Similarity-invariant signatures for partially occluded planar shapes

A methodology is described for associating local invariant signature functions to smooth planar curves in order to enable their translation, rotation, and scale-invariant recognition from arbitrarily clipped portions. The suggested framework incorporates previous approaches, based on locating inflections, curvature extrema, breakpoints, and other singular points on planar object boundaries, and provides a systematic way of deriving novel invariant signature functions based on curvature or cumulative turn angle of curves. These new signatures allow the specification of arbitrarily dense feature points on smooth curves, whose locations are invariant under similarity transformations. The results are useful for detecting and recognizing partially occluded planar objects, a key task in low-level robot vision.     

Fundamental limitations on projective invariants of planar curves

In this paper, some fundamental limitations of projective invariants of non-algebraic planar curves are discussed. It is shown that all curves within a large class can be mapped arbitrarily close to a circle by projective transformations. It is also shown that arbitrarily close to each of a finite number of closed planar curves there is one member of a set of projectively equivalent curves. Thus a continuous projective invariant on closed curves is constant. This also limits the possibility of finding so called projective normalisation schemes for closed planar curves     

Orientation-based unique representation for planar curves and shapes

This paper presents an orientation-based representation for planar curves and shapes. The new representation can uniquely represent all types, of planar shapes, be it convex, nonconvex, polygonal, smoothly curved, or piecewise smooth shapes. It is based on a new parameterization, theabsolute integral orientation. This representation is invariant under translation and rotation. The absolute integral orientation is a parameter invariant under scaling. As a result, matching of similar shapes (i.e., determination of the relative orientation and the scaling factor) using the absolute integral orientation as the parameter is easier than using the arclength as the parameter. In addition, the new representation has the feature of adaptive sampling, making it more compact and efficient than arc-length-based representations.     

Using moment invariants to recognize and locate partially occluded 2D objects

A new approach to matching of partially occluded contours is presented. The moments of curves are defined and the moment invariants are introduced. The algorithm consists in solving a system of equations based on the moment invariants.     

Application of differential geometry to recognize and locate partially occluded objects

A new method has been proposed to recognize and locate partially occluded two-dimensional rigid objects of a given scene. For this purpose we initially generate a set of local features of the shapes using the concept of differential geometry. Finally a computer vision scheme, based upon matching local features of the objects in a scene and the models which are considered as cognitive database, is described using hypothesis generation and verification of features for the best possible recognition.     

Search-by-content of partially occluded images

This paper describes a method for searching images by content that compensates for occlusions in the image. The method extends a search technique proposed by Stone and Li that is based on two criteria – sum of squares differences and average intensity, but the method can be used in conjunction with other criteria, including the normalized correlation coefficient. Image occlusions have a profound impact on template-matching image searches. A typical example of such an occlusion is a cloud over a land mass in an image taken from a satellite. Searches performed without compensation for occlusions are unable to detect matches in positions near the cloud perimeter that are not totally obscured by the cloud. The compensation method introduced here can discover good matches in regions where patterns overlap occluded regions, and would otherwise be missed. The key idea of the algorithm is to perform computations in a way that removes invalid pixels from summations. The enhanced algorithm requires no more than a factor of two increase in storage and computation costs as compared to the Stone–Li algorithm.     

Bisector curves of planar rational curves

This paper presents a simple and robust method for computing the bisector of two planar rational curves. We represent the correspondence between the foot points on two planar rational curves C₁(t) and C₂(r) as an implicit curve (t,r)=0, where (t,r) is a bivariate polynomial B-spline function. Given two rational curves of degree m in the xy-plane, the curve (t,r)=0 has degree 4m−2, which is considerably lower than that of the corresponding bisector curve in the xy-plane.     

On convexity of planar curves and its application in CAGD

This paper presents a necessary and sufficient condition for global convexity of planar curves and some applications of this condition. In addition, various ideas about the concept of convexity in CAGD are discussed.     

Random planar shapes and their statistical recognition

A two-dimensional shape as considered in this paper is the equivalence class of closed polygons under rigid motions (rotations and translations). We discuss a model for random shapes which is used as the basis for probabilistic classifiers. A maximum-likelihood approach is used to deal with the incomplete information given by the knowledge of the equivalence class only. As an example, the problem of the recognition of species of plants from the shape of their leaves is studied.     

General intensity transformations and differential invariants

We consider the group of invertible image gray-value transformations and propose a generating equation for a complete set of differential gray-value invariants up to any order. Such invariants describe the image's geometrical structure independent of how its gray-values are mapped (contrast or brightness adjustments).This work has been carried out as part of the national priority research program 3D Computer Vision, supported by the Netherlands Ministries of Economic Affairs and Education and Science through a SPIN grant. The support from the participating industrial companies is gratefully acknowledged.     

Using polygons to recognize and locate partially occluded objects

We present computer vision algorithms that recognize and locate partially occluded objects. The scene may contain unknown objects that may touch or overlap giving rise to partial occlusion. The algorithms revolve around a generate-test paradigm. The paradigm iteratively generates and tests hypotheses for compatibility with the scene until it identifies all the scene objects. Polygon representations of the object's boundary guide the hypothesis generation scheme. Choosing the polygon representation turns out to have powerful consequences in all phases of hypothesis generation and verification. Special vertices of the polygon called ``corners' help detect and locate the model in the scene. Polygon moment calculations lead to estimates of the dissimilarity between scene and model corners, and determine the model corner location in the scene. An association graph represents the matches and compatibility constraints. Extraction of the largest set of mutually compatible matches from the association graph forms a model hypothesis. Using a coordinate transform that maps the model onto the scene, the hypothesis gives the proposed model's location and orientation. Hypothesis verification requires checking for region consistency. The union of two polygons and other polygon operations combine to measure the consistency of the hypothesis with the scene. Experimental results give examples of all phases of recognizing and locating the objects.     

Projectively invariant decomposition and recognition of planar shapes

An algorithm is presented for computing a decomposition of planar shapes into convex subparts represented. by ellipses. The method is invariant to projective transformations of the shape, and thus the conic primitives can be used for matching and definition of invariants in the same way as points and lines. The method works for arbitrary planar shapes admitting at least four distinct tangents and it is based on finding ellipses with four points of contact to the given shape. The cross ratio computed from the four points on the ellipse can then be used as a projectively invariant index. It is demonstrated that a given shape has a unique parameter-free decomposition into a finite set of ellipses with unit cross ratio. For a given shape, each pair of ellipses can be used to compute two independent projective invariants. The set of invariants computed for each ellipse pair can be used as indexes to a hash table from which model hypothesis can be generated Examples of shape decomposition and recognition are given for synthetic shapes and shapes extracted from grey level images of real objects using edge detection.     

平面非规则曲线的一种快速识别与匹配算法

平面非规则曲线的识别与匹配主要用于图像识别、物体匹配等领域。文章在综合研究比较国内外的研究成果后,提出了一种新的快速提取特征进行筛选而后进行细节比对进行匹配的方法。该方法首先通过提取构成平面非规则曲线的一系列离散点的关键特征进行快速筛选,而后逐步比对细节特征,分析其变化趋势,对平面非规则曲线的匹配有着较为满意的匹配效果。该方法相比现有的匹配方法,具有识别与匹配速度快,准确率高,适应性强等优点。