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https://feeds.library.caltech.edu/people/Kajiya-J-T/combined.rss
A Caltech Library Repository Feedhttp://www.rssboard.org/rss-specificationpython-feedgenenTue, 16 Apr 2024 15:28:48 +0000Generic functions by nonstandard name scoping in APL
https://resolver.caltech.edu/CaltechAUTHORS:20161108-145757214
Authors: {'items': [{'id': 'Kajiya-J-T', 'name': {'family': 'Kajiya', 'given': 'James T.'}}]}
Year: 1981
DOI: 10.1145/390007.805354
We show how to acheive generic functions as in abstract datatypes (such as the Simula CLASS construct or ADA Package notion) for typeless languages, specifically APL. We do this by altering the standard dynamic scoping of names in APL to a scheme we call downward scoping.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/7s951-hyw11Generic functions by nonstandard name scoping in APL
https://resolver.caltech.edu/CaltechAUTHORS:20161108-145752592
Authors: {'items': [{'id': 'Kajiya-J-T', 'name': {'family': 'Kajiya', 'given': 'James T.'}}]}
Year: 1981
DOI: 10.1145/800142.805354
We show how to acheive generic functions as in abstract datatypes (such as the Simula CLASS construct or ADA Package notion) for typeless languages, specifically APL. We do this by altering the standard dynamic scoping of names in APL to a scheme we call downward scoping.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/z4ekq-w0h32Ray tracing parametric patches
https://resolver.caltech.edu/CaltechAUTHORS:20120420-151015498
Authors: {'items': [{'id': 'Kajiya-J-T', 'name': {'family': 'Kajiya', 'given': 'James T.'}}]}
Year: 1982
DOI: 10.7907/gsy5a-w9850
This paper describes an algorithm that uses
ray t racing techniques to display bivariate polynomial surface patches. A new intersection algorithm is developed
which uses ideas from algebraic geometry to obtain a numerical procedure for finding the intersection of a ray and a patch without subdivision. The algorithm may use complex coordinates for the (u, v)-parameters of the patches. The choice of these coordinates makes the computations more uniform, so that there are fewer special cases to be considered. In particular, the appearance and disappearance of silhouette edges can be handled quite naturally. The uniformity of these techniques may be suitable for implementation on either a general purpose pipelined machine, or on special purpose hardware.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/gsy5a-w9850Ray Tracing Parametric Patches
https://resolver.caltech.edu/CaltechCSTR:1982.5017-tr-82
Authors: {'items': [{'id': 'Kajiya-J-T', 'name': {'family': 'Kajiya', 'given': 'James T.'}}]}
Year: 1982
DOI: 10.7907/n7akq-eye39
This paper describes an algorithm that uses
ray tracing techniques to display bivariate polynomial surface patches. A new intersection algorithm is developed
which uses ideas from algebraic geometry to obtain a numerical procedure for finding the intersection of a ray and a patch without subdivision. The algorithm may use complex
coordinates for the (u,v)-parameters of the patches. The
choice of these coordinates makes the computations more
uniform, so that there are fewer special cases to be considered. In particular, the appearance and disappearance
of silhouette edges can be handled quite naturally. The
uniformity of these techniques may be suitable for implementation on either a general purpose pipelined machine, or on special purpose hardware.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/n7akq-eye39Ray tracing parametric patches
https://resolver.caltech.edu/CaltechAUTHORS:20161108-151316149
Authors: {'items': [{'id': 'Kajiya-J-T', 'name': {'family': 'Kajiya', 'given': 'James T.'}}]}
Year: 1982
DOI: 10.1145/800064.801287
This paper describes an algorithm that uses ray tracing techniques to display bivariate polynomial surface patches. A new intersection algorithm is developed which uses ideas from algebraic geometry to obtain a numerical procedure for finding the intersection of a ray and a patch without subdivision. The algorithm may use complex coordinates for the (u, v)-parameters of the patches. The choice of these coordinates makes the computations more uniform, so that there are fewer special cases to be considered. In particular, the appearance and disappearance of silhouette edges can be handled quite naturally. The uniformity of these techniques may be suitable for implementation on either a general purpose pipelined machine, or on special purpose hardware.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/xpt4s-31311Ray tracing parametric patches
