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This article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication. <strong>IEEE</strong> TRANSACTION ON PATTERN ANALYSIS AND MACHINE INTELLIGENCE 8 To this end, we collected 40 image pairs with rotation transformation (some ofthemalsoinvolve scale changes) from the Internet [43], each of which is related by a homography that is supplied along with the image pair. They are captured from five types of scenes as shown in Fig. 1 in the supplemental material. For each image pair, we extracted SIFT descriptors of the SIFT keypoints and matched them by the nearest neighbor of the distances of their descriptors. We focus on the orientation estimation errors between corresponding points. For a pair of corresponding points (x, y, θ) and (x ′ ,y ′ ,θ ′ ), the orientation estimation error is computed by: ε = θ ′ − f(θ; H) (1) where f(θ; H) is the ground truth orientation of θ when warping from the first image to the second image according to the homography H between the two images. Fig. 2 presents some statistical results. Fig. 2(a) is the histogram of orientation estimation errors among all corresponding points. A similar histogram was obtained by Winder and Brown [33] by applying random synthetic affine warps. Here we use real image pairs with mainly rotation transformation. Fig. 2(b) shows the histogram of orientation estimation errors among those corresponding points that are matched by their SIFT descriptors. Fig. 2(b) indicates that for SIFT descriptor, orientation estimation error of no more than 20 o is required in order to match corresponding points correctly. However, it can be clearly seen from Fig. 2(a) that many corresponding points have errors larger than 20 o . Only 63.77% of the corresponding points have orientation estimation errors in the range of [-20 o ,20 o ]. Those corresponding points with large orientation estimation errors (≥ 20 o ) may not be correctly matched by comparing their descriptors. In other words, 36.23% of the corresponding points will be incorrectly matched mainly due to their large orientation estimation errors. Therefore, orientation estimation has a significant impact on distinctive descriptor construction. In order to give more insight into the influence of the estimated orientation on the matching performance of local descriptor, we conducted some image matching experiments. The experimental images downloaded from the Internet [43] are shown in Fig. 3. The tested image pairs are selected with the most challenging ones among those in the dataset to perform experiments on image blur, JPEG compression and illumination change, i.e., the 1st and the 6th images in the dataset. For each image pair, there exists a global rotation between the two images. Specifically, 0 o for image pairs in Fig. 3(d)-3(f), and a certain degree for image pairs in Fig. 3(a)-3(c). We November 26, 2011 DRAFT
This article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication. <strong>IEEE</strong> TRANSACTION ON PATTERN ANALYSIS AND MACHINE INTELLIGENCE 9 (a) Fig. 2. Distributions of the orientation estimation errors between corresponding points. (a) The distribution among all the corresponding points, only 63.77% of the corresponding points have errors in the range of [-20 o ,20 o ]. (b) The distribution among those corresponding points that are matched by their SIFT descriptors. See text for details. used two local descriptors (SIFT and DAISY) with two different orientation assignment methods for image matching: (1) The orientation is assigned by the ground truth orientation, and the constructed local descriptors are denoted as Ori-SIFT and Ori-DAISY. (2) The orientation is assigned by the method suggested in [6], and the constructed local descriptors are denoted as SIFT and DAISY. By comparing the performance of Ori-SIFT (resp. Ori-DAISY) with SIFT (resp. DAISY), we can get a clear understanding of the influence of the orientation estimation on constructing local descriptor for image matching. Experimental results are shown below the tested image pairs in Fig. 3. It can be seen from Fig. 3 that Ori-SIFT (Ori-DAISY) significantly outperforms SIFT (DAISY). Since the only difference between Ori-SIFT (Ori-DAISY) andSIFT (DAISY) is the orientation assignment method, it demonstrates that a more accurate orientation estimation will largely improve the performance of the local descriptor. The currently used orientation estimation method based on the histogramming technique is still an error-prone procedure and will adversely affect the performance of the local descriptor. Therefore, it leaves a long way for local descriptor to be inherently rotation invariant 1 while maintaining its high distinctiveness. In this paper, we make an effort along this way and propose constructing local descriptors by 1 It means achieving rotation invariance without resorting to an estimated orientation for reference. November 26, 2011 DRAFT (b)
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