Method for image data processing

A method of optimizing a data classification for data representative of one or more physical parameters, comprising using a processor to perform the steps of:

• obtaining a first backbone data set extracted from a larger full scene data set including a plurality of data in said first data set representative of a typical within-scene variation and representative of said one or more physical parameters;
• dividing the remaining data not in the backbone into a set of smaller subsets;
• calculating a manifold coordinate system for each of said subset data sets in said plurality of data sets by:
• computing a shortest geodesic distance on a manifold between each neighboring pair of data points in said plurality of data;
• computing vantage point forests at a selected distance metric r in said backbone;
• sorting N samples into neighborhoods in said plurality of data sets by querying said vantage point forests;
• optionally expanding the neighborhood definition in said plurality of data sets to ensure that at least Kmin neighbors in the neighborhood but no more than Kmax are assembled, and implementing said optional neighborhood definition with multiple vantage point forests at different values of r;
• connecting substantially all N samples to a landmark on a final geodesic distance graph to substantially eliminate isolated data points in said plurality of data sets;
• estimating geodesic distances from the N samples to L landmarks to form an L×N landmarks geodesic distance matrix for said plurality of data sets;
• extracting q eigenvalue-eigenvector pairs from a second order variation of an L×L sub-matrix of the L×N landmarks geodesic distance matrix for said plurality of data sets;
• and
• for each point that is not a landmark point in said data sets, projecting a vector of geodesic distances from each landmark computed in said vantage point forest computation step onto the q eigenvectors to obtain q manifold coordinates, thereby obtaining an optimized data classification set of the data representative of the physical parameters;
• calculating a manifold coordinate system for said backbone by:
• computing a shortest geodesic distance on a manifold between each neighboring pair of data points in said plurality of data;
• computing vantage point forests at a selected distance metric r in said backbone;
• sorting N samples into neighborhoods in said backbone by querying said vantage point forests;
• optionally expanding the neighborhood definition in said backbone to ensure that at least Kmin neighbors in the neighborhood but no more than Kmax are assembled, and implementing said optional neighborhood definition with multiple vantage point forests at different values of r;
• connecting substantially all N samples to a landmark on a final geodesic distance graph to substantially eliminate isolated data points in said backbone;
• estimating geodesic distances from the N samples to L landmarks to form an L×N landmarks geodesic distance matrix for said backbone;
• extracting q eigenvalue-eigenvector pairs from a second order variation of an L×L sub-matrix of the L×N landmarks geodesic distance matrix for said backbone;
• and
• for each point that is not a landmark point in said backbone, projecting a vector of geodesic distances from each landmark computed in said vantage point forest computation step onto the q eigenvectors to obtain q manifold coordinates, thereby obtaining an optimized data classification set of the data representative of the physical parameters;
• and
• deriving manifold coordinates for remaining points not in the backbone data set via a reconstruction principle to thereby obtain an optimized data classification set of the data representative of the physical parameters.

A method of optimizing a data classification for data representative of one or more physical parameters, comprising using a processor to perform the steps of:

• obtaining a first backbone data set extracted from a larger full scene data set including a plurality of data in said first data set representative of a typical within-scene variation and representative of said one or more physical parameters;
• calculating a manifold coordinate system for said backbone by:
• computing a shortest geodesic distance on a manifold between each neighboring pair of data points in said plurality of data;
• computing vantage point forests at a selected distance metric r in said backbone;
• sorting N samples into neighborhoods in said backbone by querying said vantage point forests;
• optionally expanding the neighborhood definition in said backbone to ensure that at least Kmin neighbors in the neighborhood but no more than Kmax are assembled, and implementing said optional neighborhood definition with multiple vantage point forests at different values of r;
• connecting substantially all N samples to a landmark on a final geodesic distance graph to substantially eliminate isolated data points in said backbone;
• estimating geodesic distances from the N samples to L landmarks to form an L×N landmarks geodesic distance matrix for said backbone;
• extracting q eigenvalue-eigenvector pairs from a second order variation of an L×L sub-matrix of the L×N landmarks geodesic distance matrix for said backbone;
• and
• for each point that is not a landmark point in said backbone, projecting a vector of geodesic distances from each landmark computed in said vantage point forest computation step onto the q eigenvectors to obtain q manifold coordinates, thereby obtaining an optimized data classification set of the data representative of the physical parameters;
• and
• deriving manifold coordinates for remaining points not in the backbone data set via a reconstruction principle to thereby obtain an optimized data classification set of the data representative of the physical parameters.

A method of optimizing a data classification for data representative of one or more physical parameters, comprising using a processor to perform the steps of:

• obtaining a first data set including a plurality of said data representative of said one or more physical parameters;
• dividing the data set into a plurality of data sets smaller than the first data set;
• calculating a manifold coordinate system for each of said data sets in said plurality of data sets by computing a shortest geodesic distance on a manifold between each neighboring pair of data points in said plurality of data;
• computing vantage point forests at a selected distance metric r;
• sorting N samples into neighborhoods by querying said vantage point forests;
• optionally expanding the neighborhood definition to ensure that at least Kmin neighbors in the neighborhood but no more than Kmax are assembled, and implementing said optional neighborhood definition with multiple vantage point forests at different values of r;
• connecting substantially all N samples to a landmark on a final geodesic distance graph to substantially eliminate isolated data points;
• estimating geodesic distances from the N samples to L landmarks to form an L×N landmarks geodesic distance matrix;
• extracting q eigenvalue-eigenvector pairs from a second order variation of an L×L sub-matrix of the L×N landmarks geodesic distance matrix;
• for each point that is not a landmark point projecting a vector of geodesic distances from each landmark computed in said vantage point forest computation step onto the q eigenvectors to obtain q manifold coordinates, thereby obtaining an optimized data classification set of the data representative of the physical parameters;
• selecting a tile as a target tile for the global manifold coordinate system of the scene;
• aligning the manifold coordinate systems of all remaining tiles to that of the target tile using a pseudoinverse transformation, constructed by:
• reconstructing the input spectra of a subset of random or known samples drawn from each remaining tile in terms of neighbors in the target tile identified from queries to vantage point forests of the target tile;
• and
• applying the reconstruction weights to obtain the corresponding manifold spectrum of the random or known sample in the manifold coordinate system of the target tile, thereby obtaining a global manifold coordinate system for the entire data set.