cvpr cvpr2013 cvpr2013-47 knowledge-graph by maker-knowledge-mining
Source: pdf
Author: Julio Zaragoza, Tat-Jun Chin, Michael S. Brown, David Suter
Abstract: We investigate projective estimation under model inadequacies, i.e., when the underpinning assumptions oftheprojective model are not fully satisfied by the data. We focus on the task of image stitching which is customarily solved by estimating a projective warp — a model that is justified when the scene is planar or when the views differ purely by rotation. Such conditions are easily violated in practice, and this yields stitching results with ghosting artefacts that necessitate the usage of deghosting algorithms. To this end we propose as-projective-as-possible warps, i.e., warps that aim to be globally projective, yet allow local non-projective deviations to account for violations to the assumed imaging conditions. Based on a novel estimation technique called Moving Direct Linear Transformation (Moving DLT), our method seamlessly bridges image regions that are inconsistent with the projective model. The result is highly accurate image stitching, with significantly reduced ghosting effects, thus lowering the dependency on post hoc deghosting.
Reference: text
sentIndex sentText sentNum sentScore
1 Brown† David Suter∗ ∗Australian Centre for Visual Technologies, The University of Adelaide †School of Computing, National University of Singapore Abstract We investigate projective estimation under model inadequacies, i. [sent-2, score-0.342]
2 We focus on the task of image stitching which is customarily solved by estimating a projective warp — a model that is justified when the scene is planar or when the views differ purely by rotation. [sent-5, score-1.281]
3 Such conditions are easily violated in practice, and this yields stitching results with ghosting artefacts that necessitate the usage of deghosting algorithms. [sent-6, score-0.505]
4 , warps that aim to be globally projective, yet allow local non-projective deviations to account for violations to the assumed imaging conditions. [sent-9, score-0.319]
5 Based on a novel estimation technique called Moving Direct Linear Transformation (Moving DLT), our method seamlessly bridges image regions that are inconsistent with the projective model. [sent-10, score-0.342]
6 The result is highly accurate image stitching, with significantly reduced ghosting effects, thus lowering the dependency on post hoc deghosting. [sent-11, score-0.138]
7 In this paper, we are primarily concerned with model inadequacies in projective estimation. [sent-17, score-0.384]
8 More specifically, we consider situations where the enabling assumptions for the projective model are not fully met by the data, thus fundamentally limiting the achievable goodness of fit. [sent-18, score-0.397]
9 Image stitching is typically solved by estimating 2D projective warps to bring images into alignment. [sent-22, score-0.871]
10 Parametrised by 3 3 homographies, 2D projective warps arejustified ifthe scene is planar or ifthe views differ purely by rotation [17]. [sent-23, score-0.807]
11 Thus the projective model cannot adequately characterise the required warp, causing misalignments or ghosting effects. [sent-25, score-0.526]
12 Many commercial stitching software like Autostitch and Photosynth (specifically the panorama tool) use projective warps1 , arguably for their simplicity. [sent-28, score-0.636]
13 When the requisite imaging conditions are not met, their success relies on deghosting algorithms to remove unwanted artefacts [17]. [sent-29, score-0.1]
14 Here, we offer a different strategy: instead of relying on a projective model (which is often inadequate) and then fix the resulting errors, we adjust the model based on the data to improve the fit. [sent-30, score-0.342]
15 , warps that aim to be globally projective, yet allow local deviations to account for model inadequacy; Fig. [sent-33, score-0.319]
16 Our method significantly reduces alignment errors, yet is able to maintain overall geometric plausibility. [sent-35, score-0.07]
17 Note that our aim is not to perform image stitching for arbitrary camera motions (e. [sent-38, score-0.292]
