PHD Thesis - Institute for Computer Graphics and Vision - Graz ...

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6.2. Piece-wise planar scene reconstruction 99 (a) (b) (c) (d) (e) (f) (g) (h) Figure 6.3: Detecting planar regions with homographies. (a) Left image I L . (b) Right image I R . (c) Right image I R ′ after transformation with the homography induced by the top plane. (d) Overlay of I L and I R ′ with two rectangular windows marked. (e),(f) The upper window in I L and I R ′ . The similarity is high. (g),(h) The lower window in I L and I R ′ . The similarity is low. convergence, the final growing step is repeated in the full resolution images to obtain the optimal result. The uncalibrated case So far, we have assumed a calibrated setup, i.e., the projection matrices for all cameras are known, and the principal aim was a Euclidean 3D reconstruction of the planar structures. However, the relations upon which the method is built, are also valid in the uncalibrated case, when we have only a set of images with unknown camera parameters. In this case, the algorithm can still recover the scene planes, and we will argue that for scenes with a lot of planar structures, this facilitates the subsequent orientation and self-calibration. Given the corresponding regions, the homography now has to be estimated from four correspondences, without using the as yet unknown epipolar constraint. Like in the calibrated case, a robust estimator such as ransac [28] should be used to make sure that the estimate is not corrupted by any remaining matching errors. There is a subtle difference between the two methods here, which may lead to slight differences in the results: in the calibrated case, both the plane corresponding to the homography and the 3D point corresponding to the two image points are known in Euclidean space. Therefore, one can use the orthogonal distance from the point to the plane to find inliers. In the uncalibrated case, no Euclidean frame is available, hence we use the symmetric transfer error d(x 1 , Hx 0 ) 2 + d(x 0 , H −1 x 1 ) 2 in the image plane. Note that the uncalibrated case has a degenerate situation: if the camera which took the images underwent only a rotation around its projection center, then the two entire image planes are always related by a single homography, which is not due to any 3D plane.
6.2. Piece-wise planar scene reconstruction 100 When dealing with scenes, which contain a large amount of planar structure, recovering these structures beforehand can benefit subsequent structure-and-motion steps. During the growing stage, a large and well-distributed set of correspondences is recovered, which are already checked for correctness, because they satisfy the homography, a stronger constraint than the fundamental matrix. This large and outlier-free point set enables reliable and accurate estimation of the fundamental matrix. Note that as soon as at least two planar structures are found, which are different and cannot be merged, it is guaranteed that we are not dealing with a degenerate case of motion estimation, since 1. the camera motion cannot be a pure rotation, otherwise all detected homographies would be the same and would eventually merge. 2. the recovered scene points cannot be coplanar, since that would again imply that all detected homographies would be the same. Although we have not further investigated this issue, we conjecture that in the case of more than two images, the large amount of correct and well-distributed points would also benefit self-calibration to upgrade the projective reconstruction to a Euclidean one with a method such as [88]. In section 6.2.3, some experiments are given for the uncalibrated case, which show that in practice, the segmentation into planar scene parts is almost the same as for the calibrated case. 6.2.3 Experimental evaluation In this section we present experiments on synthetic and real image data. First, we evaluate the reconstruction accuracy and the robustness of the method under large baseline changes on synthetic image data. Second, we show the performance of the method on practically relevant scenes in experiments with real image data Synthetic Images The ’Cube’ data-set consists of images with resolution 800×800 pixels, which have been rendered from a CAD-model of a cube. Each plane has been textured differently using real world images from the freely available ’Graffiti’ image database of Mikolajczyk 5 . The interior and exterior orientation are known from the rendering. Seed regions were detected by an extended version of the salient region detector [31]. The following results were gained using the calibrated method. Figure 6.4(a) shows the left image with the detected matching planar regions. Figure 6.4(b) shows the initial seed regions. The homographies and planes are calculated from the point correspondences gained in the region matching process. Figure 6.4(c-g) shows the intermediate steps of iterative region growing and homography estimation, as described in the previous section. Figure 6.4(h) shows the final segmentation of the image. The delineation has been improved by intersecting the final planes and snapping to the reprojected intersection lines. The reconstruction is very accurate. Table 6.1 compares the reconstructed edge length and the angle of the planes to the z-axis with the ground truth. The detection and delineation of the planar scene regions can be regarded as a segmentation of the input images into planar regions. For the synthetic ’Cube’ data set, ground truth is also available for this segmentation process, i.e. the correct label is known for every pixel. A 5 ’Graffiti’ images from Krystian Mikolajczyk available at http://www.robots.ox.ac.uk/∼vgg/research/affine/
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Graz University of Technology Insti
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Abstract Visual map building and lo
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Contents 1 Introduction to mobile r
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CONTENTS vi 7.1.5 Sub-map linking .
