This paper presents a method for extracting distinctive invariant features from images, which can be used to perform reliable matching between different images of an object or scene. The features are invariant to image scale and rotation, and are shown to provide robust matching across a a substantial range of affine distortion, addition of noise, change in 3D viewpoint, and change in illumination. The features are highly distinctive, in the sense that a single feature can be correctly matched with high probability against a large database of features from many images. This paper also describes an approach to using these features for object recognition. The recognition proceeds by matching individual features to a database of features from known objects using a fast nearest-neighbor algorithm, followed by a Hough transform to identify clusters belonging to a single object, and finally performing verification through leastsquares solution for consistent pose parameters. This approach to recognition can robustly identify objects among clutter and occlusion while achieving near real-time performance.

An object recognition system has been developed that uses a new class of local image features. The features are invariant to image scaling, translation, and rotation, and partially invariant to illumination changes and affine or 3D projection. These features share similar properties with neurons in inferior temporal cortex that are used for object recognition in primate vision. Features are efficiently detected through a staged filtering approach that identifies stable points in scale space. Image keys are created that allow for local geometric deformations by representing blurred image gradients in multiple orientation planes and at multiple scales. The keys are used as input to a nearest-neighbor indexing method that identifies candidate object matches. Final verification of each match is achieved by finding a low-residual least-squares solution for the unknown model parameters. Experimental results show that robust object recognition can be achieved in cluttered partially-occluded images with a computation time of under 2 seconds.

This paper describes an algorithm that robustly locates convex collections of line segments in an image. The algorithm is guaranteed to find all convex sets of line segments in which the length of the line segments accounts for at least some fixed proportion of the length of their convex hull. This enables the algorithm to find convex groups whose contours are partially occluded or missing due to noise. We perform an expected case analysis of the algorithm's performance that shows that its run time is O(n 2 log(n) + nm), when we wish to find the m most salient groups in an image with n line segments. We support this analysis with experiments on real data. Our analysis not only reveals the circumstances under which our algorithm is efficient, but also tells us when the groups found are unlikely to occur at random, and so are likely to capture the underlying structure of a scene. We also demonstrate the grouping system as a module in an efficient recognition system that combines group...

This paper examines four current theoretical approaches to the representation and recognition of visual objects: structural descriptions, geometric constraints, multidimensional feature spaces, and shape-space approximation. The strengths and the weaknesses of the theories are considered, with a special focus on their approach to categorization --- a computationally challenging task which is not widely addressed in computer vision (where the stress is rather on the generalization of recognition across changes of viewpoint).

We show that the largest similar copy of a convex polygon P with m edges inside a convex polygon Q with n edges can be computed in O(mn 2 log n) time. We also show that the combinatorial complexity of the space of all similar copies of P inside Q is O(mn 2 ), and that it can also be computed in O(mn 2 log n) time. Let P be a convex polygon with m edges and Q a convex polygon with n edges. Our goal is to find the largest similar copy of P inside Q (allowing translation, rotation, and scaling of P ); see Figure 1. A restricted version of this problem, in which we just determine whether P can be placed inside Q without scaling, was solved by Chazelle [4], in O(mn 2 ) time. See also [1, 6, 12] for other approaches to the more general problem, in which Q is an arbitrary polygonal region. (We remark that the complexity of the algorithms for the general case is considerably higher, about O(m 2 n 2 ) in [1], O(m 3 n 2 ) in [12], and O(m 4 n 2 ) in [6].) Problems concernin...

This paper presents a novel approach to parts-based object recognition in the presence of occlusion. We focus on the problem of determining the pose of a 3-D object from a single 2-D image when convex parts of the object have been matched to corresponding regions in the image. We consider three types of occlusions: self-occlusion, occlusions whose locus is identified in the image, and completely arbitrary occlusions. We show that in the first two cases this is a convex optimization problem, derive efficient algorithms, and characterize their performance. For the last case, we prove that the problem of finding valid poses is computationally hard, but provide an efficient, approximate algorithm. This work generalizes our previous work on region-based object recognition, which focused on the case of planar models. This research was supported by the Unites States-Israel Binational Science Foundation, Grant No. 94-100. The vision group at the Weizmann Inst. is supported in part by...

