Affine-invariant B-spline moments for curve matching

Abstract

The article deals with the problem of matching and recognizing planar curves that are modeled by B-splines, independently of possible affine transformations to which the original curve has been subjected (for example, rotation, translation, scaling, orthographic, and semiperspective projections), and possible occlusion. It presents a fast algorithm for estimating the B-spline control points that is robust to nonuniform sampling, noise, and local deformations. Curve matching is achieved by using a similarity measure based on the B-spline knot points introduced by Cohen et al. (1991). This method, however, can neither handle the affine transformation between the curves nor the occlusion. Solutions to these two problems are presented through the use of a new class of weighted B-spline curve moments that are well defined for both open and closed curves. The method has been applied to classifying affine-transformed aircraft silhouettes, and appears to perform well.

Sampling of periodic signals: a quantitative error analysis

“…One example, where the periodic representation is especially relevant, is the parametric representation of closed curves in terms of splines [7], [8], [9] or Fourier basis functions [10]. Assuming the period to be an integer multiple of the sampling step 2 it is straightforward to adapt most of the techniques to the periodic case by simply considering periodized basis functions and by redefining the inner product accordingly [11] (see Section II).…”

Automatic Recognition of Leaves by Shape Detection Pre-Processing With Ica

“…For an interpolating process, in order to achieve reconstruction of the original shape, we may use any of the well known algorithms as mentioned in , , (Huang et al, 1996), but a simple control point's choice criterion in 1-D analysis allows for an appropriate performance ratio on uniform control point's number and approximation error for all individuals of all varieties studied.…”

Affine invariant curve matching using normalization and curvature scale-space

“…A number of shape representations have been proposed to recognize shapes even under affine transformation [6], [7], [10]], affine invariant scale space [1]- [3] and affine curvature [4] have also been explored. A number of shape representation techniques are based on level-set methods [13].…”