Introduction to Vision Science
Different animals have different visual systems and so presumably have different ways of seeing. How does the way in which we see depend on the optical, neural and motor components of our visual systems? The mathematical tools needed to answer this question are introduced in this book. Elementary linear algebra is used to describe the transformation of the stimulus that occurs in the formation of the optical, neural and motor images in the human visual system. The distinctive feature of the approach is that transformations are specified with enough rigour for readers to be able to set up their own models and generate predictions from them.
Underlying the approach of this book is the goal of providing a self-contained source for the derivation of the basic equations of vision science. An introductory section on vector and matrix algebra covers the mathematical techniques which are applied to both sensory and motor aspects of the visual system, and the intervening steps in the mathematical arguments are given in full, in order to make the derivation of the equations easier to follow. A subsidiary goal of this book is to demonstrate the utility of current desktop computer packages which make the application of mathematics very easy.
All the numerical results were produced using only a spreadsheet or mathematics package, and example calculations are included in the text.
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Chapter Binocular Vision
THE NEURAL IMAGE
Spatial Frequency Selectivity
Basic Laplace Transforms
The Neural Integrator
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amplitude angular magnification axis of rotation blur circle Cartesian base vectors cells centre colour matching functions column component cone sensitivity functions cornea corresponds cyclopean eye denoted described difference dimensional diplopia disparities associated disparity due eigenvector eigenvector transformation entrance pupil equal Euler angles exit pupil exponential eye movements factor Fourier transform frontal plane Gaussian function gaze angle given horizontal disparity integral learning rule lens line of fixation linear transformation Listing's law luminance matrix equation mechanical system millimetres muscles Nanometres neural neurons object Oja's optical axis optical system orientation orthogonal output pattern of disparities plotted in Fig point of fixation position Posterior principal planes receptive field reduced distance referred refracting surfaces refractive index respect retina right eye saccade schematic eye semicircular canals shown in Fig simplified sinusoidal spatial frequency specifies stimulus system matrix transfer function translation values vertex visual wavelength weight vector weighting functions zero
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