Interpretation of Visual Motion

Interpretation of Visual Motion

A Computational Study

1st Edition - January 1, 1988

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  • Author: Muralidhara Subbarao
  • eBook ISBN: 9781483258928

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Interpretation of Visual Motion: A Computational Study provides an information processing point of view to the phenomenon of visual motion. This book discusses the computational theory formulated for recovering the scene from monocular visual motion, determining the local geometry and rigid body motion of surfaces from spatio-temporal parameters of visual motion. This compilation also provides a theoretical and computational framework for future research on visual motion, both in human vision and machine vision areas. Other topics include the computation of image flow from intensity derivatives, instantaneous image flow due to rigid motion, time and space-time derivatives of image flow, and estimation of maximum absolute error. This publication is recommended for professionals and non-specialists intending to acquire knowledge of visual motion.

Table of Contents

  • 1 Introduction

    1.1 Problem Description

    1.2 Motivations for the Study

    1.3 The Approach

    1.4 Strategy of Formulation and Analysis

    1.5 Summary of Results

    1.6 Conclusions and New Questions

    1.7 Organization of the Book

    2 Background

    2.1 Introduction

    2.2 Visual Ambiguity and Assumptions

    2.3 Discrete Approach

    2.4 Continuous Approach

    2.4.1 Computation of Image Flow from Intensity Derivatives

    2.4.2 Computation of Image Flow from Features of the Intensity Distribution

    2.5 Interpretation of Image Flow

    2.6 Some Comments on the Approaches

    2.7 What is New?

    3 Formulation

    3.1 Computational Theory and Approach

    3.2 Image Formation

    3.3 Formulation: Instantaneous Image Flow Due to Rigid Motion

    3.4 The Nature of the Image Flow Equations

    4 Solving the Image Flow Equations

    4.1 Solution for Motion And Slopes in Terms of Θ and r

    4.2 Planar Surfaces

    4.2.1 The Planar Surface Equations

    4.2.2 Solving for Θ and r

    4.2.3 Bounds on the Velocity of Approach from First Order Flow Parameters

    4.2.4 The Two-Fold Ambiguity

    4.2.5 Resolving the Two-Fold Ambiguity of Interpretation Using Spatial or Temporal Consistency

    4.3 Curved Surfaces

    4.3.1 Solving the Image Flow Equations

    4.3.2 Conditions for the Presence of Multiple Interpretations

    4.3.3 Resolving Ambiguity of Interpretation

    4.4 Overall Summary of the Nature of the Solutions

    4.5 Fully Reduced Flow Parameters for Image Flow Analysis

    4.5.1 Motion Parameters

    4.5.2 Structure Parameters

    4.5.3 Image Flow Parameters

    4.5.4 Image Flow Equations

    4.5.5 Solving the Image Flow Equations

    5 Using Temporal Information: Rigid Motion

    5.1 Formulation and Solution

    5.2 Relating the First Order Image Flow Parameters and Scene Parameters

    5.3 Rigid and Uniform Motion

    5.3.1 The Case When V is Uniform with Respect to the Camera

    5.4 The Case When the Direction of V Changes

    5.4.1 The Case When the Camera Tracks a Point

    5.5 Accelerated Motions

    5.5.1 An Example of Non-Uniform Motion

    6 The General Formulation

    6.1 Representation and Formulation

    6.1.1 An Example of Non-Rigid Motion

    6.2 Arbitrarily Time-Varying 3D Scenes: Non-Rigid and Nonuniform Motion of General Surfaces

    6.2.1 Time and Space-Time Derivatives of Image Flow

    6.2.2 The Nature of the Problem

    7 Error Sensitivity and Numerical Examples

    7.1 Estimation of Maximum Absolute Error

    7.2 Numerical Examples of Multiple Solution Cases

    8 Conclusions


    A Expressing a Surface in Terms of Image Coordinates

    B Some Degenerate Cases and Conditions

    1 Some Degenerate Cases

    2 Condition for the Moving Surface to be Planar

    3 Condition for the Moving Surface to be Curved

    4 Solution for Orientation and Motion in Terms of r and Θ

    C Solving the Image Flow Equations: Planar Surfaces

    1 Bounds from First Order Flow Parameters

    2 A Method for Determining the Structure and Motion Parameters

    3 Solving for Θ and r

    4 Summary of the Solution Method

    5 Interpretation of the Bounds on Vz and Ωz

    D Nature of Solutions for Planar Surfaces

    1 Relation Between the Two Interpretations

    E Resolving the Ambiguity of Interpretation: Planar Surfaces

    1 Evolution of Planar Surface Solutions

    2 Uniqueness of Interpretation: Two Flow Fields

    F Solving the Image Flow Equations: Curved Surfaces

    1 Solution for Curvatures

    2 Constraints on r and Θ 113

    3 Summary of Computational Algorithm

    G Conditions for Multiple Interpretations: Curved Surfaces

    1 Solutions for Θ

    2 Multiple Interpretations Due o Multiple Solutions for Θ

    2.1 A Necessary Condition for Multiple Solutions to Θ

    2.2 Triple Solution Theorem

    2.3 Double Solution Theorem 1

    2.4 The Four Solution Theorem

    3 Multiple Interpretations Due to Multiple Solutions for r

    3.1 Double Solution Theorem 2

    4 Condition for Uniqueness of Interpretation

    H Solving for Θ When the Direction of V Changes

    I Solving for r and Θ When the Camera Tracks a Point

    J Surface Deformation Parameters

    1 Interpretation of the Velocity Gradient Tensor

    2 Interpretation of the Motion and Deformation Parameters aij



Product details

  • No. of pages: 156
  • Language: English
  • Copyright: © Morgan Kaufmann 1988
  • Published: January 1, 1988
  • Imprint: Morgan Kaufmann
  • eBook ISBN: 9781483258928

About the Author

Muralidhara Subbarao

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