https://resolver.caltech.edu/CaltechAUTHORS:20161108-151214936
Authors: {'items': [{'id': 'Kajiya-J-T', 'name': {'family': 'Kajiya', 'given': 'James T.'}}]}
Year: 1982
DOI: 10.1145/800064.801287
This paper describes an algorithm that uses ray tracing techniques to display bivariate polynomial surface patches. A new intersection algorithm is developed which uses ideas from algebraic geometry to obtain a numerical procedure for finding the intersection of a ray and a patch without subdivision. The algorithm may use complex coordinates for the (u, v)-parameters of the patches. The choice of these coordinates makes the computations more uniform, so that there are fewer special cases to be considered. In particular, the appearance and disappearance of silhouette edges can be handled quite naturally. The uniformity of these techniques may be suitable for implementation on either a general purpose pipelined machine, or on special purpose hardware.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/511kj-rxb12New techniques for ray tracing procedurally defined objects
https://resolver.caltech.edu/CaltechAUTHORS:20120420-112657704
Authors: {'items': [{'id': 'Kajiya-J-T', 'name': {'family': 'Kajiya', 'given': 'James T.'}}]}
Year: 1983
DOI: 10.1145/800059.801137
We present new algorithms for efficient ray tracing of three procedurally defined objects: fractal surfaces,
prisms, and surfaces of revolution. The fractal surface
algorithm performs recursive subdivision adaptively.
Subsurfaces which cannot intersect a given ray are culled
from further consideration. The prism algorithm transforms
the three dimensional ray-surface intersection problem
into a two dimensional ray-curve intersection problem,
which is solved by the method of strip trees. The surface of
revolution algorithm transforms the three dimensional ray-surface intersection problem into a two dimensional curve-curve intersection problem, which again is solved by strip trees.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/cbdeh-p6277Designing and implementing an array theory incorporating abstract datatypes
https://resolver.caltech.edu/CaltechAUTHORS:20161108-162335964
Authors: {'items': [{'id': 'Kajiya-J-T', 'name': {'family': 'Kajiya', 'given': 'James T.'}}]}
Year: 1983
DOI: 10.1145/390005.801230
We describe a variant of More's array theory which has an extra function we call promotion. This function effects an abstract datatype facility very similar to Smalltalk classes. We discuss how the addition of promotion solves some programming language design issues not addressed by standard array theory as well as extending the expressive power of array theory. Finally we discuss how the inclusion of classes simplifies the implementation of not only array theory but also present day APL interpreters as well.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/x4k88-3kg61Designing and implementing an array theory incorporating abstract datatypes
https://resolver.caltech.edu/CaltechAUTHORS:20161108-163011967
Authors: {'items': [{'id': 'Kajiya-J-T', 'name': {'family': 'Kajiya', 'given': 'James T.'}}]}
Year: 1983
DOI: 10.1145/800062.801230
We describe a variant of More's array theory which has an extra function we call promotion. This function effects an abstract datatype facility very similar to Smalltalk classes. We discuss how the addition of promotion solves some programming language design issues not addressed by standard array theory as well as extending the expressive power of array theory. Finally we discuss how the inclusion of classes simplifies the implementation of not only array theory but also present day APL interpreters as well.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/zgykv-t3c80New techniques for ray tracing procedurally defined objects
https://resolver.caltech.edu/CaltechAUTHORS:20161108-164204655
Authors: {'items': [{'id': 'Kajiya-J-T', 'name': {'family': 'Kajiya', 'given': 'James T.'}}]}
Year: 1983
DOI: 10.1145/800059.801137
We present new algorithms for efficient ray tracing of three procedurally defined objects: fractal surfaces, prisms, and surfaces of revolution. The fractal surface algorithm performs recursive subdivision adaptively. Subsurfaces which cannot intersect a given ray are culled from further consideration. The prism algorithm transforms the three dimensional ray-surface intersection problem into a two dimensional ray-curve intersection problem, which is solved by the method of strip trees. The surface of revolution algorithm transforms the three dimensional ray-surface intersection problem into a two dimensional curve-curve intersection problem, which again is solved by strip trees.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/4t8p9-bge60New techniques for ray tracing procedurally defined objects
