424]
9 To date the most commonly used generic techniques for fitting warps to correspondences take the form of rigid affine or homographic transforms. [sent-11, score-0.914]
10 These warps are parametric, with the small parameter size providing robustness to noise and outliers. [sent-12, score-0.31]
11 While parametric techniques are very robust, many real world scenarios involve complex motions that would benefit from less restrictive parameterization. [sent-13, score-0.123]
12 We pose this warping problem as a data fitting question: How is it possible to robustly compute a non-parametric fitting function across noisy scatter points? [sent-14, score-1.327]
13 ”The direct fitting of a fully flexible non-parametric function would almost certainly result in difficulties defining and removing outliers. [sent-15, score-0.481]
14 This would be especially difInputs Warping Results Overlays Results flow correspondences [23], allowing a visually pleasing warp. [sent-16, score-0.118]
15 ficult for piece-wise outlier corruption where certain image sections are consistently matched incorrectly. [sent-17, score-0.281]
16 However, we note that by including an additional constraint requiring data to form a smooth curve, outliers (especially piece-wise outliers) can then be readily defined. [sent-18, score-0.284]
17 While loosing some modeling flexibility, such a scheme has the potential to provide a level of robustness similar to parametric affine and homographic fitting while providing significantly greater flexibility. [sent-19, score-0.764]
18 We propose a non-parametric function fitting approach that is based upon the motion coherence formulation discussed by Yuille and Grywacz [41], Myronenko et al. [sent-20, score-0.702]
19 We observe that the original proofs based upon L2 correspondence fitting can be adapted to a robust huber loss function. [sent-22, score-0.864]
20 The resultant formulation computes a smooth, best fit curve for a noisy point set by minimizing a simple convex cost. [sent-23, score-0.254]
21 With a simple Median Absolute Deviation thresholding to replace the RANSAC [11], our proposed algorithm’s enforcement of overall smoothness makes it especially adept at handling piece-wise noise in which certain data sections are corrupted in a coherent manner. [sent-24, score-0.438]
22 When we integrate our 1-dimensional curve fitting into the over parametrized warping scheme proposed by Lin et al. [sent-25, score-0.918]
23 [22, 29], we can compute coherent warps from noisy image correspondences. [sent-27, score-0.397]
24 ooppyyrriigghhtt 22337766 As our warping technique is defined in terms of nonparametric curve fitting, rather than correspondence reestimation, it lends itself naturally to image re-projection problems. [sent-29, score-0.847]
25 In particular, it allows orthographic image projection from noisy depth estimates. [sent-30, score-0.146]
26 This is especially useful for mosaicking long lateral image sequences taken by a panning camera. [sent-31, score-0.392]
27 To summarize, our contributions are as follows: • • We propose a non-parametric curve fitting technique tWhaet pisr oropobusest ato n piecewise entroicise c. [sent-32, score-0.707]
28 We incorporate the technique into a high dimensional smoothly varying warping suceh einmtoe ath hatig gahll odwims compu- tation of visually compelling image warps from noisy correspondence in a simple minimization framework. [sent-33, score-0.958]
29 • We demonstrate a panning mosaicking algorithm that integrates images f praonmn a laterally translating camera by stitching them to a push-broom mosaicking plane. [sent-34, score-0.653]
30 Related Works Non-parametric data fitting and its associated image warping is a large and well researched computer vision field. [sent-36, score-0.748]
31 Works range from self occlusion surface fitting [3 1], full frame internet image warping [21], bio-medical contour registration [28], non-rigid surface reconstruction [36, 34], as-rigid-as-possible shape manipulation [18] and non-rigid 3-D object warping [39]. [sent-37, score-1.08]
32 Non-rigid fitting also encompasses the wide range of flow based works, [23, 25, 17, 6] and piecewise segment fitting techniques [3, 37]. [sent-38, score-1.036]
33 However, most works focus on custom applications to specific problems and their adaptation to a generic non-parametric correspondence fitting scheme is unclear since they integrate many different aspects (matching cost, descriptor information and smoothness term) within a single system. [sent-39, score-0.913]
34 The issue of adapting non-rigid matching techniques to correspondence fitting is considered in the subsequent paragraph. [sent-40, score-0.682]
35 Non-rigid correspondence estimation algorithms such as Chui et al. [sent-41, score-0.233]
36 in mixed optical flow, thin-plate spline computation [40], Myronenko et al. [sent-43, score-0.227]
37 in smoothly varying affine [22], iteratively compute a smooth warping surface and do not assume known correspondences. [sent-45, score-0.601]
38 These formulations can also be readily adapted from correspondence discovery to the simpler correspondence fitting problem by redefining the matching choices into a binary match or no-match decision. [sent-46, score-1.018]
39 However, we note that if the task is simply to decide between a match and non-match, we can eliminate the complex iterative correspondence estimation procedure that is vulnerable to local minimums. [sent-48, score-0.273]
