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Partial Edge Contour Matching for Object Detection

We propose a method for object category localization by partially matching edge contours to a single shape prototype of the category. Previous work in this area either relies on piecewise contour approximations, requires meaningful supervised decompositions, or matches coarse shape-based descriptions at local interest points. Our method avoids error-prone pre-processing steps by using all obtained edges in a partial contour matching setting. The matched fragments are efficiently summarized and aggregated to form location hypotheses. The efficiency and accuracy of our edge fragment based voting step yields high quality hypotheses in low computation time.

Partial Contours Description for Efficient Matching (PAC'EM)

Our goal is to exploit the connectedness of an edge contour implicitly yet allowing to retrieve parts of an edge as fragments. Many di erent methods have been proposed for partial contour matching. Angular representations are a natural choice due their direct encoding of geometric layout.

As a fi rst step we sample a xed number N of points from the closed reference contour that can be ordered as R = {r_1, r_2, ..., r_N}. As next step we have to extract connected and labeled edge contours from the query image, i.e. we link the results to a set of coordinate lists. For the obtained query contours, points are sampled at equal distance, resulting in a sequence of points B = {b_1, b_2, ..., b_M} per contour.



We use a matrix of angles which encode the geometry of the sampled points leading to a translation and rotation invariant description for a query contour. The descriptor is calculated from the relative spatial orientations between lines connecting the sampled points. We calculate angles ij between a line connecting the points bi and bj and a line to a third point relative to the position of the previous two points. This angle is defi ned



where b_i and b_j are the ith and jth points in the sequence of sampled points of the contour and  is an off set parameter of the descriptor (5 for all experiments). See Figure 2 for an illustration of the choice of points along the contour. The third point is chosen depending on the position of the other two points to ensure that the selected point is always inside the contour. This is the neat part which allows us to formulate the descriptor as a self-containing descriptor of any of its parts. Here are some properties of this descriptor:

  1. Its angular description makes it translation and rotation invariant.
  2. A shift along the diagonal of the descriptor handles the uncertainty of the starting point in edge detection.
  3. it represents the connectedness of contours by using the sequence information providing a local (close to matrix diagonal) and global (far from matrix diagonal) description.
  4. A larger scale is simply a subsampling of the 2D descriptor, since any larger scales are implicitly included as a hierarchy.
  5. The de finition as a self-containing descriptor allows to implicitly retrieve partial matches which is a key requirement for cluttered and broken edge results.
So in short: translation and rotation invariant, connectedness due sequence information, scale as dimension reduction subsampling included, and most importantly self-containing description to allow any partial matching.



Publications

  1. Using Partial Edge Contour Matches for Efficient Object Category Localization (Paper as PDF)
    Hayko Riemenschneider, Michael Donoser and Horst Bischof
    Proceedings of European Conference on Computer Vision (ECCV), 2010
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