https://resolver.caltech.edu/CaltechAUTHORS:20161108-165051440
Authors: {'items': [{'id': 'Kajiya-J-T', 'name': {'family': 'Kajiya', 'given': 'James T.'}}]}
Year: 1983
DOI: 10.1145/964967.801137
We present new algorithms for efficient ray tracing of three procedurally defined objects: fractal surfaces, prisms, and surfaces of revolution. The fractal surface algorithm performs recursive subdivision adaptively. Subsurfaces which cannot intersect a given ray are culled from further consideration. The prism algorithm transforms the three dimensional ray-surface intersection problem into a two dimensional ray-curve intersection problem, which is solved by the method of strip trees. The surface of revolution algorithm transforms the three dimensional ray-surface intersection problem into a two dimensional curve-curve intersection problem, which again is solved by strip trees.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/w30b8-yzg59New Techniques for Ray Tracing Procedurally Defined Objects
https://resolver.caltech.edu/CaltechAUTHORS:20161108-171134964
Authors: {'items': [{'id': 'Kajiya-J-T', 'name': {'family': 'Kajiya', 'given': 'James T.'}}]}
Year: 1983
DOI: 10.1145/357323.357324
We present new algorithms for efficient ray tracing of three procedurally defined objects: fractal surfaces, prisms, and surfaces of revolution. The fractal surface algorithm performs recursive subdivision adaptively. Subsurfaces which cannot intersect a given ray are culled from further consideration. The prism algorithm transforms the three-dimensional ray-surface intersection problem into a two-dimensional ray-curve intersection problem, which is solved by the method of strip trees. The surface-of-revolution algorithm transforms the three-dimensional ray-surface intersection problem into a two-dimensional curve-curve intersection problem, which again is solved by strip trees.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/1t9je-wh896An Object Oriented Architecture
https://resolver.caltech.edu/CaltechCSTR:1984.5168-tr-84
Authors: {'items': [{'id': 'Dally-W-J', 'name': {'family': 'Dally', 'given': 'William J.'}}, {'id': 'Kajiya-J-T', 'name': {'family': 'Kajiya', 'given': 'James T.'}}]}
Year: 1984
DOI: 10.7907/69pav-tep43
We propose a new machine architecture for high performance execution of late binding object
oriented languages The two principal mechanisms for attaining this goal are a fast context allocation/access
scheme and an instruction translation lookaside buffer New ideas in this paper include the concept and
implementation of abstract instructions, using floating point addresses to solve the small object problem, and a
novel context allocation/access mechanismhttps://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/69pav-tep43Ray tracing volume densities
https://resolver.caltech.edu/CaltechAUTHORS:20161108-174413704
Authors: {'items': [{'id': 'Kajiya-J-T', 'name': {'family': 'Kajiya', 'given': 'James T.'}}, {'id': 'Von-Herzen-B', 'name': {'family': 'Von Herzen', 'given': 'Brian P.'}}]}
Year: 1984
DOI: 10.1145/800031.808594
This paper presents new algorithms to trace objects represented by densities within a volume grid, e.g. clouds, fog, flames, dust, particle systems. We develop the light scattering equations, discuss previous methods of solution, and present a new approximate solution to the full three-dimensional radiative scattering problem suitable for use in computer graphics. Additionally we review dynamical models for clouds used to make an animated movie.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/fw587-b8f49Ray tracing volume densities
https://resolver.caltech.edu/CaltechAUTHORS:20161108-174929802
Authors: {'items': [{'id': 'Kajiya-J-T', 'name': {'family': 'Kajiya', 'given': 'James T.'}}, {'id': 'Von-Herzen-B', 'name': {'family': 'Von Herzen', 'given': 'Brian P.'}}]}
Year: 1984
DOI: 10.1145/10.1145/964965.808594
This paper presents new algorithms to trace objects represented by densities within a volume grid, e.g. clouds, fog, flames, dust, particle systems. We develop the light scattering equations, discuss previous methods of solution, and present a new approximate solution to the full three-dimensional radiative scattering problem suitable for use in computer graphics. Additionally we review dynamical models for clouds used to make an animated movie.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/h66ej-mhn57Submicron Systems Architecture: Semiannual Technical Report
