Abstract
Multiscale representation is a methodology that is being used more and more when describing real-world structures. Scale-space representation is one formulation of multiscale representation that has received considerable interest in the literature because of its efficiency in several practical applications and the distinct properties of the Gaussian kernel that generate the scale space. Together, some of these properties make the Gaussian unique. Unfortunately, the Gaussian kernel has two practical limitations: information loss caused by the unavoidable Gaussian truncation and the prohibitive processing time due to the mask size. In this paper, we propose a new kernel family derived from the Gaussian with compact supports that are able to recover the information loss while drastically reducing processing time. This family preserves a great part of the useful Gaussian properties without contradicting the uniqueness of the Gaussian kernel. The construction and analysis of the properties of the proposed kernels are presented in this paper. To assess the developed theory, an application of extracting handwritten data from noisy document images is presented, including a qualitative comparison between the results obtained by the Gaussian and the proposed kernels.