of a doctoral thesis, accepted by the faculty of Electrical Engineering and Information Sciences of the Technische Universität München

Invariant Description of Pictorial Patterns via Auto-Comparison Functions

The main part of this work consists of three chapters. Following the introduction an extensive exposition is given of a new and systematic concept for the invariant description of pictorial patterns. The approach is based on the analysis of patterns by so-called auto-comparison functions that are a generalization of the auto-correlation analysis, well-known in signal theory. Features are presented that are invariant under all similarity transformations. They are discussed in depth, together with methods for their extraction. It is demonstrated that the descriptive power of these features surpasses that of the only competing kind of features, comparable with respect to their invariance properties. In the following chapter it is shown that neural networks are well suited for the parallel computation of the proposed features. Invariant pattern analysis can be performed within the same network that serves the pattern-independent extraction of motion parameters based on an also new cross-correlation method. This dualistic principle of analysis is an essential condition for the feasibility of self-organization of the required neural circuitry with its highly specific interconnection scheme. Systems for the analysis of motion with the claimed properties have recently been identified in monkey and cat.

Data and algorithms are contained in a second part. The proposed features have been computed from 30 characters, using a specially designed opto-digital processor. Algorithms for the serial computation of the features are presented and illustrated by two basic examples. An appendix concludes the work. It deals with several selected topics from the field of analytic geometry and gives a systems-theoretical analysis of the optical zoom-correlator.

d’une thèse doctorale acceptée par la faculté d’Electrotechnique et des Sciences de l’Information à la Technische Universität München

Description Invariante des Formes Picturales par des Fonctions d’Autocomparaison

La partie principale du traité est composée de trois chapitres. Après l’introduction vient une présentation étendue du concept nouveau et systématique de la description invariante des formes picturales. Ceci repose sur l’analyse des formes par des fonctions dites d’autocomparaison, qui forment une généralisation de l’analyse d’autocorrélation, déjà bien connue dans le domaine de la théorie du signal. Les propriétés des caractéristiques, qui sont invariantes par toutes les transformations par similitude (générale), et certaines méthodes de calculs sont présentées et discutées par la suite. Il est également démontré, que la force de description de ces caractéristiques dépasse de beaucoup celle des caractéristiques qui résultent du seul procédé comparable concernant la propriété d’invariance. Dans le chapitre suivant, il est montré que les réseaux neuronaux conviennent parfaitement pour le calcul parallèle des caractéristiques proposées. L’analyse invariante des formes peut être faite dans le même réseau que celui qui permet l’extraction indépendante des formes des paramètres de mouvement, par un nouveau procédé d’intercorrélation. Ce principe d’analyse dualiste représente une condition essentielle à la faisabilité d’une autostructuration du circuit neuronal requis, avec son schéma d’interconnections à haut degré de spécifité. Des systèmes de l’analyse du mouvement avec les propriétés exigées ont été découvertes, il y a peu, grâce à des expériences sur des singes et des chats.

Les données et les algorithmes se trouvent dans la deuxième partie. Grâce à un processeur opto-digital, spécialement développé pour cette expérience, les caractéristiques proposées ont été évaluées à partir de 30 signes graphiques. Deux exemples simples permettent d’expliquer les algorithmes pour le traitement en série de ces caractéristiques. Une annexe termine le traité. On y trouve quelques thèmes choisis de la géométrie analytique et une analyse, rapportée à la théorie des systèmes, du zoom-corrélateur optique.

Back Traduction par S. Desmoulin

einer von der Fakultät für Elektrotechnik und Informationstechnik der Technischen Universität München angenommenen Dissertation

Invariante Bildbeschreibung mit Hilfe von Autovergleichs-Funktionen

Der Hauptteil der Abhandlung besteht aus drei Kapiteln. Auf die Einführung folgt die umfassende Darstellung des neuen und systematischen Ansatzes zur invarianten Bildmuster-Beschreibung. Er beruht auf der Musteranalyse mit Hilfe sogenannter Autovergleichs-Funktionen, einer Verallgemeinerung der von der Signaltheorie her bekannten Autokorrelations-Analyse. Merkmale, die gegenüber allen Ähnlichkeits-Transformationen invariant sind und Verfahren zu ihrer Berechnung, werden vorgestellt und ausführlich diskutiert. Es wird nachgewiesen, daß die Merkmale in ihrer Beschreibungskraft denen des einzigen hinsichtlich der Invarianzleistungen vergleichbaren Verfahrens weit überlegen sind. Im folgenden Kapitel wird gezeigt, daß sich neuronale Netzwerke vorzüglich zur parallelen Berechnung der vorgeschlagenen Merkmale eignen. Die invariante Musteranalyse kann im selben Netzwerk erfolgen wie ein ebenfalls neuartiges Kreuzkorrelations-Verfahren zur musterunabhängigen Gewinnung von Bewegungsparametern. Dieses dualistische Analyseprinzip stellt eine wesentliche Bedingung der Möglichkeit zur Selbststrukturierung der hochspezifischen neuronalen Verschaltung dar. Bewegungsanalyse-Systeme der geforderten Eigenschaften wurden unlängst bei Affe und Katze nachgewiesen.

