Statistical Hough Transform

Abstract

The Standard Hough Transform is a popular method in image processing and is traditionally estimated using histograms. Densities modeled with histograms in high dimensional space and/or with few observations, can be very sparse and highly demanding in memory. In this paper, we propose first to extend the formulation to continuous kernel estimates. Second, when dependencies in between variables are well taken into account, the estimated density is also robust to noise and insensitive to the choice of the origin of the spatial coordinates. Finally, our new statistical framework is unsupervised (all needed parameters are automatically estimated) and flexible (priors can easily be attached to the observations). We show experimentally that our new modeling encodes better the alignment content of images.

A Closed-Form Solution to Tensor Voting: Theory and Applications

“…The Hough transform [13] is a robust voting-based technique operating in a parameter space capable of extracting multiple models from noisy data. Statistical Hough transform [6] can be used for high dimensional spaces with sparse observations. Mean shift [5] has been widely used since its introduction to computer vision for robust feature space analysis.…”

Face Alignment under Partial Occlusion in near Infrared Images

“…The Hough transform [11][12][13] provides another way of parameter estimation via a voting strategy and has been widely used in object detection and pose estimation problems. Taking The overview of our approach: (a)Building correspondences between partial frame and canonical facial image, (b)Pruning wrong candidates by Geometric Constraint designed according to geometric relationship between correspondences, (c)Transformed partial face, and(d)the weighed hough votes' distribution in parameter space, the green dots are valid candidate with maximum votes, and we set the result as the median of these valid ones, as illustrated in purple diamond the advantage of voting, this approach can effectively find inliers aggregated in space and prune outliers that usually more sparse and scattered in space in many parameter estimation cases, see Fig.…”

“…The first term represents the hough voting and its parameter distribution can be approximated using Parzen-window estimation [11][12][13]. For the sack of computing complexity we make the 4-D space into discrete grids where each parameters will fall into its closest grid node, as following:…”

Lane Detection Method of Statistical Hough Transform Based on Gradient Constraint

“…Lane detection and tracking technology based on visual are the key technology on the applications of driver assistance systems for automobiles [1]. Many researchers have done a lot of work on that [2][3][4][5][6][7][8]. Road standard in our country formulates that the highway minimum plane curve radius is 650m.Taking the lane line curvature radius of 650m, 40m bending lane line in front of the vehicle can be approximate to straight lines.…”

“…Classical Hough transformation works well for line finding when the roads are mostly straight; however, it also has shortcomings as the probability density function of the parameters in classical Hough transform is estimated using a discrete two-dimensional histogram [2], Here are two of them: First, in the classical Hough transform, every pixel in the original image space participate in the transformation from image space to parameter space. At the same time, the voting of the parameter point do not always come from the same line in the image space, also may be caused by the chance to arrange of lane marking points which are not in the same straight line.…”