iccv iccv2013 iccv2013-255 knowledge-graph by maker-knowledge-mining
Source: pdf
Author: Derek Bradley, Thabo Beeler
Abstract: Correspondence matching is one of the most common problems in computer vision, and it is often solved using photo-consistency of local regions. These approaches typically assume that the frequency content in the local region is consistent in the image pair, such that matching is performed on similar signals. However, in many practical situations this is not the case, for example with low depth of field cameras a scene point may be out of focus in one view and in-focus in the other, causing a mismatch of frequency signals. Furthermore, this mismatch can vary spatially over the entire image. In this paper we propose a local signal equalization approach for correspondence matching. Using a measure of local image frequency, we equalize local signals using an efficient scale-space image representation such that their frequency contents are optimally suited for matching. Our approach allows better correspondence matching, which we demonstrate with a number of stereo reconstruction examples on synthetic and real datasets.
Reference: text
sentIndex sentText sentNum sentScore
1 These approaches typically assume that the frequency content in the local region is consistent in the image pair, such that matching is performed on similar signals. [sent-2, score-0.649]
2 However, in many practical situations this is not the case, for example with low depth of field cameras a scene point may be out of focus in one view and in-focus in the other, causing a mismatch of frequency signals. [sent-3, score-0.618]
3 In this paper we propose a local signal equalization approach for correspondence matching. [sent-5, score-0.968]
4 Using a measure of local image frequency, we equalize local signals using an efficient scale-space image representation such that their frequency contents are optimally suited for matching. [sent-6, score-0.998]
5 Our approach allows better correspondence matching, which we demonstrate with a number of stereo reconstruction examples on synthetic and real datasets. [sent-7, score-0.524]
6 Correspondence matching is key to many applications including stereo and multi-view reconstruction, optical flow, template matching, image registration and video stabilization (to name just a few). [sent-10, score-0.43]
7 In this work we focus on patch-based correspondence matching, often used for dense stereo reconstruction. [sent-11, score-0.444]
8 The drawback of NCC is that it assumes the input images contain the same signal content, either all images are true representations of the original scene signal or all are equally distorted through defocus, motion blur, under-sampling, etc. [sent-14, score-0.578]
9 However, in many practical situations we have to compute correspondence of mixed-signals, caused by different amounts of defocus blur for example. [sent-15, score-0.472]
10 Furthermore, the signal degradation will vary spatially in most practical situations causing different mixed-signals for every pixel in an image. [sent-16, score-0.509]
11 Thabo Beeler Disney Research Zurich In this paper, we take a pre-processing approach to solve the signal mismatch problem. [sent-17, score-0.355]
12 Rather than defining new measures and devising new algorithms for matching mixed- signals, we believe it is more advantageous to modify the input signals in an optimal way to enable the wide range of existing algorithms which assume the signals are already equalized. [sent-18, score-0.601]
13 To this end, we propose to locally equalize the image signals before computing correspondence matches. [sent-19, score-0.721]
14 Given two images patches, our technique involves a frequency equalization step in order to generate patches with similar spatial signals, and an optimal frequency scaling step that ensures the patches can be matched reliably. [sent-20, score-1.471]
15 This is achieved using a notion of local image frequency, which quantifies the highest spatial frequency in a local region, and an efficient implementation of scale-space that builds multi-resolution image patches on demand. [sent-21, score-0.598]
16 We demonstrate the power of the proposed signal equalization technique by improving the performance of a na¨ ıve window matching algorithm by an order of magnitude on several examples of dense stereo reconstruction, using a synthetic data set with ground truth, and additional realworld examples. [sent-23, score-1.325]
17 Related Work Correspondence matching is very common in several domains, including stereo reconstruction [20], multi-view reconstruction [21], optical flow [1], and many more. [sent-27, score-0.536]
