Invariant matching and identification of curves using B-splines curve representation

Abstract

There have been many techniques for curve shape representation and analysis, ranging from Fourier descriptors, to moments, to implicit polynomials, to differential geometry features, to time series models, to B-splines, etc. The B-splines stand as one of the most efficient curve (surface) representations and possess very attractive properties such as spatial uniqueness, boundedness and continuity, local shape controllability, and invariance to affine transformations. These properties made them very attractive for curve representation, and consequently, they have been extensively used in computer-aided design and computer graphics. Very little work, however, has been devoted to them for recognition purposes. One possible reason might be due to the fact that the B-spline curve is not uniquely described by a single set of parameters (control points), which made the curve matching (recognition) process difficult when comparing the respective parameters of the curves to be matched. This paper is an attempt to find matching solutions despite this limitation, and as such, it deals the problem of using B-splines for shape recognition and identification from curves, with an emphasis on the following applications: affine invariant matching and classification of 2-D curves with applications in identification of aircraft types based on image silhouettes and writer-identification based on handwritten text.

An efficient parameterless quadrilateral-based image segmentation method

“…The boundaries can be easily detected as the location at which two different regions meet, but with only those pixel-wise boundary points, further processing such as polygonal approximations [21], [22] B-spline approximations [23], [24], mesh-based approximations [25], [26], etc., are required before any high level region representation can be generated. Such further processing techniques, however, can be computationally intensive.…”

Human tracking with an infrared camera using a curve matching framework

“…There have been many articles which deal with curve matching using splines [42][43][44][45][46]. Other algorithms for curve matching use polygonal arc methods [47], matching the curve structure on the most significant scales [48], unary and binary measurements invariant for curves [49], fuzzy logic [50] or Sethian's Fast Marching method [51].…”

Automated Atlas-Based Clustering of White Matter Fiber Tracts from DTMRI

“…Quintic splines are sometimes used to smooth out the data and to perform the differentiation through convolution with spline kernels instead of simple differentiation [15]. In our clustering approach, we use the B-spline representation [16] of the fiber tracts for pairwise comparison of the fiber tracts extracted from the subject to those from the atlas. The spline representation contains information of both spatial location and shape of the tracts.…”