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

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3.2. Scale invariant detectors 29 locations H(w) does not contain a peak, but is monotonic increasing or decreasing. Such pixel locations will be discarded. The remaining triplets indicate salient regions, however a sort of non-maximum suppression is needed. With clustering in x, y, s space close nearby detections are merged and the cluster centers are the resulting salient regions, containing a position x, y and a scale s. Different to other detectors an absolute saliency measure can be computed for each detection which introduces an ordering of the detections. The saliency Y is computed by Y = H(w)W (w). (3.17) W (w) is a weight function which measures the intra-scale unpredictability. In simple words, it measures the gray-value difference between two adjacent scales. A scale step which produces a high gray-value difference is a measure for high saliency. The intra-scale unpredictability W (w) is defined as ∫ ∣ ∣∣∣ ∂ W (w) = w ∂w p(d i, w) ∣ dI. (3.18) W (w) can be computed practically by the absolute sum of differences between the histograms of the adjacent scales and multiplied with the current window size. The absolute saliency measure Y allows to limit the detection to the most n salient features. In Figure 3.6(b) examples for detected salient regions are shown. Each salient region is visualized by the center point (yellow cross) and the characteristic scale drawn as a circle around the center point. The entropy may not necessarily be computed from the image gray-values. The method can also be applied to directional data as produced by an edge detector as shown in [52]. The method can readily be applied to a lot of different descriptors, which gives the method a large versatility. For example, in [31] salient regions are detected by computing the entropy on the cornerness value of the Harris detector. 3.2.5 Normalization The additional scale information of the scale-invariant interest detectors can be used for normalization. The scale parameter defines a circular measurement region around the detection. This is important for image matching, where corresponding detections are searched. In most cases matching works by extracting an image descriptor from the measurement region of the detection or by area based correlation of the measurement regions. Scale changes are therefore a big problem for matching. This can be overcome by normalization of the detection. By knowing the characteristic scale of the detection the measurement region can be re-sampled to a fixed canonical size which is used for correlation or descriptor extraction. Re-sampling and interpolation however have to be performed carefully. Best results will be gained if the bigger measurement region is downsized to fit the smaller one. If the scale change is high downsizing according to the scale-space theory (Gauss filtering and re-sizing) should be performed. Normalizing the measurement region in the described way is possible for all previously described detector methods. In addition to scale normalization Lowe describes a method to normalize the DOG-keypoints for an arbitrary rotation [66]. The method works by computing a histogram of the gradients which occur in the measurement region. A histogram with 36 bins covering the 360 ◦ is reported to give good results. The histogram maximum defines the principal orientation of the detection. If the histogram contains multiple equally strong local maxima the detection gets assigned multiple orientations. To compensate for the low resolution of the histogram (every bin accounts for 10 ◦ )
3.3. Affine invariant detectors 30 (a) (b) Figure 3.6: Detection examples for scale invariant DOG and salient region detector on ”Group” scene. (a) DOG detector. (b) Salient region detector. a parabola is fit to the maxima and its neighbors and the interpolated peak of the parabola is used as the principal orientation. This principal orientation can now be used in the re-sampling stage of the normalization to rotate the detection into a canonical orientation. This orientation estimation has be successfully used for the DOG-keypoints. However, the method can also be applied without restrictions to all of the previously described scale-invariant interest detectors. 3.3 Affine invariant detectors Affine invariant detectors are designed to produce repetitive detections despite of an arbitrary affine transformation of the image. For an example see Figure 3.7. Figure 3.7(a) shows a single detection on the original image. Figure 3.7(b) shows the detection on an affine transformed version of the original. The affine transformation contains a rotation of 30 ◦ , an axis shear of 10 ◦ , a scale change in x and y of 90% and 80% respectively. Despite the distortion the center point is detected repetitively and the ellipse detected in the transformed image covers the same content as in the original image. Affine invariant detectors were developed to cope with heavy perspective distortions in wide-baseline scenarios where large view-point changes occur. The effect of a perspective distortion can be approximated locally by an affine transformation. Locally means in this respect a small area (measurement region) around an interest point detection. The in the following presented affine invariant detectors are based on different concepts. The affine-invariant Harris and Hessian detectors are based on simple interest point detectors and searches an affine invariant measurement region for each point detection. An other method, the MSER detector finds homogeneous, characteristic delineated image regions with a method not affected by an affine transformation. However, independent of the detection method each detector detects a measurement region and a characteristic point within the measurement region. The shape of the
Page 1 and 2: Graz University of Technology Insti
Page 3 and 4: Abstract Visual map building and lo
Page 5 and 6: Contents 1 Introduction to mobile r
Page 7 and 8: CONTENTS vi 7.1.5 Sub-map linking .
Page 9 and 10: 1.1. Localization and map building
Page 11 and 12: 1.3. What has already been achieved
Page 13 and 14: 1.5. How can it get solved? 6 fully
Page 15 and 16: 1.6. Contribution of this thesis 8
Page 17 and 18: 1.7. Structure of the thesis 10 com
Page 19 and 20: 2.2. Localization from point featur
Page 21 and 22: 2.2. Localization from point featur
Page 23 and 24: 2.4. Localization from plane featur
Page 25 and 26: 2.5. Summary 18 or not. Clearly thi
Page 27 and 28: Chapter 3 Local detectors Research
Page 29 and 30: 3.1. Interest point detectors 22 fu
Page 31 and 32: 3.2. Scale invariant detectors 24 r
Page 33 and 34: 3.2. Scale invariant detectors 26 (
Page 35: 3.2. Scale invariant detectors 28 3
Page 39 and 40: 3.3. Affine invariant detectors 32
Page 47 and 48: 3.4. Comparison of the described me
Page 49 and 50: 3.4. Comparison of the described me
Page 51 and 52: 44 But using a plane to plane homog
Page 53 and 54: 4.2. Representation of the detectio
Page 55 and 56: 4.3. Detection correspondence 48 th
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
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5.6. Detector evaluation: Repeatabi
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5.7. Combining MSCC with other loca
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6.1. Wide-baseline region matching
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6.1. Wide-baseline region matching
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6.2. Piece-wise planar scene recons
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Chapter 7 Living in a piecewise pla
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7.1. Map building 112 s,R,t sub-map
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7.1. Map building 114 x = (x 1 ...x
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7.1. Map building 116 distance is u
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7.1. Map building 118 normalization
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7.2. Localization 120 where N = |D
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7.2. Localization 122 registration
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7.2. Localization 124 (a) (b) (c) F
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7.2. Localization 126 3D structure
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7.2. Localization 128 other landmar
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Chapter 8 Map building and localiza
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8.2. Map building experiments 132 8
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8.2. Map building experiments 134 D
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8.2. Map building experiments 136 (
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8.2. Map building experiments 138 F
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8.2. Map building experiments 140 F
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8.3. Localization experiments 142 8
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8.3. Localization experiments 144 F
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8.3. Localization experiments 146 F
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8.3. Localization experiments 148 8
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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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