We propose a new method for computing the 2-d Minkowski sum of non-convex polygons. Our method is convolution based. The main idea is to use the reduced convolution and filter the boundary by using the topological properties of the Minkowski sum. The main benefit of this proposed approach is from the fact that, in most cases, the complexity of the complete convolution is much higher than the co...

The quaternion Fourier transform (qFT) is an important tool in multi-dimensional data analysis, in particular for the study of color images. An important problem when applying the qFT is the mismatch between the spatial and frequency domains: the convolution of two quaternion signals does not map to the pointwise product of their qFT images. The recently defined ‘Mustard’ convolution behaves ni...

This paper proposes a convolution forest kernel to effectively explore rich structured features embedded in a packed parse forest. As opposed to the convolution tree kernel, the proposed forest kernel does not have to commit to a single best parse tree, is thus able to explore very large object spaces and much more structured features embedded in a forest. This makes the proposed kernel more ro...

Convolution and Deconvolution is having wide area of application in Digital Signal Processing. Convolution helps to estimate the output of a system with arbitrary input, with knowledge of impulse response of the system. Linear systems characteristics are completely specified by the systems impulse response, as governed by the mathematics of convolution. And with the knowledge of impulse respons...

This paper continues the investigation in digital signal processing of spectral analysis on certain non-commutative nite groups|wreath product groups. We describe here the generalization of discrete cyclic convolution to convolution over these groups and show how it reduces to multiplication in the spectral domain. Finite group based convolution is deened in both the spatial and spectral domain...

We present a very simple and fast algorithm to compute the convolution of an arbitrary sequence x with a sequence of a specific type, a. The sequence a is any linear combination of polynomials, exponentials and trigonometric terms. The number of steps for computing the convolution depends on a certain complexity of a and not on its length, thus making it feasible to convolve a sequence with ver...

Since the introduction of the behavioral approach to systems theory by Willems [13, 14, 15, 16, 17] the main emphasis has been on discrete time systems. Papers dealing with continuous time systems generally have assumed from the start that a set of differential equations was given. In his thesis Soethoudt has given necessary and sufficient conditions on the behavior of a continuous time system ...

Depthwise convolution and grouped convolution has been successfully applied to improve the efficiency of convolutional neural network (CNN). We suggest that these models can be considered as special cases of a generalized convolution operation, named channel local convolution(CLC), where an output channel is computed using a subset of the input channels. This definition entails computation depe...