40 In this paper, we adapt the motion coherence formulation [28] such that : outliers A B C Figure 2. [sent-49, score-0.377]
41 While the outlier points in B can be potentially fitted using a spline, their outlier status becomes much less ambiguous if we define the problem as a smooth curve fitting. [sent-50, score-0.525]
42 the matching cost is penalized with a simple huber function. [sent-51, score-0.222]
43 This adaptation allows a simple convex cost that can be minimized to find the desired warping field. [sent-52, score-0.376]
44 Our work also bears close relation to spline fitting tech- niques such as Reinsch [35], Akima [2], Garcia [15]. [sent-53, score-0.716]
45 Unlike spline fitting, we require our fitted function to be a smooth curve. [sent-54, score-0.437]
46 This is less flexible than a spline, but it allows the fitting of a trend through piece-wise outlier corruption. [sent-55, score-0.526]
47 Formulation We pose the correspondence modeling problem as one of robust non-parametric curve fitting. [sent-58, score-0.345]
48 Traditionally, nonparametric function estimation is viewed as more unstable than its parametrized cousin. [sent-59, score-0.189]
49 We feel that this is in large part due to the difficulty in defining noise and outliers in a non-parametric setting. [sent-60, score-0.215]
50 In particular piece-wise noise in which a section of the signal is corrupted consistently can be difficult to handle. [sent-61, score-0.156]
51 However, by reducing the non-parametric space to a smaller one consisting of smooth continuous functions, such outliers can be well defined as illustrated in Figure 2. [sent-62, score-0.234]
52 As such, we propose a non-parametric curve fitting that is robust to piecewise corruption and extend our results to the creation of smooth warps from noisy correspondences. [sent-63, score-1.168]
53 Our proposed solution can provide high stability levels usually only associated with parametric algorithms. [sent-64, score-0.084]
54 Using Motion Coherence to formulate a function fitting problem The problem is formulated as the fitting of a smooth function to data. [sent-67, score-0.969]
55 Given a set of N scatter points {pj , qˆj }, wfuhnecrteio pj are aDta-. [sent-68, score-0.205]
56 d Gimievnesnio an saelt tv oefcNt ors s canatdte qˆj are tssca {lpars. [sent-69, score-0.106]
57 W}e, assume that data comes from a linear combination of K smooth functions fk (p), corrupted with noise. [sent-70, score-0.461]
58 1 22337777 represents noise and ajk are given weight values for the linear combination of fk (. [sent-76, score-0.236]
59 ) functions are composed of two terms, fk (p) = Hk + φk (p). [sent-79, score-0.246]
60 Hk is a scalar offset and φk (p) is a smooth function with motion coherence smoothness penalty [41, 28] given as follows nj Ψk=? [sent-80, score-0.494]
61 ), while g(ω) is the Fourier transform of a Gaussian with spatial distribution γ. [sent-84, score-0.038]
62 ) functions consistent with the given {pj , qˆj } data points. [sent-88, score-0.056]
63 ) represents some cost function that penalizes deviation of the estimated function predictions from given ˆq estimates. [sent-102, score-0.043]
64 Throughout this paper, we use the huber function in Eqn. [sent-103, score-0.144]
65 λ represents the weight given to the smoothness constraint Ψk. [sent-105, score-0.091]
66 The cost E can be re-expressed in terms of a finite number of wk, Hk using Eqn. [sent-106, score-0.09]
67 Directly minimizing E with respect to functions fk (. [sent-109, score-0.246]
68 However, motion coherence can reduce the problem to an optimization over a finite number of variables. [sent-111, score-0.301]
69 A brief summary is as follows: Note the Fourier transform relation, φk (p) = ? [sent-112, score-0.038]
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Abstract: Dense motion field estimation (typically Romain Dupont1 romain . dupont @ cea . fr Adrien Bartoli2 adrien . bart o l @ gmai l com i . 2 ISIT, Universit e´ d’Auvergne/CNRS, France sions are explicitly modeled [32, 13]. Coarse-to-fine warping improves global convergence by making the assumption that optical flow, the motion of smaller structures is similar to the motion of stereo disparity and surface registration) is a key computer vision problem. Many solutions have been proposed to compute small or large displacements, narrow or wide baseline stereo disparity, but a unified methodology is still lacking. We here introduce a general framework that robustly combines direct and feature-based matching. The feature-based cost is built around a novel robust distance function that handles keypoints and “weak” features such as segments. It allows us to use putative feature matches which may contain mismatches to guide dense motion estimation out of local minima. Our framework uses a robust direct data term (AD-Census). It is implemented with a powerful second order Total Generalized Variation regularization with external and self-occlusion reasoning. Our framework achieves state of the art performance in several cases (standard optical flow benchmarks, wide-baseline stereo and non-rigid surface registration). Our framework has a modular design that customizes to specific application needs.
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