Let N , N1 and N2 be point processes such that N1 is obtained from N by homogeneous independent thinning and N2 = N −N1. We give a new elementary proof that N1 and N2 are independent if and only if N is a Poisson point process. We present some applications of this result to test if a homogeneous point process is a Poisson point process.

The maximum of the linking number between two lattice polygons of lengths n1, n2 (with n1 ≤ n2) is proven to be of the order of n1(n2) 1 3 . This result is generalized to smooth links of unit thickness. The result also implies that the writhe of a lattice knot K of length n is at most 26 n4/3/π. In the second half of the paper examples are given to show that linking numbers of order n1(n2) 1 3 ...

Image processing is a science that uncovers information about images. Enhancement of an image is necessary to improve appearance or to highlight some aspect of the information contained in the image. Whenever an image is converted from one form to another, e.g., acquired, copied, scanned, digitized, transmitted, displayed, printed, or compressed, many types of noise or noiselike degradations ca...