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Vision_Notes_1 - Vision Notes Wilson S Geisler University...

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1 Vision Notes * Wilson S. Geisler University of Texas January, 2003 * These notes are in an unfinished state; there are gaps, some missing sections and possibly some minor errors (but hopefully no major errors).
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2 I. Vision and visual systems ......................................................................................... 5 A. Some general comments ....................................................................................... 5 1. Light as a source of information ............................................................................ 5 2. Importance of vision .............................................................................................. 5 3. Steps in the process of vision ................................................................................. 6 4. Biological and artificial vision systems .................................................................. 6 B. Visual tasks and visual performance ............................................................... 7 1. Objective versus subjective tasks ........................................................................... 8 2. Identification and estimation tasks ....................................................................... 10 3. Measures of performance ..................................................................................... 10 4. Feedback in visual tasks ....................................................................................... 11 5. Two-alternative forced-choice tasks .................................................................... 12 6. N-alternative forced choice tasks ......................................................................... 23 7. Testing physiological theories with behavioral measurements ........................... 23 8. Classical detection and discrimination tasks ........................................................ 23 9. Direct estimation tasks ......................................................................................... 23 10. Partition tasks ..................................................................................................... 23 C. Physical constraints on visual processing .................................................... 23 D. Physiological constraints on visual processing ............................................ 25 E. Bayesian/Optimal Models ................................................................................. 25 1. Description of tasks .............................................................................................. 25 2. Model of the environmental and biological constraints ....................................... 25 3. Theory of how to complete the processing tasks with optimal efficiency ........... 25 F. Actual-performance models .............................................................................. 25 1. Anatomy ............................................................................................................... 25 2. Physiology ............................................................................................................. 26 3. Behavioral performance ........................................................................................ 26 4. Linear and nonlinear systems analysis .................................................................. 26 II. Visual Stimuli .......................................................................................................... 27 A. Light and light sources ....................................................................................... 27 1. Visible light ........................................................................................................... 27 2. Definition of power ............................................................................................... 28 3. Coherent and incoherent light ............................................................................... 28 4. Spectral power distribution .................................................................................. 29 5. Photons .................................................................................................................. 29 6. Randomness of light ............................................................................................. 30 7. Spectral quantum distribution ............................................................................... 31 8. Radiometry ............................................................................................................ 32 9. Photometry ............................................................................................................ 32 10. Colorimetry ......................................................................................................... 34 B. Light, surfaces and reflectance ......................................................................... 35 1. Primary and secondary (reflected) light sources .................................................. 35 2. Description of reflected light ................................................................................ 35 3. Extracting the reflectance function ....................................................................... 36 4. Extracting surface texture and region boundaries ................................................. 38
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3 5. Extracting surface orientation and distance .......................................................... 38 III. Image formation: geometrical optics ................................................................. 38 A. Visual scene as a collection of point sources ................................................. 39 B. Two point sources ................................................................................................ 39 C. Imaging with pin-holes ...................................................................................... 39 D. Imaging with lenses ............................................................................................ 40 1. The image and object planes ................................................................................ 41 2. The image distance depends on the object distance .............................................. 41 3. Lens focal length and power ................................................................................. 41 4. Aperture size and depth-of-focus .......................................................................... 42 E. Geometrical optics ............................................................................................... 42 1. Snell's law ............................................................................................................. 42 2. Ray tracing ............................................................................................................ 43 3. The cardinal points ................................................................................................ 43 4. Monochromatic aberrations .................................................................................. 44 5. Chromatic aberrations ........................................................................................... 45 F. Optics of the eye ................................................................................................... 45 1. The cornea ............................................................................................................. 46 2. The iris .................................................................................................................. 46 3. The lens ................................................................................................................. 47 4. Schematic eye ....................................................................................................... 47 5. Reduced schematic eye ......................................................................................... 47 6. Size and location of retinal images ....................................................................... 50 7. Ocular transmittance ............................................................................................. 50 8. Retinal illumination .............................................................................................. 51 9. Aberrations ............................................................................................................ 53 10. Diffraction ........................................................................................................... 54 IV. Linear systems analysis ....................................................................................... 56 A. Constraints defining linear systems ............................................................... 56 B. Impulse-response functions and convolution ................................................ 58 1. Convolution formula for one-dimensional systems .............................................. 59 2. Convolution formula for two-dimensional systems .............................................. 60 3. Measuring the impulse-response function ........................................................... 60 C. Linear weighting functions and cross correlation ........................................ 61 1. Cross-correlation formula for one-dimensional systems ...................................... 61 2. Cross-correlation formula for two-dimensional systems ...................................... 62 3. Measurement of the weighting function ............................................................... 62 D. The Fourier transform ....................................................................................... 63 1. One-dimensional systems ..................................................................................... 67 2. Two-dimensional systems ..................................................................................... 72 V.
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