Die Daten und Algorithmen finden sich in einem zweiten Teil. Mit einem eigens entwickelten opto-digitalen Prozessor wurden die vorgeschlagenen Merkmale aus 30 Zeichen ermittelt. Algorithmen zur seriellen Merkmals-Berechnung werden vorgestellt und anhand zweier einfacher Beispiele erläutert. Ein Anhang zur analytischen Geometrie sowie zur Beschreibung und system-theoretischen Analyse des verwendeten optischen Zoom-Korrelators beschließt die Abhandlung.

Original Abstract :
Motion- and Invariant Form-Analysis: A Dualism?

A new and systematic concept for the extraction of invariant shape-descriptors is based on the detection of defined spatial coincidences within a spatially discrete pattern representation. These features express pattern congruences, similarities, various symmetries and other more abstract properties such as compactness, complexity, etc. For the computation of a subclass of such features that is invariant under the whole group of similarity transformations, a parallel processing network is proposed acting preferably on a retinotopic representation containing line-like pattern versions. The network consists of many identical processing (sub)units, each combining two signals (from points in the representation) in a non-linear way (e.g. multiplicative). Results from these elementary operations are summed according to a specific scheme (called “generalized dipole-moments”). Thus, the computing-elements have properties attributed to neurons: large number of non-linear synaptic interactions of input signals on dendrites and (linear) somatic summation of the results (cf. the extensive investigations by Poggio, Koch and Torre).
Because of the highly specific interconnection schemes between pairs of pixels (axonal projections from the representation —> interacting synapses) on one hand, as well as between the subunits (interacting synapses —> soma, via dendrites) on the other, ways for their formation must be found. With the definition of invariance in mind, it is argued that geometric pattern transformations, introduced by various kinds of motion, are the appropriate stimuli for the maturation of neural structures that can serve both: motion-analysis and invariant pattern description. As examples, two networks for the pattern independent extraction of motion parameters are described (depth-motion of [planar] objects—which is perhaps the most prominent of all natural motions [movement]—and rotations in fronto-parallel planes). These networks consist of units similar to Reichardt-detectors (RD), i.e. spatio-temporal coincidence detectors (multipliers) with two inputs, one of which is delayed by ∆T = const. In order to obtain motion parameters, the RDs must be spatially arranged and their output signals must be summed, both according to the investigated kind of motion. The resulting system then cross-correlates dynamic scenes with structurally stored models of various kinds of motion. For static patterns (t > ∆T) however, RDs behave like common multipliers (subunits). Under this aspect, networks serving for pattern independent motion-analysis are identical to those required for invariant form-descriptions. It is conjectured that both tasks are actually performed within the same neural structure (dualism).
A modular model structure for this kind of local/global motion/shape-analysis is introduced. The properties (mainly receptive fields) of the involved model neurons (e.g. local summation units) are compared with neurons found in motion analyzing systems in monkey and cat as they were recently studied among others, for instance by Sakata et al. and Rauschecker et al. (The model accords well with the available experimental results that deal, up to now, mainly with dynamic properties.) Thereby the role subunits can play for receptive fields is discussed. It turns out that receptive fields alone do not always permit conclusions about signal processing principles.

Abstract of :
Relational Processing: A Concept for the Explanation of Invariant Visual Pattern Recognition

Results from extensive studies and simulations of Perceptron-like pattern recognition structures are reported. As this type of concept is quite popular not only for technical purposes but also widely accepted for the explanation of visual pattern recognition, its processing capabilities were compared with some demonstrated by the human visual system, especially invariant recognition and Gestalt-related pattern description. It can be shown, though invariant classification is not impossible within a Perceptron structure (if there are no restrictions concerning the effort), that invariant features are not involved in such processing (except trivial ones) hence the approach does not suffice, e.g. for the explanation of invariant pattern description.
Consequently, a concept is proposed that delivers invariant features which express inner geometric relations of a pattern, namely symmetries, similarities, congruences, etc. Pattern descriptions in such terms correspond well to those used in Gestalt psychology. A mathematical formulation of the concept, based on generalized autocomparison functions, and examples are given. The biological plausibility is discussed.
Results from simulations of the space invariant processing—that is typical for a first Perceptron stage—and of a relational system are shown. They were computed analog-optically in parallel. This illustrative method essentially supports the understanding of linear, parallel working pattern processors. A refined version of the basic relational approach is presented and accompanied by results from digitally performed simulations.