https://resolver.caltech.edu/CaltechCSTR:1985.5202-tr-85
Authors: {'items': [{'id': 'Seitz-C-L', 'name': {'family': 'Seitz', 'given': 'Charles L.'}}, {'id': 'Kajiya-J-T', 'name': {'family': 'Kajiya', 'given': 'James T.'}}, {'id': 'Martin-A-J', 'name': {'family': 'Martin', 'given': 'Alain J.'}}, {'id': 'McEliece-R-J', 'name': {'family': 'McEliece', 'given': 'Robert J.'}}, {'id': 'Rem-M', 'name': {'family': 'Rem', 'given': 'Martin'}}]}
Year: 1985
DOI: 10.7907/mrh1j-cjp65
No abstract available.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/mrh1j-cjp65An object oriented architecture
https://resolver.caltech.edu/CaltechAUTHORS:20161018-145600518
Authors: {'items': [{'id': 'Dally-W-J', 'name': {'family': 'Dally', 'given': 'William J.'}}, {'id': 'Kajiya-J-T', 'name': {'family': 'Kajiya', 'given': 'James T.'}}]}
Year: 1985
We propose a new machine architecture for high performance
execution of late binding object oriented languages. The two principal mechanisms for attaining this goal are a fast context allocation/access scheme and an instruction translation lookaside buffer. New ideas in this
paper include the concept and implementation of abstract instructions, using floating point addresses to solve the small object problem, and a novel context allocation/access mechanism.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/b3k6m-eee21An object oriented architecture
https://resolver.caltech.edu/CaltechAUTHORS:20161018-145557181
Authors: {'items': [{'id': 'Dally-W-J', 'name': {'family': 'Dally', 'given': 'William J.'}}, {'id': 'Kajiya-J-T', 'name': {'family': 'Kajiya', 'given': 'James T.'}}]}
Year: 1985
DOI: 10.1145/327070.327151
We propose a new machine architecture for high performance
execution of late binding object oriented languages. The two principal mechanisms for attaining this goal are a fast context allocation/access scheme and an instruction translation lookaside buffer. New ideas in this
paper include the concept and implementation of abstract instructions, using floating point addresses to solve the small object problem, and a novel context allocation/access mechanism.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/gx1bq-eb040Anisotropic reflection models
https://resolver.caltech.edu/CaltechAUTHORS:20161108-173644069
Authors: {'items': [{'id': 'Kajiya-J-T', 'name': {'family': 'Kajiya', 'given': 'James T.'}}]}
Year: 1985
DOI: 10.1145/325165.325167
We present a new set of lighting models derived from the questions of electromagnetism. These models describe the reflection and refraction of light from surfaces which exhibit anisotropy---surfaces with preferred directions. The model allows a new mapping technique, which we call frame mapping. We also discuss the general relationship between geometric models, surface mapping of all types, and lighting models in the context of rendering images with extreme complexity.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/gersc-7tv42Anisotropic reflection models
https://resolver.caltech.edu/CaltechAUTHORS:20161108-173153920
Authors: {'items': [{'id': 'Kajiya-J-T', 'name': {'family': 'Kajiya', 'given': 'James T.'}}]}
Year: 1985
DOI: 10.1145/325334.325167
We present a new set of lighting models derived from the questions of electromagnetism. These models describe the reflection and refraction of light from surfaces which exhibit anisotropy---surfaces with preferred directions. The model allows a new mapping technique, which we call frame mapping. We also discuss the general relationship between geometric models, surface mapping of all types, and lighting models in the context of rendering images with extreme complexity.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/v43mt-n4x13Submicron Systems Architecture: Semiannual Technical Report
https://resolver.caltech.edu/CaltechCSTR:1986.5220-tr-86
Authors: {'items': [{'id': 'Seitz-C-L', 'name': {'family': 'Seitz', 'given': 'Charles L.'}}, {'id': 'Kajiya-J-T', 'name': {'family': 'Kajiya', 'given': 'James T.'}}, {'id': 'Martin-A-J', 'name': {'family': 'Martin', 'given': 'Alain J.'}}, {'id': 'McEliece-R-J', 'name': {'family': 'McEliece', 'given': 'Robert J.'}}, {'id': 'Rem-M', 'name': {'family': 'Rem', 'given': 'Martin'}}]}
Year: 1986
DOI: 10.7907/rzewj-csb10
No abstract available.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/rzewj-csb10Submicron Systems Architecture: Semiannual Technical Report
