We present CHILS , the Convex Hull Inductive Learning System, a novel supervised learning algorithm based on approximating concepts with sets of convex hulls. We introduce a theoretical methodology for describing the power of a concept representation language and use it to compare convex hulls with other geometrical concept representations. The Domain Transform framework (DT) provides a clear w...

We utilize support functions to transform the problem of constructing the convex hull of a finite set of spherical objects into the problem of computing the upper envelope of piecewise linear functions. This approach is particularly suited if the objects are (possibly intersecting) circular arcs in the plane or spheres in three-space.

The Discriminative Generalized Hough Transform (DGHT) is a method for object localization, which combines the standard Generalized Hough Transform (GHT) with a discriminative training technique. In this setup the aim of the discriminative training is to equip the models used in the GHT with individual model point weights such that the localization error in the GHT becomes minimal. In this paper...

A fast SVM learning algorithm is proposed according to incremental learning and center convex hull operator. It is established on analyzing the relevance of support vector and convex hull from the angle of calculation geometry. The convex hull of current training samples is solved in the first place. Further, Euclidean distance elimination is applied to convex hull. Meanwhile, every time when t...

This paper studies the use of the generalised Hough transform to locate objects possessing concavities. Hhen locating objects with internal symmetries, ambiguities can arise which nay not be resolvable in the presence of occlusions. On the other hand concavities can help to lake object location more accurate. The boundary orientation distribution can be used to analyse the situation: it shows t...

Hough transform is a well-known and popular algorithm for detecting lines in raster images. The standard Hough transform is rather slow to be usable in real-time, so different accelerated and approximated algorithms exist. This paper proposes a modified accumulation scheme for the Hough transform, which makes it suitable for computer systems with small but fast read-write memory – such as the t...

In this paper, we study the Hough transform theory images by generating the peak point from gray scale images, and seek for the effect caused by the distance and the angles. Lines will appear on the edge of images, which has been processed edge detection theorem. The input to a Hough transform is normally an image that has been edge detected with a Robert, Sobel or Canny edge detector, for inst...

We provide an explicit description of the convex hull of the set of matrices of bounded rank, restricted to balls for the spectral norm. As applications, we deduce two relaxed forms of the rank function restricted to balls for the spectral norm: one is the quasiconvex hull of this rank function, another one is the convex hull of the rank function, thus retrieving Fazel's theorem (2002). Key-wor...