Iris Fermin

Voting method for planarity and motion detection

The recognition of planar shapes in an important problem in computer vision and many methods have been proposed for the analysis of planar motion and spatial motion. For the analysis of motion we must first determine whether the motion is planar or spatial. Here we propose a voting method for planarity detection and planar motion estimation. This algorithm does not require any pre-prepared database. Further, a numerical analysis implies that our algorithm is stable against numerical and digitalization errors.

Motion Analysis by Random Sampling and Voting Process

In computer vision, motion analysis is a fundamental problem. Applying the concepts of congruence checking in computational geometry and geometric hashing, which is a technique used for the recognition of partially occluded objects from noisy data, we present a new random sampling approach for the estimation of the motion parameters in two- and three-dimensional Euclidean spaces of both a completely measured rigid object and a partially occluded rigid object. We assume that the two- and three-dimensional positions of the vertices of the object in each image frame are determined using appropriate methods such as a range sensor or stereo techniques. We also analyze the relationships between the quantization errors and the errors in the estimation of the motion parameters by random sampling, and we show that the solutions obtained using our algorithm converge to the true solutions if the resolution of the digitalization is increased.

Randomized polygon search for planar motion detection

In this paper, we propose a randomized algorithm to estimate the motion parameters of a planar shape without knowing a priori the point-to-point correspondences. By randomly searching points on two shapes measured at different times, we determine the centroids, after which the algorithm proceeds to determine the rotation by randomly searching points on each shape that form congruent polygons.

Symmetry detection by random sampling and voting process

We propose a randomized method for the detection of symmetry in polyhedra without assuming the predetermination of the centroids of the objects. Using a voting process, which is the main concept of the Hough transform in image processing, we transform the geometric computation for symmetry detection based on graph theory, to the peak detection problem in a voting space in the context of the Hough transform.

Discovery of symmetry by voting method

Abstract We propose a randomized method for the detection of symmetry in planar polygons without assuming the predetermination of the centroids of the objects. In this paper, we show that voting method converts the feature discovery process in noisy data to a simple search process in the dual space and that signal analysis for the peak distribution in the accumulator space yields symbolic features of figures such as symmetry.

Planar motion detection by randomized triangle matching

Abstract This paper proposes a randomized algorithm for the estimation of the planar motion parameters of a bounded closed set. By randomly searching triangles on two shapes measured at different times, the algorithm solves the rigid motion equation using correspondences between edges of triangles which are detected using a random search and a voting procedure.

Planar Symmetry Detection by Random Sampling and Voting Process

We propose a randomized method for the detection of symmetry in planar polygons without assuming the predetermination of the centroids of the objects. Using a voting process, which is the main concept of the Hough transform in image processing, we transform the geometric computation for symmetry detection which is usually based on graph theory and combinatorial optimization, to the peak detection problem in a voting space in the context of the Hough transform.

Randomized method for planar motion detection

In this paper, we propose a randomized algorithm to estimate the planar motion parameters of a finite closed set. By randomly searching points on two shapes measured at different times, we determine the centroids and translation of the planar shapes. Taking these centroids as reference points, the algorithm proceeds to determine the point-to- point correspondences by randomly searching three points on each shape that form congruent triangles. After the point correspondences have been determined, the rotation is estimated by solving the rigid motion equation.

SYMMETRY DETECTION BY RANDOM SAMPLING AND VOTING PROCESS FOR MOTION ANALYSIS

Symmetry of an object on a plane and in a space is an important geometric feature for biology, chemistry, and the understanding of human perception of figures. We propose a randomized method for the detection of symmetry in planar polygons and polyhedrons without assuming the predetermination of the centroids of the objects. Using a voting process, which is the main concept of the Hough transform in image processing, we transform the geometric computation for symmetry detection which is usually based on graph theory and combinatorial optimization, to the peak detection problem in a voting space in the context of the Hough transform. Our algorithm detects the centroid after detecting symmetry of an object for both planar and spatial objects.

Randomized method for planar motion estimation and matching points

We present a random sampling and voting approach for the estimation of two-dimensional planar motion of a planar object moving in a plane parallel to the camera image plane. Since we are using random sampling, the correspondences between points in two different image frames are not required. However, the point correspondences can be determined after the planar motion is computed.