https://resolver.caltech.edu/CaltechCSTR:1986.5235-tr-86
Authors: {'items': [{'id': 'Seitz-C-L', 'name': {'family': 'Seitz', 'given': 'Charles L.'}}, {'id': 'Kajiya-J-T', 'name': {'family': 'Kajiya', 'given': 'James T.'}}, {'id': 'Martin-A-J', 'name': {'family': 'Martin', 'given': 'Alain J.'}}, {'id': 'McEliece-R-J', 'name': {'family': 'McEliece', 'given': 'Robert J.'}}, {'id': 'Rem-M', 'name': {'family': 'Rem', 'given': 'Martin'}}]}
Year: 1986
DOI: 10.7907/my65t-e9565
No abstract available.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/my65t-e9565Generative modeling: a symbolic system for geometric modeling
https://resolver.caltech.edu/CaltechAUTHORS:20161219-172224559
Authors: {'items': [{'id': 'Snyder-J-M', 'name': {'family': 'Snyder', 'given': 'John M.'}}, {'id': 'Kajiya-J-T', 'name': {'family': 'Kajiya', 'given': 'James T.'}}]}
Year: 1992
DOI: 10.1145/133994.134094
This paper discusses a new, symbolic approach to geometric modeling called generative modeling. The approach allows specification, rendering, and analysis of a wide variety of shapes including 3D curves, surfaces, and solids, as well as higher-dimensioned shapes such as surfaces deforming in
time, and volumes with a spatially varying mass density. The system also supports powerful operations on shapes such as "reparameterize this curve by arclength", "compute the volume, center of mass, and moments of inertia
of the solid bounded by these surfaces", or "solve this constraint or ODE system". The system has been used for a wide variety of applications, including creating surfaces for computer graphics animations, modeling the
fur and body shape of a teddy bear, constructing 3D solid models of elastic bodies, and extracting surfaces from magnetic resonance (MR) data.
Shapes in the system are specified using a language which builds multidimensional parametric functions. The language is baaed on a set of symbolic operators on continuous, piecewise differentiable parametric functions. We
present several shape examples to show bow conveniently shapes can be specified in the system. We also discuss the kinds of operators useful in a geometric modeling system, including arithmetic operators, vector and
matrix operators, integration, differentiation, constraint solution, and constrained minimisation. Associated with each operator are several methods, which compute properties about the parametric functions represented with
the operators. We show how many powerful rendering and analytical operations can be supported with only three methods: evaluation of the parametric function at a point, symbolic dlfferentiation of the parametric function, and
evacuation of an inclusion function for the parametric function.
Like CSG, and unlike most other geometric modeling approaches, 3Ms modeling approach is closed, meaning that further modeling operations cart be applied to any results of modeling operations, yielding valid models. Because
of this closure property, the symbolic operators can be composed very flexibly, allowing the construction of higher-level operators without changing
the underlying implementation of the system. Because the modeling operations are described symbolically, specified models can capture the designer's intent without approximation error.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/2rhq6-23292Generative modeling: a symbolic system for geometric modeling
https://resolver.caltech.edu/CaltechAUTHORS:20161219-173716782
Authors: {'items': [{'id': 'Snyder-J-M', 'name': {'family': 'Snyder', 'given': 'John M.'}}, {'id': 'Kajiya-J-T', 'name': {'family': 'Kajiya', 'given': 'James T.'}}]}
Year: 1992
DOI: 10.1145/142920.134094
This paper discusses a new, symbolic approach to geometric modeling called generative modeling. The approach allows specification, rendering, and analysis of a wide variety of shapes including 3D curves, surfaces, and solids, as well as higher-dimensioned shapes such as surfaces deforming in
time, and volumes with a spatially varying mass density. The system also supports powerful operations on shapes such as "reparameterize this curve by arclength", "compute the volume, center of mass, and moments of inertia
of the solid bounded by these surfaces", or "solve this constraint or ODE system". The system has been used for a wide variety of applications, including creating surfaces for computer graphics animations, modeling the
fur and body shape of a teddy bear, constructing 3D solid models of elastic bodies, and extracting surfaces from magnetic resonance (MR) data.