18 In this work we address the general issue of inconsistent spatial frequency signals between multiple images when performing correspondence estimation. [sent-28, score-0.846]
19 While there exist many patch-based correlation measures [10] for stereo, they typically assume that frequency signals are consistent in the images before matching. [sent-29, score-0.655]
20 We present a technique for establishing consistent frequency signals automatically. [sent-30, score-0.671]
21 While some approaches have been developed for recovering depth from defocus information [6, 23, 12], we have a different goal, which is to improve correspondence matching between multiple images containing different signals. [sent-32, score-0.475]
22 However, these approaches do not solve the ”mixed” signal problem, and in contrast we aim to explicitly locally equalize the signal of both images before computing correspondences. [sent-36, score-0.883]
23 Signal analysis in stereo reconstruction is not an entirely new concept. [sent-37, score-0.309]
24 [14] analyze signal content in patch-based stereo systems, showing that the amplitude of high-frequency details is diminished in reconstructions, and they derive a modulation transfer function in frequency space that can be inverted to restore details. [sent-39, score-1.103]
25 Following this theory, they show how Gaussian weighting of stereo patch correspondences links reconstruction to a scale-space representation of the underlying surface [15]. [sent-40, score-0.351]
26 Our method is complementary to this work, since our signal equalization approach can be applied before any type of descriptor matching or learning techniques. [sent-44, score-0.886]
27 We aim to equalize two signals G1(ω) and G2 (ω), which are degraded versions of the same signal Gˆ(ω), such that their frequency contents are both compatible and optimally suited for matching with respect to a given matching function Ψ. [sent-47, score-1.625]
28 We first discuss the equalization of two different signals, and then a theory of frequency scaling to produce optimal conditions for correspondence matching. [sent-53, score-1.09]
29 Signal Equalization - Two degraded versions (G1, G2) of the same signal can be equalized. [sent-55, score-0.4]
30 Left: A threshold α is applied in frequency domain to find the highest frequencies ω˜1 and ω˜2 . [sent-56, score-0.597]
31 Center: The lower of the two is used as cutoff frequency ˜ω for a lowpass filter Π ω˜. [sent-57, score-0.598]
32 Inter-Signal Equalization In the frequency domain, the degradation is modeled as G(ω) = D(ω)Gˆ(ω) + μ(ω), (2) where D(ω) is the degradation function and μ(ω) is the noise model. [sent-61, score-0.602]
33 Since the degradation we are primarily interested in is spatial blur due to de-focus, which corresponds to low-pass filtering Gˆ, we model D as box filter Π ω˜, where ω˜ is the cutoff frequency. [sent-62, score-0.335]
34 The cutoff frequency is set to be the highest frequency present in the spectrum. [sent-63, score-0.984]
35 To be robust with respect to noise, we employ a threshold α to find the highest frequencies ω˜1 and ω˜2 of the two signals G1 and G2, respectively. [sent-64, score-0.406]
36 The lower of the two is then used as cutoff frequency for the lowpass filter ω˜ = min( ω˜1 , ˜ω 2) (Fig. [sent-65, score-0.598]
37 Multiplying both signals in frequency domain by Π ω˜ will render them compatible for matching (Fig. [sent-67, score-0.841]
38 However, the frequency content is not guaranteed to be optimal for the matching function ΨNCC, which we address in the next section. [sent-69, score-0.616]
39 Frequency Scaling We are interested in finding the frequency for which spatial localization is best. [sent-72, score-0.43]
40 Considering only a single frequency ω this can be formalized as ? [sent-74, score-0.398]
41 spatial frequency ω the better the signal can be localized. [sent-96, score-0.719]
42 Due to the discrete nature of an image, the shortest wavelength possible is λ = 2 pixels and thus the highest frequency is ωmax = 2π1λ = π. [sent-97, score-0.453]
43 2 the fully equalized signal is given as G˜(ω) = Π ω˜G? [sent-104, score-0.356]
44 Equalization Implementation In this section we will describe our implementation of local signal equalization for correspondence matching. [sent-108, score-0.968]
45 Following the theoretical considerations introduced in Section 3, the algorithm requires to identify the joint cutoff frequency ˜ω to equalize the signals and scale the signal frequencies. [sent-109, score-1.329]
