New Model of Heteroasociative Min Memory Robust to Acquisition Noise

Abstract

Associative memories in min and max algebra are of great interest for pattern recognition. One property of these is that they are one-shot, that is, in an attempt they converge to the solution without having to iterate. These memories have proven to be very efficient, but they manifest some weakness with mixed noise. If an appropriate kernel is not used, that is, a subset of the pattern to be recalled that is not affected by noise, memories fail noticeably. A possible problem for building kernels with sufficient conditions, using binary and gray-scale images, is not knowing how the noise is registered in these images. A solution to this problem is presented by analyzing the behavior of the acquisition noise. What is new about this analysis is that, noise can be mapped to a distance obtained by a distance transform. Furthermore, this analysis provides the basis for a new model of min heteroassociative memory that is robust to the acquisition/mixed noise. The proposed model is novel because min associative memories are typically inoperative to mixed noise. The new model of heteroassocitative memory obtains very interesting results with this type of noise.

Generic Model of Max Heteroassociative Memory Robust to Acquisition Noise

“…As a result of their outstanding performance, associative memories have found numerous applications across various fields [7,[9][10][11][12][13][14][15][16][17][18][19], including medicine [9,10,20] and robotics [1,[21][22][23]. Associative memories can be categorized according to their design into two main types: those that are based on the algebra of the reals [24][25][26][27][28][29][30][31][32][33][34][35][36] and those that are based on the minmax algebra [2][3][4][5][6][7]16,18,37,38]. In this paper, we will focus specifically on memories in minmax algebra.…”

“…It is worth noting that the morphological associative memories, which emerged in the 1990s, were the first to use this particular algebraic approach [2,3], during the 2000s, a new type of memory called αβ memories was developed [16,18] and another memory model based on minmax algebra was developed in 2021 [6]. The benefits offered by memory models based on minmax algebra have spurred numerous advances in this field [16][17][18][19][37][38][39][40]. One of the main challenges facing associative memories in minmax algebra is the creation of a kernel-a subset of the input pattern x-that remains unaffected by noise.…”

“…This is a non-trivial problem, as the behavior of noise must be accounted for during the construction of the kernel. If noise affects the kernel, memories based on minmax algebra will not work [2,3,6,16,18,37,38]. This paper proposes a novel solution to the aforementioned challenge faced by associative memories in minmax algebra.…”

“…Although the construction of associative memories in minmax algebra varies in the way of associating input patterns with output patterns, they apply minmax algebra in the same way. Therefore, when applying kernel creation models to morphological memories, they are also functional for αβ memories [38] and, by extension, to the memory proposed by Gamino and Díaz-De-León [6,41].…”

Lossless Medical Image Compression by Using Difference Transform

“…To address this issue, researchers have developed methods of lossless image compression to be used in medical pursuits and other areas [ 17 , 18 , 20 , 21 , 22 , 23 , 24 , 25 , 26 , 27 , 28 , 29 , 30 , 31 , 32 , 33 ]. The second issue is how to eliminate acquisition of noise in images, a topic that has been the inspiration for much research [ 34 , 35 , 36 , 37 , 38 , 39 ].…”