Abstract This paper describes how corner detection can be realised using a new feature representation based on a magneto-static analogy. The idea is to compute a vector-potential by appealing to an analogy in which the Canny edge-map is regarded as an elementary current density residing on the image plane. In this paper, we demonstrate that corners are located at the saddle-points of the magnitude of the vector-potential. These points correspond to the intersections of saddle-ridge and saddle-valley structures, i.e. to junctions of the edge and symmetry lines. We describe a template-based method for locating the saddle-points. This involves performing a non-minimum suppression test in the direction of the vector-potential and a non-maximum suppression test in the orthogonal direction. Experimental results using both synthetic and real images are given. We investigate the angle and scale sensitivity of the new corner detector and compare it with a number of alternative corner detectors.

This paper describes physically based model for detecting closed edge-contours. According to our model, the magnitude of the Canny edge-gradient represents a raw charge-density. Edge segmentation is realised by considering the damped-motion of charged test-particles in the resulting electric field. The attractor regions of the electric field represent continuous regions that are separated by closed edge-contours. In order to strike a compromise between over and under smoothing the resulting edge-map, we provide a hierarchical algorithm for controlling the dynamics of the region attractors. We illustrate the method on both synthetic and real world data.

This paper describes how corner detection can be realised using a new feature representation that has recently been successfully exploited for edge and symmetry detection. The feature representation based on an magneto-static analogy. The idea is to compute a vector potential by appealing to an analogy in which the Canny edge-map is regarded as an elementary current density residing on the image plane. In our previous work we demonstrated that edges are the local maxima of the vector potential while points of symmetry correspond to the local minimum. In this paper we demonstrate that corners are located at the saddle points of the magnitude of the vector potential. These points corresponds to the intersections of saddle-ridge and saddle-valley structures, i.e. to junctions of the edge and symmetry lines. We describe a template-based method for locating the saddle-points. This involves performing a nonminimum suppression test in the direction of the vector potential and a nonmaximum suppression test in the orthogonal direction. Experimental results of both synthetic and real images are given.

This paper describes a new approach to matching geometric structure in 2D point-sets. The novel feature is to unify the tasks of estimating transformation geometry and identifying point-correspondence matches. Unification is realized by constructing a mixture model over the bipartite graph representing the correspondence match and by affecting optimization using the EM algorithm. According to our EM framework, the probabilities of structural correspondence gate contributions to the expected likelihood function used to estimate maximum likelihood transformation parameters. These gating probabilities measure the consistency of the matched neighborhoods in the graphs. The recovery of transformational geometry and hard correspondence matches are interleaved and are realized by applying coupled update operations to the expected log-likelihood function. We evaluate the technique on two real-world problems.

This paper describes a vectorial representation that can be used to assess the symmetry of objects in 2D images. The method exploits a magneto-static analogy. Commencing from the gradient-field extracted from filtered grey-scale images we construct a vector-potential. Our magneto-static analogy is that tangential gradient vectors represent the elements of a current distribution on the image plane. By embedding the image plane in an augmented 3-dimensional space, we compute the vector potential by performing volume integration over the current distribution. The associated magnetic field is computed by taking the curl of the vector-potential. The auxiliary spatial dimension provides a natural scale-space sampling of the generating current distribution; as the height above the image plane is increased, so the volume over which averaging is effected also increases. We extract edge and symmetry lines through a topographic analysis of the vector-field at various heights above the image plane. Symmetry axes are lines where the curl of the vector-potential vanishes; at edges the divergence of the vector-potential vanishes.

The aim of this paper is to explore the sensitivity of relational matching to attribute and structural information. Broadly speaking there are two main aspects to this study. First, we determine the relative importance of attribute and structural information in matching noise corrupted graphs. The second aspect of our analysis concerns the nature of the relational structures used in matching. Here we compare the matching results obtained using four different graph structures, namely the Delaunay graph, the N-nearest neighbour graph, the Gabriel graph and the relative neighbourhood graph. Our results are presented as noise sensitivity curves. The main conclusion of the study is that attributes are essential when the fractional corruption exceeds 20% and that the Delaunay graph has optimal noise robustness.