18 Rather, our aim is to tweak the projective model to fit the data as accurately as possible. [sent-41, score-0.342]
19 It is also not our goal to dispense with deghosting algorithms, which are still useful if there are serious misalignments or moving objects. [sent-42, score-0.175]
20 However, we argue that a good initial stitch is very desirable since it imposes a much lower requirement on subsequent deghosting and postprocessing; the result in Fig. [sent-43, score-0.074]
21 More fundamentally, we learn the proposed warp based on a novel estimation technique called Moving DLT. [sent-45, score-0.482]
22 It is inspired by the Moving Least Squares (MLS) method [2] for image manipulation [14], but our method applies projective regularisation instead of rigid or affine regularisation. [sent-46, score-0.5]
23 This is essential to ensure that the warp extrapolates correctly beyond the image overlap (interpolation) region to maintain perceptual realism. [sent-47, score-0.516]
24 1(b) and 1(c) contrast warps from × 1Both tools require the camera to rotate about a point, or that the photos be taken from the same spot and with the same focal length. [sent-49, score-0.287]
25 aspx 222333333977 ’x1FDitecdorwreasrp xondences’xF1iDtecdorwreasrp oxndences’xF1iDt ecdorwreasrp oxndences (a) Projective warp. [sent-57, score-0.084]
26 The two views differ by a rotation and translation, and the data are not corrupted by noise. [sent-63, score-0.112]
27 (a) A 1D projective warp, parametrised by a 2 2 homography, is unable to model the local deviations of the data. [sent-64, score-0.43]
28 Note that these deviations are caused purely by model inadequacy since there is no noise in the data. [sent-65, score-0.16]
29 (b) An as-affine-as-possible warp, estimated based on [14], can interpolate the local deviations better, but fails to impose global projectivity. [sent-66, score-0.097]
30 (c) Our as-projective-as-possible warp interpolates the local deviations flexibly and extrapolates correctly following a global projective trend. [sent-68, score-1.023]
31 Being able to interpolate to minimise ghosting and extrapolate flexibly corectly to maintain geometric consistency are vital qualities for image stitching. [sent-70, score-0.314]
32 Our work is different in that we fit projective functions instead of geometric surfaces. [sent-72, score-0.342]
33 Further, function extrapolation is a crucial aspect that was not stressed in [6]. [sent-73, score-0.083]
34 2 and 3 introduce the proposed warp and its efficient learning for image stitching. [sent-78, score-0.482]
35 Related work While the fundamentals of image stitching are well studied (see [17] for an excellent survey), how to produce good results when the data is noisy or uncooperative is an open problem. [sent-84, score-0.267]
36 In our context, we categorise previous works into two groups: (1) methods that reduce ghosting by constructing better alignment functions, and (2) methods that reduce ghosting after alignment using advanced methods in compositing, pixel selection or blending. [sent-85, score-0.36]
37 In the second group, seam cutting [1, 3] and Poisson blending [13] are influential. [sent-86, score-0.07]
38 Given matching features between the original and target image frames, the novel view is synthesised by warping the original image using an as-similar-as-possible warp [8] that jointly minimises the registration error and preserves the rigidity of the scene. [sent-95, score-0.686]
39 The method also pre-warps the original image with a homography, thus effectively yielding a smoothly interpolating projective warp. [sent-96, score-0.381]
40 Imposing scene rigidity minimises the dreaded “wobbling” effect in the smoothed video. [sent-97, score-0.117]
41 4, in image stitching where there can be large rotational and translational difference between views, their method does not interpolate flexibly enough due to the rigidity constraints. [sent-99, score-0.498]
42 A recent work proposed smoothly varying affine warps for image stitching [9]. [sent-104, score-0.649]
43 An interesting innovation of [9] is an affine initialisation of the registration function, which is then deformed locally to minimise registration errors while maintaining global affinity. [sent-106, score-0.211]
