Rimon Elias

The detection of junction features in images

This paper presents a new junction detection operator that defines junctions as points where linear ridges in the gradient domain intersect. The radial lines that compose the junction are therefore identified by searching, in a circular neighborhood, for directional maxima of the intensity gradient. The proposed algorithm operates on two binary edge maps, the computational complexity of the detection process is then considerably reduced.

JUDOCA: JUnction Detection Operator Based on Circumferential Anchors

In this paper, we propose an edge-based junction detector. In addition to detecting the locations of junctions, this operator specifies their orientations as well. In this respect, a junction is defined as a meeting point of two or more ridges in the gradient domain into which an image can be transformed through Gaussian derivative filters. To accelerate the detection process, two binary edge maps are produced; a thick-edge map is obtained by imposing a threshold on the gradient magnitude image, and another thin-edge map is obtained by calculating the local maxima. Circular masks are centered at putative junctions in the thick-edge map, and the so-called circumferential anchors or CA points are detected in the thin map. Radial lines are scanned to determine the presence of junctions. Comparisons are made with other well-known detectors. This paper proposes a new formula for measuring the detection accuracy. In addition, the so-called junction coordinate systems are introduced. Our operator has been successfully used to solve many problems such as wide-baseline matching, 3-D reconstruction, camera parameter enhancing, and indoor and obstacle localization.

Sparse view stereo matching

This paper addresses the sparse view matching problem where the camera parameters lie within ranges depending on the sensor used. An approach, based on homographic transformation, is proposed. The operation is split into two phases. The first phase deals with matches on the ground surface, which is considered planar. The second phase detects matches on arbitrary planes. This is done by detecting junctions of different shapes and reconstructing planes inferred by them. Two versions of that approach are suggested based on the sum of absolute differences and the variance normalized correlation techniques. The first technique is computationally inexpensive while the later is more robust to changes in lighting condition between views. Experiments show that our approach outperforms non-homographic correlation.

Fast localization in indoor environments

In this paper, we propose an algorithm for fast indoor localization. The algorithm does not require any sensors to be installed; instead, localization is determined using image matching. Our system studies (or learns) the indoor environment through detecting image junctions using the so-called JUDOCA detector. Any 2-edge junction forms a triangle that can be used to store information and recognize the environment afterwards. Correlation is applied to points denoted with respect to one side of the triangle formed by the junction. Experiments show that this approach reaches similar accuracy of the affine-based correlation approach in less processing time.

Enhancing accuracy of camera rotation angles detected by inaccurate sensors and expressing them in different systems for wide baseline stereo

This article suggests an algorithm based on information deduced from a pair of wide baseline (or sparse view) stereo images to enhance the accuracy of camera rotation angles detected using inaccurate sensors. The so-called JUDOCA operator; a fast junction detector, is used to extract important interest points. Through the output information from that operator, affine transformation is then estimated and employed to guide a variance normalized correlation process in order to get a set of possible matches. The so-called RANSAC scheme is used to estimate the fundamental matrix; hence, the essential matrix can be estimated and SVD decomposed. In addition to a translation vector, this decomposition results in an accurate rotation matrix with accurate rotation angles involved. Mathematical derivation is done to extract and express angles in terms of different rotation systems.

Wide baseline matching through homographic transformation

This work discusses the wide baseline matching problem where the camera parameters are known up to an error factor and the ground surface is considered planar. Junctions of different shapes and orientations are detected. Homographic correlation, an invariant measure to projective transformation, is utilized using reconstructed planes made of detected junctions. Two variants of homographic correlation are proposed showing that this approach outperforms non-homographic correlation.

Wide baseline obstacle detection and localization

This paper studies the problem of an autonomous robot equipped with a single camera and that must locate the obstacles on a ground plane. The algorithm proposed here proceeds by first matching feature points on widely separated images of the work area using an overhead view transformation. The homography thus obtained is used to estimate the camera motion parameters. Obstacles are then located through a second matching phase.

Cones: a new approach towards corner detection

This paper presents a new approach to detect corners and determine their orientations. This is done through a data structure similar to pyramids but of circular levels. Thus, we refer to it as the cone. The operation starts at the top level where only one node exists. If the node is inhomogeneous, it will be split into two nodes forming the next lower level of the cone. Splitting continues until all nodes become homogeneous. At the base and according to a threshold, similar nodes are grouped together to shape the orientation of the corner.

Geometric Modeling in Computer Vision: An Introduction to Projective Geometry

This article surveys many fundamental aspects of projective geometry that have been used extensively in computer vision literature. Geometrical relationships are investigated when one, two, or more cameras are observing the scene. Camera parameters in terms of locations and orientations with respect to three dimensional (3D) space and with respect to other cameras create relationships that can be expressed mathematically. Expressing these relationships is the main focus of this article. Keywords: projective geometry; single view geometry; pinhole camera; perspective projection matrix; intrinsic parameters; extinsic parameters; rotation system; stero vision; binocular vision; epipolar geometry; fundamental matrix; essential matrix; homography matrix; plane homography; three-view geometry; trifocal tensor; 3-d reconstruction

Clustering points in nD space through hierarchical structures

This article presents a technique for clustering points in nD space based on the concepts of irregular pyramids and minimum-distance classification. The structure we present consists of a number of levels. Each level consists of a number of clusters and each cluster contains one or more point nodes. The base of the structure is the set of input points (or feature vectors). The apex is a set of roots where every root is distant from every other root according to some proximity criteria.