MIT Press
Visual Reconstruction presents a unified and highly original approach to
the treatment of continuity in vision. It introduces, analyzes, and illustrates two
new concepts. The first -- the weak continuity constraint -- is a concise,
computational formalization of piecewise continuity. It is a mechanism for
expressing the expectation that visual quantities such as intensity, surface color,
and surface depth vary continuously almost everywhere, but with occasional abrupt
changes. The second concept -- the graduated nonconvexity algorithm -- arises
naturally from the first. It is an efficient, deterministic (nonrandom) algorithm
for fitting piecewise continuous functions to visual data.The book first illustrates
the breadth of application of reconstruction processes in vision with results that
the authors' theory and program yield for a variety of problems. The mathematics of
weak continuity and the graduated nonconvexity (GNC) algorithm are then developed
carefully and progressively.Contents: Modeling Piecewise Continuity. Applications of
Piecewise Continuous Reconstruction. Introducing Weak Continuity Constraints.
Properties of the Weak String and Membrane. Properties of Weak Rod and Plate. The
Discrete Problem. The Graduated Nonconvexity (GNC) Algorithm. Appendixes: Energy
Calculations for the String and Membrane. Noise Performance of the Weak Elastic
String. Energy Calculations for the Rod and Plate. Establishing Convexity. Analysis
of the GNC Algorithm.Visual Reconstruction is included in the Artificial
Intelligence series, edited by Michael Brady and Patrick Winston.
Blake / Zisserman
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the treatment of continuity in vision. It introduces, analyzes, and illustrates two
new concepts. The first -- the weak continuity constraint -- is a concise,
computational formalization of piecewise continuity. It is a mechanism for
expressing the expectation that visual quantities such as intensity, surface color,
and surface depth vary continuously almost everywhere, but with occasional abrupt
changes. The second concept -- the graduated nonconvexity algorithm -- arises
naturally from the first. It is an efficient, deterministic (nonrandom) algorithm
for fitting piecewise continuous functions to visual data.The book first illustrates
the breadth of application of reconstruction processes in vision with results that
the authors' theory and program yield for a variety of problems. The mathematics of
weak continuity and the graduated nonconvexity (GNC) algorithm are then developed
carefully and progressively.Contents: Modeling Piecewise Continuity. Applications of
Piecewise Continuous Reconstruction. Introducing Weak Continuity Constraints.
Properties of the Weak String and Membrane. Properties of Weak Rod and Plate. The
Discrete Problem. The Graduated Nonconvexity (GNC) Algorithm. Appendixes: Energy
Calculations for the String and Membrane. Noise Performance of the Weak Elastic
String. Energy Calculations for the Rod and Plate. Establishing Convexity. Analysis
of the GNC Algorithm.Visual Reconstruction is included in the Artificial
Intelligence series, edited by Michael Brady and Patrick Winston.
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