Volumetric characterization using covariance estimation from scale-space hessian matrices
View Patent ↗A method for determining a volume of interest in data includes determining fixed-bandwidth estimations of a plurality of analysis bandwidths, wherein the estimation of the fixed-bandwidth comprises, providing an estimate of a mode location of the volume of interest in the data, and determining a covariance of the volume of interest using a local Hessian matrix. The method further includes determining the volume of interest as a most stable fixed-bandwidth estimation across each of the plurality of analysis bandwidths.
1. A computer-implemented method for determining a volume of interest in data comprising:
determining, by a processor, fixed-bandwidth estimations of a plurality of analysis bandwidths, wherein the estimation of the fixed-bandwidth comprises,
providing an estimate of a mode location of the volume of interest in the data, and
determining a covariance of the volume of interest using a local Hessian matrix, comprising determining a scale-space representation of the volume of interest;
determining a scale-space Hessian of the volume of interest at the mode location given the scale-space representation; and
determining the covariance of the volume of interest from the scale-space Hessian,
wherein the covariance defines a boundary of the volume of interest around the mode location, wherein the covariance is determined based on a truncated Gaussian fitted to the volume of interest, the truncated Gaussian comprising a plurality of arbitrarily missing tails; and
determining, by the processor, the volume of interest as a most stable fixed-bandwidth estimation across each of the plurality of analysis bandwidths.
2. The method of claim 1 , wherein the estimate of the mode location is provided manually.
3. The method of claim 1 wherein providing the estimate of the mode location comprises determining a mean shift estimation of the volume of interest within each analysis bandwidth.
4. The method of claim 1 , wherein the data is volumetric image data.
5. The method of claim 4 , wherein the volume of interest is determined as a confidence ellipsoid of a fitted Gaussian in the data.
6. A non-transitory computer readable medium embodying a program of instructions executed by a processor to perform method steps for determining a volume of interest in data, the method comprising:
determining fixed-bandwidth estimations of a plurality of analysis bandwidths, wherein the estimation of the fixed-bandwidth comprises,
providing an estimate of a mode location of the volume of interest in the data, and
determining a covariance of the volume of interest using a local Hessian matrix comprising
determining a scale-space representation of the volume of interest;
determining a scale-space Hessian of the volume of interest at the mode location given the scale-space representation; and
determining the covariance of the volume of interest from the scale-space Hessian, wherein the covariance defines a boundary of the volume of interest around the mode location, wherein the covariance is determined based on a truncated Gaussian fitted to the volume of interest, the truncated Gaussian comprising a plurality of arbitrarily missing tails; and
determining the volume of interest as a most stable fixed-bandwidth estimation across each of the plurality of analysis bandwidths.
7. The computer readable medium of claim 6 , wherein the estimate of the mode is provided manually.
8. The computer readable medium of claim 6 , wherein providing the estimate of the mode comprises determining a mean shift estimation of the volume of interest within each analysis bandwidth.
9. The computer readable medium of claim 6 , wherein the data is volumetric image data.
10. The computer readable medium of claim 9 , wherein the volume of interest is determined as a confidence ellipsoid of a fitted Gaussian in the data.