3-D curve matching using splines

Pattern Recognition Letters, 2009

We present a curve matching framework for planar open curves under similarity transform 1 based on a new scale invariant signature. The signature is derived from the concept of integral of unsigned curvatures. If one input curve as a whole can be aligned with some part in the second curve then the algorithm will find the requisite starting and end positions and will estimate the similarity transform in OðN logðNÞÞ time. We extend our frame work to a more general case where some part of the first input curve can be aligned with some part of the second input curve. This is a more difficult problem that we solve in OðN 3 Þ time. The contributions of the paper are the new signature as well as faster algorithms for matching open 2D curves. We present examples from diverse application set to show that our algorithm can work across several domains.

2008 International Workshop on Content-Based Multimedia Indexing, 2008

In this paper, an affine invariant curve matching method using curvature scale-space and normalization is proposed. Prior to curve matching, curve normalization with respect to affine transformations is applied, allowing a lossless affine invariant curve representation. The maxima points of the curvature scale-space (CSS) image are then used to represent the normalized curve, while retaining the local properties of the curve. The matching algorithm that follows, matches the maxima sets of CSS images and the resulting matching cost provides a measure of similarity. The method's performance and robustness is evaluated through a variety of curves and affine transformations, obtaining precise shape similarity and retrieval.

Journal of Intelligent and Robotic Systems, 2000

Space curves are highly descriptive features for 3-D objects. Two invariant representations for space curves are discussed in this paper. One represents space curves by complex waveforms. The other represents space curves using the 3-D moment invariants of the data points on the curves. Space curve matching using invariant global features is discussed. An algorithm for matching partially occluded 3-D curves is also presented, in which rigidity constraints on pairwise curve segments are used to determine the globally consistent matching. An association graph can be constructed from the local matches. The maximal cliques of the graph will determine the visible part of the model curves in the scene. Experimental results using 3-D curves obtained from stereo matching and edges detected from the range data are also presented.

2011

—This paper is devoted to presenting a novel algorithm for curve matching and character recognition. This algorithm is based on constructing and comparing B-spline curves of object boundaries. At first, the dominant points are calculated on the objects boundary by using Local Curvature Maximum (LCM), then, control points are obtained by using B-spline least square fitting technique. Curve matching and character recognition is done by comparing result B-spline curves. The result from proposed method shows good accuracy besides low computational complexity of proposed method for curve matching and character recognition.

European Workshop on Computational Geometry, 2006

2007

In image processing and visualization, comparing two bitmapped images needs to be compared from their pixels by matching pixel-by-pixel. Consequently, it takes a lot of computational time while the comparison of two vector-based images is significantly faster. Sometimes these raster graphics images can be approximately converted into the vector-based images by various techniques. After conversion, the problem of comparing two raster graphics images can be reduced to the problem of comparing vector graphics images. Hence, the problem of comparing pixel-by-pixel can be reduced to the problem of polynomial comparisons. In computer aided geometric design (CAGD), the vector graphics images are the composition of curves and surfaces. Curves are defined by a sequence of control points and their polynomials. In this paper, the control points will be considerably used to compare curves. The same curves after relocated or rotated are treated to be equivalent while two curves after different s...

Algorithmica, 2013

Back in 1995, Alt and Godau gave an efficient algorithm for deciding whether a given curve resembles some part of a larger curve under a fixed Fréchet distance, achieving a running time of O(nm log(nm)), for n and m being the number of segments in the two curves, respectively. We improve this long-standing result by presenting an algorithm that solves this decision problem in O(nm) time. Our solution is based on constructing a simple data structure which we call free-space map. Using this data structure, we obtain improved algorithms for several variants of the Fréchet distance problem, including the Fréchet distance between two closed curves, and the so-called minimum/maximum walk problems. We also improve the map matching algorithm of Alt et al. for the case when the map is a directed acyclic graph.

TURKISH JOURNAL OF ELECTRICAL ENGINEERING & COMPUTER SCIENCES

This paper proposes a minimal length difference algorithm for construction of a line in an image by solving the problem of optimal contour approximation. In this algorithm, a method for finding interest points is proposed, and the object matching (classification) is done by mapping interest points onto a vector space. In cases where the lines in the representation of the images are not smooth, the algorithm converges rapidly. The results of the experiments showed that for convergence of the contour simplification, there were 5-6 iterations for n = 13. To check how close the curve approximation calculated by the algorithm above, the researchers have calculated the length of the curve simplification manually. This length was then compared to the length of the original curve. The results showed that the length of the simplified curve grew rapidly to 92%-95% of the original curve length. The further increase in the number of points does not affect this indicator. According to the obtained results, the relative difference and the relative difference distance are good metrics to match objects.

2004

The process of classifying objects is a fundamental feature of most human pursuits, and the idea that people classify together those things that people find similar is both intuitive and popular across a wide range of disciplines. Estimation of difference between curves (curve matching) is an useful and often necessary technique in many applications, including: pattern recognition, image object recognition, robotic applications, computational geometry, etc. In this paper, three methods for curve matching using turning functions are presented. While the first two, called plain and polygonal method, are based on a simple adaptation of the existing approaches, the third one, called penalty method, is a new one and tries to overcome some important problems from the first two. The advantages and essential problems of the proposed methods are also discussed. A number of examples are presented to show major differences among the methods and their potential usefulness.

2009 IEEE International Conference on Acoustics, Speech and Signal Processing, 2009

We present a new similarity invariant signature for space curves. This signature is based on the information contained in the turning angles of both the tangent and the binormal vectors at each point on the curve. For an accurate comparison of these signatures, we define a Riemannian metric on the space of the invariant. We show through relevant examples that, unlike classical invariants, the one we define in this paper enjoys multiple important properties at the same time, namely, a high discrimination level, independence of any reference point, uniqueness property, as well as a good preservation of the correspondence between curves. Moreover, we illustrate how to match 3D objects by extracting and comparing the invariant signatures of their curved skeletons.