11 research outputs found
Morphological Network: How Far Can We Go with Morphological Neurons?
In recent years, the idea of using morphological operations as networks has
received much attention. Mathematical morphology provides very efficient and
useful image processing and image analysis tools based on basic operators like
dilation and erosion, defined in terms of kernels. Many other morphological
operations are built up using the dilation and erosion operations. Although the
learning of structuring elements such as dilation or erosion using the
backpropagation algorithm is not new, the order and the way these morphological
operations are used is not standard. In this paper, we have theoretically
analyzed the use of morphological operations for processing 1D feature vectors
and shown that this gets extended to the 2D case in a simple manner. Our
theoretical results show that a morphological block represents a sum of hinge
functions. Hinge functions are used in many places for classification and
regression tasks (Breiman (1993)). We have also proved a universal
approximation theorem -- a stack of two morphological blocks can approximate
any continuous function over arbitrary compact sets. To experimentally validate
the efficacy of this network in real-life applications, we have evaluated its
performance on satellite image classification datasets since morphological
operations are very sensitive to geometrical shapes and structures. We have
also shown results on a few tasks like segmentation of blood vessels from
fundus images, segmentation of lungs from chest x-ray and image dehazing. The
results are encouraging and further establishes the potential of morphological
networks.Comment: 35 pages, 19 figures, 7 table
Fuzzy Lattice Reasoning for Pattern Classification Using a New Positive Valuation Function
This paper describes an enhancement of fuzzy lattice reasoning (FLR) classifier for pattern classification based on a positive valuation function. Fuzzy lattice reasoning (FLR) was described lately as a lattice data domain extension of fuzzy ARTMAP neural classifier based on a lattice inclusion measure function. In this work, we improve the performance of FLR classifier by defining a new nonlinear positive valuation function. As a consequence, the modified algorithm achieves better classification results. The effectiveness of the modified FLR is demonstrated by examples on several well-known pattern recognition benchmarks
Multi-argument fuzzy measures on lattices of fuzzy sets
In this paper, we axiomatically introduce fuzzy multi-measures on bounded lattices. In particular, we
make a distinction between four different types of fuzzy set multi-measures on a universe X, considering
both the usual or inverse real number ordering of this lattice and increasing or decreasing monotonicity
with respect to the number of arguments. We provide results from which we can derive families of measures
that hold for the applicable conditions in each case
Signal Perceptron: On the Identifiability of Boolean Function Spaces and Beyond
In a seminal book, Minsky and Papert define the perceptron as a limited implementation of what they called “parallel machines.” They showed that some binary Boolean functions including XOR are not definable in a single layer perceptron due to its limited capacity to learn only linearly separable functions. In this work, we propose a new more powerful implementation of such parallel machines. This new mathematical tool is defined using analytic sinusoids—instead of linear combinations—to form an analytic signal representation of the function that we want to learn. We show that this re-formulated parallel mechanism can learn, with a single layer, any non-linear k-ary Boolean function. Finally, to provide an example of its practical applications, we show that it outperforms the single hidden layer multilayer perceptron in both Boolean function learning and image classification tasks, while also being faster and requiring fewer parameters
A comparative study on associative memories with emphasis on morphological associative memories
Orientador: Peter SussnerDissertação (mestrado) - Universidade Estadual de Campinas, Instituto de Matematica, Estatistica e Computação CientificaResumo: Memórias associativas neurais são modelos do fenômeno biológico que permite o armazenamento de padrões e a recordação destes apos a apresentação de uma versão ruidosa ou incompleta de um padrão armazenado. Existem vários modelos de memórias associativas neurais na literatura, entretanto, existem poucos trabalhos comparando as varias propostas. Nesta dissertação comparamos sistematicamente o desempenho dos modelos mais influentes de memórias associativas neurais encontrados na literatura. Esta comparação está baseada nos seguintes critérios: capacidade de armazenamento, distribuição da informação nos pesos sinápticos, raio da bacia de atração, memórias espúrias e esforço computacional. Especial ênfase dado para as memórias associativas morfológicas cuja fundamentação matemática encontra-se na morfologia matemática e na álgebra de imagensAbstract: Associative neural memories are models of biological phenomena that allow for the storage of pattern associations and the retrieval of the desired output pattern upon presentation of a possibly noisy or incomplete version of an input pattern. There are several models of neural associative memories in the literature, however, there are few works relating them. In this thesis, we present a systematic comparison of the performances of some of the most widely known models of neural associative memories. This comparison is based on the following criteria: storage capacity, distribution of the information over the synaptic weights, basin of attraction, number of spurious memories, and computational effort. The thesis places a special emphasis on morphological associative memories whose mathematical foundations lie in mathematical morphology and image algebraMestradoMatematica AplicadaMestre em Matemática Aplicad