The renormalisation technique of Kanatani is intended to iteratively minimise a cost function of a certain form while avoiding systematic bias inherent in the common method of minimisation due to Sampson. Within the computer vision community, the technique has generally proven difficult to absorb. This work presents an alternative derivation of the technique, and places it in the context of other approaches. We first show that the minimiser of the cost function must satisfy a special variational equation. A Newton-like, fundamental numerical scheme is presented with the property that its theoretical limit coincides with the minimiser. Standard statistical techniques are then employed to derive afresh several renormalisation schemes. The fundamental scheme proves pivotal in the rationalising of the renormalisation and other schemes, and enables us to show that the renormalisation schemes do not have as their theoretical limit the desired minimiser. The various minimisation schemes are finally subjected to a comparative performance analysis under controlled conditions.

We present a general strategy for shape-based image retrieval which considers similarity modulo a given transformation group G. The shape content of an image is summarized by recording what geometric primitives, such as line segments and circular arcs, fit where in the image. Geometric hashing is used to compute a set of primitive features which are invariant under a G-transformation of the image. Our search engine is feature-based in the sense that similarity is determined by looping over the features in the query and asking: Which database images have features that are close to a given query feature? The most similar database images are ones that have many features which are close to query features. We apply our approach to an example database of 500 chinese character bitmaps. 1 Introduction The function of a content-based image retrieval system [ Niblack et al., 1993, Guibas and Tomasi, 1996 ] is typically to find database images that look similar to a given query image or drawing....

This paper presents a statistical approach for detecting corners from chain encoded digital arcs. An arc point is declared as a corner if the estimated parameters of the two fitted lines of the two arc segments immediately to the right and left of the arc point are statistically significantly different. The corner detection algorithm consists of two steps: corner detection and optimization. While corner detection involves statistically identifying the most likely corner points along an arc sequence, corner optimization deals with improving the locational errors of the detected corners. The major contributions of this research include developing a method for analytically estimating the covariance matrix of the fitted line parameters and developing a hypothesis test statistic to statistically test the difference between the parameters of two fitted lines. Performance evaluation study showed that the algorithm is robust and accurate for complex images. It has an average misdetection rate ...

We present an algorithm that extracts curves from a set of edgels within a specific class in a decreasing order of their "length". The algorithm inherits the perceptual grouping approaches. But, instead of using only local cues, a global constraint is imposed to each extracted subset of edgels, that the underlying curve belongs to a specific class. In order to reduce the complexity of the solution, we work with a linearly parameterized class of curves, function of one image coordinate. This allows, first, to use a recursive Kalman based fitting and, second, to cast the problem as an optimal path search in an directed graph. Experiments on finding lane-markings on roads demonstrate that real-time processing is achievable.

We present a new method for automatically detecting circular objects in images: we detect an osculating circle to an elliptic arc using a Hough transform, iteratively deforming it into an ellipse, removing outlier pixels, and searching for a separate edge. The voting space for the Hough transform is restricted to one and two dimensions for efficiency, and special weighting schemes are introduced to enhance the accuracy. We demonstrate the effectiveness of our method using real images. Finally, we apply our method to the calibration of a turntable for 3-D object shape reconstruction. 1

We consider the segmentation of a trajectory into piecewise polynomial parts, or possibly other forms. Segmentation is typically formulated as an optimization problem which trades off model fitting error versus the cost of introducing new segments. Heuristics such as split-and-merge are used to find the best segmentation. We show that for ordered data (eg., single curves or trajectories) the global optimum segmentation can be found by dynamic programming. The approach is easily extended to handle different segment types and top down information about segment boundaries, when available. We show segmentation results for video sequences of a basketball undergoing gravitional and non-gravitaional motion. 1

The recovery of generic solid parts is a fundamental step towards the realization of general-purpose vision systems. This thesis investigates issues in grouping, segmentation and recognition of parts from two-dimensional edge images.

The Perceptive Workbench endeavors to create a spontaneous and unimpeded interface between the physical and virtual worlds. Its vision-based methods for interaction constitute an alternative to wired input devices and tethered tracking. Objects are recognized and tracked when placed on the display surface. By using multiple infrared light sources, the object’s 3D shape can be captured and inserted into the virtual interface. This ability permits spontaneity since either preloaded objects or those objects selected at run-time by the user can become physical icons. Integrated into the same vision-based interface is the ability to identify 3D hand position, pointing direction, and sweeping arm gestures. Such gestures can enhance selection, manipulation, and navigation tasks. In previous publications, the Perceptive Workbench has demonstrated its utility for a variety of applications, including augmented reality gaming and terrain navigation. This paper will focus on the implementation and performance aspects and will introduce recent enhancements to the system.

We propose a new complete method to extract si gni ficant descri tii (s) of planar curves accordi g to constant curvature segments. Th i methodi s based (i) on a multi -scale segmentatiR and curve approxiM = iM algori hm, defined by two groupi ng processes (polygonal and constant curvature approxi mati ons), leadi ng to a multi -scale coveri ng of the curve, and (ii) on an i traandi nter-scaleclassi cat it of th i mult i scale coveri g gui ded by heurik ik]R-defined quali at i e labels leadi g to paiM (scale,lia of constant curvature segments) that best descri e the shape of the curve. Experi ments show that the proposed methodi s able to prov i esali] t segmentatik and approxiR] iR results whi ch respect shape descri tir and recogn iogn crin1RMM 1 Int roduct In ordert easily manipulat a planar curve or da t bases composed of planar curves,it would be int1est#/ t represent dat a accordingt primit/ es which describet hem in a waytG t resp ecttt: act: l shape for recognit/ n and co...

this paper is to fill this gap. We first evolve a fundamental Newtonlike algorithm for calculating b