46 We then address frequency scaling using a scale-space approach, which is implemented using a locally centered pyramid structure. [sent-111, score-0.577]
47 Finally, these tools are used to perform local signal equalization before correspondence matching, for example in stereo reconstruction. [sent-112, score-1.207]
48 Local Frequency Maps As we discussed in Section 3, an image patch that contains high spatial frequencies matches more robustly than one with only low frequency information, and the best matching frequency is the highest possible. [sent-117, score-1.175]
49 Motivated by this theory, we aim to compute local frequency information at each point in an image and analyze the highest spatial frequency within the local region. [sent-118, score-0.949]
50 The user-defined correspondence matching window of size k is also used as the region of interest for the DFT, ensuring that we compute exactly the frequencies that will be used when matching. [sent-120, score-0.533]
51 2 illustrates the local frequency at two different points in an image. [sent-122, score-0.431]
52 In order to determine the highest reliable frequency in each local patch we need to account for noise, by thresholding on the frequency amplitudes. [sent-128, score-0.926]
53 We then determine the highest frequency ω˜p as ω˜p = maix(Ωp |aip > α) , (5) where α characterizes the amplitude of the image noise in the frequency domain. [sent-130, score-0.882]
54 Computing ω˜p for every pixel results in a local frequency map, which we illustrate for two images in Fig. [sent-134, score-0.459]
55 Notice that the local frequency map is highly correlated with the image focus. [sent-137, score-0.431]
56 This measure of local highest frequency will guide us to equalize local signals for image correspondence matching. [sent-138, score-1.185]
57 Efficient Scale-Space Representation In order to perform frequency scaling, the local signal at an image pixel can be altered by traversing the scalespace ofthe image. [sent-141, score-0.81]
58 Specifically, changing levels in the scale space corresponds to frequency scaling of the original signal. [sent-142, score-0.467]
59 However, this technique only works if the signal content is consistent between images at each level. [sent-148, score-0.413]
60 If the signal is inconsistent on any level, then matching can become erroneous (see our experiments in Section 5). [sent-149, score-0.422]
61 We build on the concept of centered pyramids [4] and construct a set of locally centered image pyramids that span the scale-space of the image (Fig. [sent-151, score-0.393]
62 First, since we are only ever interested in a region-of-interest around each pixel (defined by the matching window), we do not need to compute or store × the full image at each level, only a k k centered window as itlhleufs utrlalte imd aigne Fig. [sent-161, score-0.393]
63 Using these slices of locally centered pyramids, we will next describe our signal equalization algorithm for correspondence matching. [sent-164, score-1.103]
64 EkxqLualiztonALgcrMaliS sFit-arghm entaqcmtluh e n-cyWeontiualyxkRtravesu10n3p2 the scale-space of two images centered on xL and xR, respectively, until the local frequency signals are equalized and optimal for correspondence matching. [sent-171, score-0.992]
65 We will describe the algorithm for the application of stereo correspondence of rectified images. [sent-172, score-0.421]
66 Then for each potential correspondence (xL , xR) we determine if the highest local frequencies ω˜L and ω˜R are sufficiently high for matching. [sent-174, score-0.387]
67 If either local patch does not meet the required frequency content, then we traverse up both respective pyramids one level and repeat the process until both patches contain sufficiently high frequencies. [sent-175, score-0.635]
68 5), the patches can be used directly for correspondence computation since they are locally centered on xL and xR respectively, they contain the optimal frequency content for matching, and they contain consistent signals, allowing the best possible correspondence match. [sent-178, score-1.027]
69 Note that since the frequency information is computed only locally, we use an iterative technique to proceed through the scale-space sequentially in practice, rather than immediately computing the final equalized signal as proposed in Eqn. [sent-179, score-0.793]
70 Synthetic Plane To quantitatively evaluate the effect of the proposed signal equalization we generated a synthetic plane with wavelet noise texture and rendered it using the Mitsuba physically-based renderer [11] with simulated shallow depth of field. [sent-190, score-0.862]
