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    Book

    Pattern Analysis

    Lectures in Pattern Theory Volume II

    U. Grenander in Applied Mathematical Sciences (1978)

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    Chapter

    Introduction

    In this book we shall continue the mathematical study of regular structures begun in Volume I. With the help of the concepts of pattern synthesis introduced in the previous volume, we now turn to the inverse p...

    U. Grenander in Pattern Analysis (1978)

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    Chapter

    Point Patterns

    Let us consider lattice point patterns as described in Volume 1, Section 3.5, subject to deformations of the type jittered crystal, Volume 1, Section 4.2.

    U. Grenander in Pattern Analysis (1978)

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    Chapter

    Network Pattern Processors

    Imagine a hypothetical being — let us use the name Ω — living in an environment or microworld from which it receives sensory inputs. The pattern structure that Ω is confronted by is assumed unknown to start wi...

    U. Grenander in Pattern Analysis (1978)

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    Chapter

    Ends and Means in Pattern Analysis

    The basic concepts of pattern theory consist of objects and relations. The pattern objects are generators, configurations, pure and deformed images, pattern classes. The pattern relations are given in terms of si...

    U. Grenander in Pattern Analysis (1978)

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    Chapter

    Analysis of Certain Temporal Patterns

    Temporal patterns are defined through generators of contrast type: they can be given as functions on the real line and taking values in some contrast space. There are many sorts of temporal patterns where the ...

    U. Grenander in Pattern Analysis (1978)

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    Chapter

    Set Patterns and Statistical Geometry

    In this chapter the generators will be given as certain subsets of the background space X = R2 or R3 with similarity groups EG(2) - EG(3) or TRANS(2) - TRANS(3). Examples of combinatory rules ℛ suitable for set p...

    U. Grenander in Pattern Analysis (1978)

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    Chapter

    Pattern Processors for Language Abduction

    In Chapter 6, we studied a network 𝒩 that could modify itself in order to learn at least some of the patterns appearing in its environment. This was done by modifying the coupling coefficients of 𝒩, i.e. by chang...

    U. Grenander in Pattern Analysis (1978)

  9. No Access

    Chapter

    Analysis of Abstract Patterns

    In Sections 2.1 – 2.3 we shall treat (linear) sequence images with abstract symbols. The configurations need not have linear connection type, however, and we shall study what happens when different deformation...

    U. Grenander in Pattern Analysis (1978)