We study two problems involving collision-free placements of a convex m-gon P in a planar polygonal environment: (i) We first show that the largest similar copy of P inside another convex polygon Q with n edges can be computed in O(mn 2 log n) time. We also show that the combinatorial complexity of the space of all similar copies of P inside Q is O(mn 2 ), and that it can also be computed in O(mn 2 log n) time. (ii) We then consider the case where Q is an arbitrary polygonal environment with n edges. We give the first (and relatively simple) algorithm that constructs the entire free configuration space (the 3-dimensional space of all free placements of P in Q) in time that is near- Pankaj Agarwal has been supported by NSF Grant CCR93 --01259, an NYI award, and by matching funds from Xerox Corp. Nina Amenta has been supported by the Geometry Center, which is officially the Center for Computation and Visualization of Geometric Structures, supported by NSF/DMS8920161. Boris Aro...

Abstract—This paper presents a novel and efficient surface matching and visualization framework through the geodesic distanceweighted shape vector image diffusion. Based on conformal geometry, our approach can uniquely map a 3D surface to a canonical rectangular domain and encode the shape characteristics (e.g., mean curvatures and conformal factors) of the surface in the 2D domain to construct a geodesic distance-weighted shape vector image, where the distances between sampling pixels are not uniform but the actual geodesic distances on the manifold. Through the novel geodesic distance-weighted shape vector image diffusion presented in this paper, we can create a multiscale diffusion space, in which the cross-scale extrema can be detected as the robust geometric features for the matching and registration of surfaces. Therefore, statistical analysis and visualization of surface properties across subjects become readily available. The experiments on scanned surface models show that our method is very robust for feature extraction and surface matching even under noise and resolution change. We have also applied the framework on the real 3D human neocortical surfaces, and demonstrated the excellent performance of our approach in statistical analysis and integrated visualization of the multimodality volumetric data over the shape vector image. Index Terms—Surface Matching, Shape Vector Image, Multiscale Diffusion, Visualization. 1

This paper presents an approach to region-based hierarchical image matching, where, given two images, the goal is to identify the largest part in image 1 and its match in image 2 having the maximum similarity measure defined in terms of geometric and photometric properties of regions (e.g., area, boundary shape, and color), as well as region topology (e.g., recursive embedding of regions). To this end, each image is represented by a tree of recursively embedded regions, obtained by a multiscale segmentation algorithm. This allows us to pose image matching as the tree matching problem. To overcome imaging noise, one-to-one, many-to-one, and many-to-many node correspondences are allowed. The trees are first augmented with new nodes generated by merging adjacent sibling nodes, which produces directed acyclic graphs (DAGs). Then, transitive closures of the DAGs are constructed, and the tree matching problem reformulated as finding a bijection between the two transitive closures on DAGs, while preserving the connectivity and ancestor-descendant relationships of the original trees. The proposed approach is validated on real images showing similar objects, captured under different types of noise, including differences in lighting conditions, scales, or viewpoints, amidst limited occlusion and clutter.

We describe a robust method for spatial registration, which relies on the coarse correspondence of structures extracted from images, avoiding the establishment of point correspondences. These structures #tokens# are points, chains, polygons and regions at the level of intermediate symbolic representation #ISR#. The algorithm recovers conformal transformations #4 affine parameters#, so that 2-dimensional scenes as well as planar structures in 3D scenes can be handled. The affine transformation between two different tokensets is found by minimization of an exponentially decreasing distance function. As long as the tokensets are kept sparse, the method is very robust against a broad variety of common disturbances #e.g. incomplete segmentations, missing tokens, partial overlap#. The performance of the algorithm is demonstrated using simple 2D shapes, medical, and remote sensing satellite images. The complexity of the algorithm is quadratic on the number of affine parameters.