44 Fundamentally, using affine regularisation may be suboptimal, since an affinity does not contain sufficient degrees of freedom to achieve a fully perspective warp [17], e. [sent-107, score-0.64]
45 4 and 5 (second row) show, while the method can interpolate flexibly, it produces highly distorted results in the extrapolation region, where there are no data to guide the local deformation and the warp reverts to global affinity; Fig. [sent-111, score-0.628]
46 Essentially theirs is a special case of a piece-wise projective warp, which is more flexible than using a single homography. [sent-115, score-0.342]
47 As-Projective-As-Possible Warps We first review the estimation of projective transformations customarily used in image stitching, and then describe the proposed as-projective-as-possible warp. [sent-120, score-0.379]
48 A projective warp or and homography aims to map x to x? [sent-128, score-0.952]
49 The divisions in (2) cause the warp to be non-linear, as Fig. [sent-134, score-0.482]
50 do not differ purely by rotation or are not of a planar scene, using a basic projective warp inevitably yields ghosting effects in the alignment. [sent-166, score-1.07]
51 To alleviate this problem, our idea is to warp each x∗ using a location dependent homography ˜x? [sent-167, score-0.61]
52 of Intuitively, since (8) assigns higher weights to data closer to x∗, the projective warp H∗ better respects the local structure around x∗ . [sent-179, score-0.853]
53 Contrast this to (5) which uses a single and global projective warp H for all x∗ . [sent-180, score-0.824]
54 Moreover, as x∗ is moved continuously in its domain I, the warp H∗ also varies smoothly. [sent-181, score-0.482]
55 This produces an overall warp that adapts flexibly to the data, yet attempts to be as-projectiveas-possible. [sent-182, score-0.627]
56 1(c) and 3(c) illustrate such a warp in 1D and 2D. [sent-184, score-0.482]
57 , when x∗ is in a data poor or extrapolation region. [sent-195, score-0.083]
58 (11) This also serves to regularise the warp, whereby a high γ reduces the warp complexity; in fact as γ → 1 the warp reduces to the global projective warp. [sent-201, score-1.362]
59 Conceptually, Moving DLT can be seen as the projective version of MLS [2]. [sent-205, score-0.342]
60 In the context of warping points in 2D for image manipulation [14], MLS estimates for each x∗ an affine transformation defined by a matrix F∗ ∈ R2×3 x? [sent-206, score-0.129]
61 ible warps, but such warps are ultimately only as-affine-aspossible; see Fig. [sent-224, score-0.262]
62 222333334199 ’x1FiDt ecdorwreasrp xondences ×× Figure 2. [sent-227, score-0.084]
63 Results from Moving DLT without regularisation for a 1D projective estimation problem on synthetic data. [sent-228, score-0.419]
64 Efficient Learning for Image Stitching Here we describe an efficient algorithm for image stitching based on the proposed warp. [sent-230, score-0.267]
65 One might argue against RANSAC since we consider cases where the inliers may deviate from the projective model. [sent-233, score-0.385]
66 3(c) illustrates a warp learnt with 100 100 cells for a 1500 2000-pixel image pair. [sent-241, score-0.539]
67 Note that, even without parallel computations, learning the warp in Fig. [sent-244, score-0.482]
68 3 with 100 100 cells and N = 2100 × keypoint matches (A is of size 4200 9) takes less than a minute on a Pentium i7 2. [sent-245, score-0.146]
69 Further speedups are possible if we realise that, for most cells, due to the offsetting (11) many of the weights do not differ from the offset γ. [sent-248, score-0.122]
70 3(d) histograms across all cells the number of weights that differ from γ (here, γ = 0. [sent-251, score-0.153]
71 A vast majority of cells (> 40%) have fewer than 20 weights (out of 2100) that differ from γ. [sent-253, score-0.153]
72 Observe that the warp is globally projective for extrapolation, but adapts flexibly in the overlap region for better alignment. [sent-262, score-0.969]
73 (d) Histogram of number of weights γ for the cells in (b). [sent-335, score-0.086]
74 The input images correspond to views that differ by rotation and translation. [sent-338, score-0.112]