Shapes in the system are specified using a language which builds multidimensional parametric functions. The language is based on a set of symbolic operators on continuous, piecewise differentiable parametric functions. We
present several shape examples to show bow conveniently shapes can be specified in the system. We also discuss the kinds of operators useful in a geometric modeling system, including arithmetic operators, vector and
matrix operators, integration, differentiation, constraint solution, and constrained minimisation. Associated with each operator are several methods, which compute properties about the parametric functions represented with
the operators. We show how many powerful rendering and analytical operations can be supported with only three methods: evaluation of the parametric function at a point, symbolic dlfferentiation of the parametric function, and
evacuation of an inclusion function for the parametric function.
Like CSG, and unlike most other geometric modeling approaches, 3Ms modeling approach is closed, meaning that further modeling operations cart be applied to any results of modeling operations, yielding valid models. Because
of this closure property, the symbolic operators can be composed very flexibly, allowing the construction of higher-level operators without changing
the underlying implementation of the system. Because the modeling operations are described symbolically, specified models can capture the designer's intent without approximation error.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/brr34-8ke79Submicron Systems Architecture: Semiannual Technical Report
https://resolver.caltech.edu/CaltechCSTR:1985.5178-tr-85
Authors: {'items': [{'id': 'Seitz-C-L', 'name': {'family': 'Seitz', 'given': 'Charles L.'}}, {'id': 'Kajiya-J-T', 'name': {'family': 'Kajiya', 'given': 'James T.'}}, {'id': 'Martin-A-J', 'name': {'family': 'Martin', 'given': 'Alain J.'}}, {'id': 'McEliece-R-J', 'name': {'family': 'McEliece', 'given': 'Robert J.'}}, {'id': 'Rem-M', 'name': {'family': 'Rem', 'given': 'Martin'}}, {'id': 'Van-Tilborg-H-C-A', 'name': {'family': 'Van Tilborg', 'given': 'Henk'}}]}
Year: 2001
DOI: 10.7907/7fbb9-smt37
No abstract available.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/7fbb9-smt37Toward a mathematical theory of perception
https://resolver.caltech.edu/CaltechAUTHORS:20120424-144344175
Authors: {'items': [{'id': 'Kajiya-J-T', 'name': {'family': 'Kajiya', 'given': 'James Thomas'}}]}
Year: 2012
DOI: 10.7907/Z99Z92V3
A new technique for the modelling of perceptual
systems called formal modelling is developed. This
technique begins with qualitative observations about the
perceptual system, the so-called perceptual symmetries, to
obtain through mathematical analysis certain model
structures which may then be calibrated by experiment.
The analysis proceeds in two different ways depending upon
the choice of linear or nonlinear models. For the linear
case, the analysis proceeds through the methods of unitary
representation theory. It begins with a unitary group
representation on the image space and produces what we
have called the fundamental structure theorem. For the
nonlinear case, the analysis makes essential use of
infinite-dimensional manifold theory. It begins with a
Lie group action on an image manifold and produces the
fundamental structure formula.
These techniques will be used to study the brightness
perception mechanism of the human visual system. Several
visual groups are defined and their corresponding
structures for visual system models are obtained. A new
transform called the Mandala transform will be deduced
from a certain visual group and its implications for image processing will be discussed. Several new phenomena of
brightness perception will be presented. New facts about
the Mach band illusion along with new adaptation phenomena
will be presented. Also a new visual illusion will be
presented. A visual model based on the above techniques
will be presented. It will also be shown how use of
statistical estimation theory can be made in the study of
contrast adaptation. Furthermore, a mathematical
interpretation of unconscious inference and a simple
explanation of the Tolhurst effect without mutual channel
inhibition will be given. Finally, image processing
algorithms suggested by the model will be used to process
a real-world image for enhancement and for "form" and
texture extraction.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/jf19m-ktj32