Abstract
Shape analysis of curves in Rn is an active research topic in computer vision. While shape itself is important in many applications, there is also a need to study shape in conjunction with other features, such as scale and orientation. The combination of these features, shape, orientation and scale (size), gives different geometrical spaces. In this work, we define a new metric in the shape and size space, S2, which allows us to decompose S2 into a product space consisting of two components: S4×R, where S4 is the shape space. This new metric will be associated with a distance function, which will clearly distinguish the contribution that the difference in shape and the difference in size of the elements considered makes to the distance in S2, unlike the previous proposals. The performance of this metric is checked on a simulated data set, where our proposal performs better than other alternatives and shows its advantages, such as its invariance to changes of scale. Finally, we propose a procedure to detect outlier contours in S2 considering the square-root velocity function (SRVF) representation. For the first time, this problem has been addressed with nearest-neighbor techniques. Our proposal is applied to a novel data set of foot contours. Foot outliers can help shoe designers improve their designs.
Highlights
Shape analysis of curves in Rn, where n ≥ 2, is an important branch in many applications, including computer vision and medical imaging
Srivastava et al [4] presented a special representation of curves, called the square-root velocity function, or SRVF, under which a specific elastic metric becomes an L2 metric and simplifies the shape analysis
There are a variety of techniques for outlier detection for different types of data in any metric space based on nearest-neighbor techniques, they have not been fully exploited in the shape and size space of curves
Summary
Shape analysis of curves in Rn , where n ≥ 2, is an important branch in many applications, including computer vision and medical imaging. In [6], the Sobolev-type metric given in [3] for the shape space of planar closed curves is extended to the space of all planar closed curves where the metric considered exhibits a decomposition of the space of closed planar curves into a product space consisting of three components; that is, centroid translations, scale changes and curves in the shape space In this approach, we will consider representations of curves in Rn from square-root velocity functions (SRVF).
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