75 log2 We compare our as-projective-as-possible (APAP) warp against other warp improvement methods for image stitching, namely, content preserving warps (CPW) [10], dual homography warps (DHW) [4], and smoothly varying affine (SVA) [9]. [sent-352, score-1.76]
76 To cogently differentiate the methods, we avoid sophisticated postprocessing like seam cutting and straightening such as in [4], and simply blend the aligned images by intensity averaging such that any misalignments remain obvious. [sent-353, score-0.149]
77 We select testing images which correspond to views that differ by more than a pure rotation. [sent-356, score-0.112]
78 In addition, following [10], for CPW we pre-warp the source image with the global homography estimated via DLT on the inliers returned by RANSAC. [sent-369, score-0.171]
79 4 and 5 depict results on the railtracks and temple image pairs. [sent-374, score-0.073]
80 The baseline warp (global homography via DLT on inliers) is clearly unable to satisfactorily align the images since the views do not differ purely by rotation. [sent-376, score-0.791]
81 SVA, DHW and Autostitch are marginally better, but significant ghosting remains. [sent-377, score-0.138]
82 Further, note the highly distorted warp produced by SVA, especially in the extrapolation regions. [sent-378, score-0.588]
83 was not completely successful; observe the misaligned rail tracks and tiles on the ground. [sent-381, score-0.066]
84 This reduces the burden on postprocessing; we have confirmed that pyramid blending [17] is sufficient to account for exposure differences and to smoothen the blend. [sent-383, score-0.069]
85 While CPW with pre-warping is able to produce good results, the rigidity constraints (a grid like in Fig. [sent-384, score-0.083]
86 3(b) is defined and discouraged from deforming) may counterproductively limit the flexibility of the warp (observe the only slightly nonlinear outlines of the warped images3). [sent-385, score-0.551]
87 Thus although the rail tracks and tiles are aligned correctly (more × × keypoint matches exist in these relatively texture-rich areas to influence the warp), ghosting occurs in regions near the skyline. [sent-386, score-0.293]
88 For DHW, CPW, SVA and APAP (without WSVD updating), we record the total duration for warp estimation (plus any data structure preparation time), pixel warping and blending. [sent-389, score-0.53]
89 While 8 mins was reported in [9] for 500 500 images, in our experiments SVA takes 15 mins for temple (1024 768) and 1hour for railtracks (1500 2000). [sent-393, score-0.131]
90 We then incrementally warp the other images via APAP onto the panorama. [sent-396, score-0.509]
91 Quantitative benchmarking To quantify the alignment accuracy of an estimated warp f : R2 → R2, we compute the root mean squared error (RMSE) of f on a set of keypoint matches {xi, x? [sent-401, score-0.613]
92 mly partitioned the available SIFT keypoint matches into a “training” and “testing” set. [sent-412, score-0.089]
93 1, imposing warp rigidity is essential to prevent wobbling in video stabilisation, which is the original aim of [10]. [sent-419, score-0.607]
94 This permits the direct application of the various warp estimation methods. [sent-426, score-0.482]
95 For SVA this is most likely due to its affine instead of projective regularisation; cf. [sent-433, score-0.423]
96 Additionally, for CPW, it appears that enforcing rigidity has perturbed the effects of the pre-warping by a global homography. [sent-436, score-0.083]
97 In contrast, APAP reduces gracefully to a global homography as the camera centres coincide, and provides the most accurate alignment as the translation increases. [sent-437, score-0.31]
98 The results on image stitching showed encouraging results, where our method was able to accurately align images that differ by more than a pure rotation. [sent-440, score-0.362]
99 The experiments also demonstrated that the proposed warp reduces gracefully to a global homography as the camera translation tends to zero, but adapts flexibly to account for model inadequacy as the translation increases. [sent-441, score-0.955]
100 Seamless image stitching of scenes with large motions and expoure differences. [sent-469, score-0.267]
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