Finite-element method for image alignment and morphing

Claim 1

A method of processing images by determining a point in a target image comprising electronically encoded target points that corresponds to a given point in a source image comprising electronically encoded source points, the method comprising the steps of: A) defining first and second simulated elastic bodies associated with the source and target images, respectively, each body comprising body points which include nodal points; B) identifying source and target feature points among the source and target points, respectively; C) for each of the images, computing the mode shapes of the modes of collective motion of nodal points of the body associated with that image and whose positions with respect to each other are the same as those of the feature points in the associated image, each of said mode shapes being an eigenvector comprising eigenvector components, each eigenvector component being associated with a different nodal point and representing the relative participation of that nodal point in the mode to which the eigenvector corresponds, and thereby associating with each feature point a generalized feature vector whose components represent the participations as embodied in the eigenvector components, of that feature point's associated nodal point in respective modes; D) assigning to each of a plurality of the source feature points a target feature point associated with a generalized feature vector whose difference from that associated with that source feature point is sufficiently small according to a predetermined criterion; E) determining a mapping function of source points to target points in accordance with the relationships between the target feature points to which source feature points are assigned and the points to which the mapping function maps those same feature points; F) identify the point in the target image that corresponds to the given source point by applying the mapping function to the given source point; and G) based on the correspondence, processing at least one of the source and target images or generating at least one intermediate image therebetween.

Claim 2

A method of processing images by determining a point in a target image comprising electronically encoded target points that corresponds to a given point in a source image comprising electronically encoded source points, the method comprising the steps of: A) defining first and second simulated elastic bodies associated with the source and target images, respectively, each body comprising body points which include nodal points; B) identifying source and target feature points among the source and target points, respectively; C) for each of the images, computing the mode shapes of the modes of collective motion of nodal points of the body associated with that image and whose positions with respect to each other are the same as those of the feature points in the associated image, each of said mode shapes being an eigenvector comprising eigenvector components, each eigenvector component being associated with a different nodal point and representing the relative participation of that nodal point in the mode to which the eigenvector corresponds, and thereby associating with each feature point a generalized feature vector whose components represent the participations as embodied in the eigenvector components, of that feature point's associated nodal point in respective modes; D) assigning to each of a plurality of the source feature points a target feature point associated with a generalized feature vector whose difference from that associated with that source feature point is sufficiently small according to a predetermined criterion; E) determining a mapping function of source points to target points in accordance with the relationships between the target feature points to which source feature points are assigned and the points to which the mapping function maps those same feature points; F) identify the point in the target image that corresponds to the given source point by applying the mapping function to the given source point; and G) based on the correspondence, processing at least one of the source and target images or generating at least one intermediate image therebetween.

Claim 11

An apparatus for processing images by determining a point in an electronically encoded target image comprising target points which include target feature points that corresponds to a given point in an electronically encoded source image comprising source points which include source feature points, the apparatus comprising: A) body-defining circuitry for defining first and second simulated elastic bodies associated with the source and target images, respectively, each body comprising body points which include nodal points; B) mode-shape-computation circuitry for computing, for each of the images, the mode shapes of the modes of collective motion of nodal points of the body associated with that image and whose positions with respect to each other are the same as those of the feature points in the associated image, each of said mode shapes being an eigenvector comprising eigenvector components, each eigenvector component being associated with a different nodal point and representing the relative participation of that nodal point in the mode to which the eigenvector corresponds, and thereby associating with each feature point a generalized feature vector whose components represent the participations, as embodied in the eigenvector components, of that feature point's associated nodal point in respective modes; C) correspondence circuitry for assigning to each of a plurality of the source feature points a target feature point associated with a generalized feature vector whose difference from that associated with that source feature point is sufficiently small according to a predetermined criterion; D) map-determination circuitry for determining a mapping function of source points to target points in accordance with the relationships between the target feature points to which source feature points are assigned and the points to which the mapping function maps those same feature points; E) point-identifying circuitry for identifying the point in the target image that corresponds to the given source point by applying the mapping function to the given source point and generating an indication of the point thus identified; and F) image-processing circuitry for processing, based on the correspondence, at least one of the source and target images or generating at least one intermediate image therebetween.

Claim 12

An apparatus for processing images by determining a point in an electronically encoded target image comprising target points which include target feature points that corresponds to a given point in an electronically encoded source image comprising source points which include source feature points, the apparatus comprising: A) body-defining circuitry for defining first and second simulated elastic bodies associated with the source and target images, respectively, each body comprising body points which include nodal points; B) mode-shape-computation circuitry for computing, for each of the images, the mode shapes of the modes of collective motion of nodal points of the body associated with that image and whose positions with respect to each other are the same as those of the feature points in the associated image, each of said mode shapes being an eigenvector comprising eigenvector components, each eigenvector component being associated with a different nodal point and representing the relative participation of that nodal point in the mode to which the eigenvector corresponds, and thereby associating with each feature point a generalized feature vector whose components represent the participations, as embodied in the eigenvector components, of that feature point's associated nodal point in respective modes; C) correspondence circuitry for assigning to each of a plurality of the source feature points a target feature point associated with a generalized feature vector whose difference from that associated with that source feature point is sufficiently small according to a predetermined criterion; D) map-determination circuitry for determining a mapping function of source points to target points in accordance with the relationships between the target feature points to which source feature points are assigned and the points to which the mapping function maps those same feature points; E) point-identifying circuitry for identifying the point in the target image that corresponds to the given source point by applying the mapping function to the given source point and generating an indication of the point thus identified; and F) image-processing circuitry for processing, based on the correspondence, at least one of the source and target images or generating at least one intermediate image therebetween.