71 The second algorithm extends the na¨ ıve approach using the proposed signal equalization 11888844 sizes. [sent-195, score-0.753]
72 As a third algorithm we employ PMVS [7], a state-of-the-art multi-view stereo matching algorithm. [sent-207, score-0.372]
73 Signal equalization helps the na¨ ıve approach to overcome this limitation. [sent-218, score-0.464]
74 Even for small window sizes, with signal equalization the algorithm successfully reconstructs almost the complete plane (96%) while increasing the accuracy by more than an order of magnitude. [sent-219, score-0.93]
75 This indicates that signal equalization is likely to also improve the performance of sophisticated state-of-theart matching algorithms. [sent-222, score-0.886]
76 With smaller window sizes matching is spread out over many layers in the scale-space because the frequencies present in such a limited neighborhood vary substantially across patches. [sent-226, score-0.405]
77 For smaller window sizes the frequency content varies more between patches, leading to a wider spread in matching levels. [sent-230, score-0.771]
78 dow sizes the variation of frequency content is lower and thus the matching levels are spatially more correlated, revealing the expected behavior that the matching level is a function of signal dissimilarity due to degradation. [sent-231, score-1.116]
79 Real-world Examples As a first practical example, we demonstrate the improvement of signal equalization for the reconstruction of a human face from stereo views. [sent-234, score-1.087]
80 9 (left) shows the two images acquired by the stereo rig as well as closeups of various corresponding areas with different amounts of defocus blur. [sent-238, score-0.474]
81 9 visualizes the difference in local frequency content which is directly related to camera focus and shows the problem, where for camera C2 the neck is in focus (purple) while camera C1 focuses more on the cheek (yellow). [sent-240, score-0.586]
82 Signal equalization greatly extends the reconstructable area and improves reconstruction quality as depicted in Fig. [sent-242, score-0.558]
83 A second example is stereo reconstruction from macro photography. [sent-244, score-0.364]
84 Inevitably, a stereo rig of macro images will contain different defocus regions. [sent-246, score-0.45]
85 Again, our signal equalization approach greatly improves reconstruction quality as shown in Fig. [sent-249, score-0.847]
86 Conclusion In this paper we aim to alleviate correspondence errors when matching two images that differ in signal content due to degradation. [sent-252, score-0.689]
87 Our approach is to locally equalize and optimize image signals before computing correspondence matches. [sent-254, score-0.721]
88 This is made possible by a local frequency estimation technique and an efficient scalespace image representation. [sent-255, score-0.532]
89 In our current implementation, we model signal degradation as isotropic lowpass filtering. [sent-256, score-0.458]
90 Another interesting venue for future research would be to use the differently degraded signals after matching to recover the original signal as well as possible. [sent-259, score-0.741]
91 We have described and evaluated our technique in the context of improving dense stereo reconstruction given images that are degraded by different amounts of defocus blur due to low depth of field. [sent-261, score-0.702]
92 However, correspondence matching is a fundamental tool in computer vision, and our algorithm can be applied in a variety of other contexts. [sent-262, score-0.315]
93 An example would be to equalize frame-to-frame signals for optical flow estimation or video stabilization that have been degraded by time varying blur, such as motion blur or focus change. [sent-263, score-0.718]
94 Another example is to equalize local signals for template matching or image registration. [sent-264, score-0.65]
95 The na¨ ıve algorithm successfully reconstructs areas where the signals are similar but quickly degrades with increasing signal mismatch. [sent-314, score-0.602]
96 Signal equalization greatly improves accuracy and robustness in areas of signal mismatch. [sent-315, score-0.815]
97 A stereo matching algorithm with an adaptive window: Theory and experiment. [sent-357, score-0.399]
98 An area-based stereo matching using adaptive search range and window size. [sent-377, score-0.5]
99 A taxonomy and evaluation of dense two-frame stereo correspondence algorithms. [sent-400, score-0.421]
100 Fast dense stereo matching using adaptive window in hierarchical framework. [sent-430, score-0.5]
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