Abstract: A neural network uses a fuzzy membership function, the parameters of which are adaptive during the training process, to parameterize the interconnection weights between an (n-1)'th layer and an n'th layer of the network. Each j'th node in each k'th layer of the network except the input layer produces its output value y.sub.k,j according to the function ##EQU1## where N.sub.k-1 is the number of nodes in layer k-1, i indexes the nodes of layer k-1 and all the w.sub.k,i,j are interconnection weights. The interconnection weights to all nodes j in the n'th layer are given by w.sub.n,i,j =w.sub.n,j (i, p.sub.n,j,1, . . . , p.sub.n,j,p.sbsb.n).The apparatus is trained by setting values for at least one of the parameters p.sub.n,j,1, . . . , p.sub.n,j,Pn. Preferably the number of parameters P.sub.n is less than the number of nodes N.sub.n-1 in layer n-1. w.sub.n,j (i,p.sub.n,j,1, . . . , p.sub.n,j,Pn) can be convex in i, and it can be bell-shaped. Sample functions for w.sub.n,j (i, p.sub.n,j,1, . . . , p.sub.

Abstract: An image is compressed by identifying edge pixels of the image; creating a filled edge array of pixels each of the pixels in the filled edge array which corresponds to an edge pixel having a value equal to the value of a pixel of the image array selected in response to the edge pixel, and each of the pixels in the filled edge array which does not correspond to an edge pixel having a value which is a weighted average of the values of surrounding pixels in the filled edge array which do correspond to edge pixels; and subtracting the filled edge array from the image array to create a difference array. The edge file and the difference array are then separately compressed and transmitted or stored. The original image is later reconstructed by creating a preliminary array in response to the received edge file, and adding the preliminary array to the received difference array. Filling is accomplished by solving Laplace's equation using a multi-grid technique.