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1.1. Localization and map building
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1.3. What has already been achieved
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1.5. How can it get solved? 6 fully
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1.6. Contribution of this thesis 8
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1.7. Structure of the thesis 10 com
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2.2. Localization from point featur
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2.2. Localization from point featur
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2.4. Localization from plane featur
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2.5. Summary 18 or not. Clearly thi
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Chapter 3 Local detectors Research
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3.1. Interest point detectors 22 fu
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3.2. Scale invariant detectors 24 r
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3.2. Scale invariant detectors 26 (
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3.2. Scale invariant detectors 28 3
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3.3. Affine invariant detectors 30
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3.4. Comparison of the described me
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3.4. Comparison of the described me
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44 But using a plane to plane homog
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4.2. Representation of the detectio
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Page 57 and 58: 4.4. Point transfer using the trifo
Page 59 and 60: 4.5. Ground truth generation 52 usi
Page 61 and 62: 4.6. Experimental evaluation 54 Fig
Page 63 and 64: 4.6. Experimental evaluation 56 rep
Page 65 and 66: 4.6. Experimental evaluation 58 MSE
Page 67 and 68: 4.6. Experimental evaluation 60 mat
Page 69 and 70: 4.6. Experimental evaluation 62 vie
Page 71 and 72: 4.6. Experimental evaluation 64 vie
Page 73 and 74: 4.6. Experimental evaluation 66 rel
Page 75 and 76: Chapter 5 Maximally Stable Corner C
Page 77 and 78: 5.1. The MSCC detector 70 (a) (b) (
Page 79 and 80: 5.2. Region representation 72 400 (
Page 81 and 82: 5.3. Computational complexity 74 6.
Page 83 and 84: 5.5. Detection examples 76 paramete
Page 85 and 86: 5.5. Detection examples 78 Figure 5
Page 87 and 88: 5.6. Detector evaluation: Repeatabi
Page 89 and 90: 5.7. Combining MSCC with other loca
Page 99 and 100: 6.1. Wide-baseline region matching
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Page 103 and 104: 6.2. Piece-wise planar scene recons
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Page 117 and 118: Chapter 7 Living in a piecewise pla
Page 119 and 120: 7.1. Map building 112 s,R,t sub-map
Page 121 and 122: 7.1. Map building 114 x = (x 1 ...x
Page 123 and 124: 7.1. Map building 116 distance is u
Page 125 and 126: 7.1. Map building 118 normalization
Page 127 and 128: 7.2. Localization 120 where N = |D
Page 129 and 130: 7.2. Localization 122 registration
Page 131 and 132: 7.2. Localization 124 (a) (b) (c) F
Page 133 and 134: 7.2. Localization 126 3D structure
Page 135 and 136: 7.2. Localization 128 other landmar
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8.3. Localization experiments 150 (
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Chapter 9 Conclusion More than 25 y
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9.1. Future work 154 Map building a
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9.1. Future work 156 information ca
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A.1. Projective ellipse transfer 15
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A.1. Projective ellipse transfer 16
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A.2. Affine approximation of ellips
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Appendix B The trifocal tensor and
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Bibliography [1] S. Atiya and G. Ha
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168 [31] F. Fraundorfer and H. Bisc
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170 [61] U. Köthe. Edge and juncti
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172 [92] F. Schaffalitzky and A. Zi
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PHD Thesis - Institute for Computer Graphics and Vision - Graz ...

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