No abstract

Local moments have attracted attention as local features in applications such as edge detection and texture segmentation. The main reason for this is that they are inherently integral-based features, so that their use reduces the effect of uncorrelated noise. The computation of local moments, when viewed as a neighborhood operation, can be interpreted as a convolution of the image with a set of masks. Nevertheless, moments computed inside overlapping windows are not independent and convolution does not take this fact into account. By introducing a matrix formulation and the concept of accumulation moments, this paper presents an algorithm which is computationally much more efficient than convolving and yet as simple.

No abstract

Abstract. An image can be seen as an element of a vector space and hence it can be expressed in as a linear combination of the elements of any non necessarily orthogonal basis of this space. After giving a matrix formulation of this well-known fact, this paper presents a reconstruction method of an image from its moments that sheds new light on this inverse problem. Two main contributions are presented: (a) the results using the standard approach based on the least squares approximation of the result using orthogonal polynomials can also be obtained using matrix pseudoinverses, which implies higher control on the numerical stability of the problem; and (b) it is possible to use basis functions in the reconstruction different from orthogonal polynomials, such as Fourier or Haar basis, allowing to introduce constraints relative to the bandwidth or the spatial resolution on the image to be reconstructed.