Abstract: Methods for estimating joint geometric and radiometric deformations relating two observations of the same object provide methods for identifying and matching images (as in face recognition) and for characterizing and determining the relationship between a pair of observations (as in target recognition).

Abstract: In object registration and recognition based on a set of known templates, the tremendous set of possible transformations that may relate the template and an observed signature makes any detection and recognition problem ill-defined unless this variability is taken into account. The present invention estimates the deformation that transforms some pre-chosen representation of an object (template) into the current observation. The method employs a set of non-linear operators to replace a high dimensional problem by an equivalent linear problem, expressed in terms of the unknown parameters of the transformation model. The solution is applicable to any homeomorphic transformation regardless of its magnitude. In the special case where the transformation is affine the solution is shown to be exact.

Abstract: In object registration and recognition based on a set of known templates, the tremendous set of possible transformations that may relate the template and an observed signature makes any detection and recognition problem ill-defined unless this variability is taken into account. The present invention estimates the deformation that transforms some pre-chosen representation of an object (template) into the current observation. The method employs a set of non-linear operators to replace a high dimensional problem by an equivalent linear problem, expressed in terms of the unknown parameters of the transformation model. The solution is applicable to any homeomorphic transformation regardless of its magnitude. In the special case where the transformation is affine the solution is shown to be exact.

Abstract: In object registration and recognition based on a set of known templates, the tremendous set of possible transformations that may relate the template and an observed signature makes any detection and recognition problem ill-defined unless this variability is taken into account. The present invention estimates the deformation that transforms some pre-chosen representation of an object (template) into the current observation. The method employs a set of non-linear operators to replace a high dimensional problem by an equivalent linear problem, expressed in terms of the unknown parameters of the transformation model. The solution is applicable to any homeomorphic transformation regardless of its magnitude. In the special case where the transformation is affine the solution is shown to be exact.

Abstract: A support for a roof scaffold including a triangular frame with one adjustable leg and two other channels each with an end hingably joined to the other channel end and arranged to fold together to form a space where the adjustable leg may be positioned and where accessories may be stored for convenient transport. An outrigger brace having one end attached to the support and another end attachable to the roof remote from the frame provides lateral stability in the direction perpendicular to the channels. The adjustment of leg length and locatin of attachment of one end of the leg to a channel member permits adaptation of the frame to any roof pitch to support a scaffold platform in a horizontal position.