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Logo (graphic entity that contains colors, shapes, textures and identifies organizations, goods, etc.) localization and recognition is a subproblem of object detection and recognition and a challenging pattern recognition task. Applications are in the automotive industry, sports transmissions, legal or feedback for advertising. Logos in natural images are approached within retrieval systems [1] [6], [4], etc. or by integrated detection (localization and recognition) [2], [7], etc. Our contribution falls in the second category and consists in: (1) a new class prototyping method based on a central image extracted by analyzing the homographies graph and re-projecting the relevant keypoints on that image (2) a logo detection system that exhibits great performance. The main conceptual difference to previous systems is that they manually branched their process to deal with corner-cases, while we perform the branching automatically, proposing a compact and self-adjusting system. Class Description. In the training phase (detailed in Fig. 1) we construct models (prototypes) to describe classes. In the testing phase (Fig. 2) the query image is compared with class prototypes and if they are enough similar we count a detection. Feature extraction. The logo images are described by the Affine Difference of Gausssians (ADoG) [5] followed by the description with oriented SIFT elliptical local features. ADoG provides more keypoints on logos than other choices, while elliptical features are able to provide correctly the orientation even for circular logos. Class Graph. All the logo crops from the same class are grouped in a weighted graph: the nodes are the logos, while an edge is created if a homography is found between that pair of logos-nodes. The edge has an weight equal to the inverse of the number of keypoints pairs matched. The homography between two logos is found with the direct linear transformation (DLT) and 4 keypoint pairs are needed for this determination. The matching between the reference logo and the subject logo is found with RANSAC. Yet, to provide the best match, one needs to iterate more subsets than usual [3]. Next, the quality of the homographic fit is evaluated using an error map built as the Hellinger distance between the reference logo and the back-projected logo described with Dense SIFT. Given the class graph, the central image is the node with the most connections. Class Model. The class model is built by agglomerating onto the central image the suitable keypoints and their SIFT description. This information is taken from all the logo images from the main cluster of the class graph, by projecting them on the plane of the central image. Keypoints in images directly connected to the central image are backprojected (by inverting the matching homography) on the central one. The equivalent homography between images that are not directly connected to the central image is determined by composing the homographies placed on the path between that image and the central one. The chosen path is the one that ensures minimum cumulative weight. The corresponding SIFT Figure 2: The schematic of the system used to locate and classify a logo in a testing image.

Elliptical ASIFT Agglomeration in Class Prototype for Logo Detection