Title :
On the equivalence of normalized convolution and normalized differential convolution
Author :
Westin, Carl-Fredrik ; Nordberg, Klas ; Knutsson, Hans
Author_Institution :
Dept. of Electr. Eng., Linkoping Univ., Sweden
Abstract :
This paper establishes an algebraic relation between two methods recently reported; normalized convolution and normalized differential convolution. These are general methods for filtering incomplete or uncertain data and are based on the separation of both data and operator into a signal part and a certainty part. General filtering can be performed without preprocessing input data with an interpolation step. The methods allow both data and operators to be scalars, vectors or tensors of higher order. Normalized differential convolution has been used in a wide range of applications. Examples are estimation of gradient estimation in irregularly sampled data, estimation of differential invariants in sparse image flow fields and image edge effect reduction. It was previously shown that normalized convolution produces a description of the neighbourhood which is optimal in a least square sense. The algebraic relation to normalized differential convolution presented in this paper proves that the latter method is also optimal in the same sense as well
Keywords :
algebra; convolution; edge detection; filtering theory; image processing; interpolation; least squares approximations; parameter estimation; algebraic relation; differential invariants; equivalence; estimation; filtering; gradient estimation; image analysis; image edge effect reduction; interpolation; irregularly sampled data; least square optimisation; normalized convolution; normalized differential convolution; operators; scalars; sparse image flow fields; tensors; vectors; Computer vision; Convolution; Data preprocessing; Filtering; Image edge detection; Interpolation; Laboratories; Least squares methods; Sampling methods; Tensile stress;
Conference_Titel :
Acoustics, Speech, and Signal Processing, 1994. ICASSP-94., 1994 IEEE International Conference on
Conference_Location :
Adelaide, SA
Print_ISBN :
0-7803-1775-0
DOI :
10.1109/ICASSP.1994.389389