System and method for sequential kernel density approximation through mode propagation
AssigneeSiemens Corporate Research, Inc.
InventorsBohyung Han, Dorin Comaniciu, Ying Zhu, Xiang Sean Zhou
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Abstract
A system and method for sequential kernel density approximation uses mode propagation to determine mode locations by the mean-shift method and reduce the generated modes. Hessians are calculated corresponding to the mode locations to determine the covariance. Density is approximated to update the density function depending on whether the Hessian is a negative indefinite.
Claims31
A system for sequential kernel density approximation in video data comprising frames, the system comprising:
- a mean-shift vector module for finding a gradient ascent direction in a density function, wherein the density function determines a plurality of modes in each frame of the video data, the modes corresponding to potential visual features to be tracked between frames, and a mode reduction module reduces the number of modes located in each frame of the video data, wherein each mode location is a visual feature to be tracked;
- a Hessian module for generating at least one Hessian matrix corresponding to the mode location of the visual feature in each frame of the video data;
- a covariance module for determining a covariance of the modes using the Hessian matrix;
- and
- a density approximation module for determining an update to the density function at each of the mode locations using the Hessian matrix and the covariance, wherein the update tracks the visual feature in the video data between frames.
A program storage device readable by machine, tangibly embodying a program of instructions executable by the machine to perform method steps for sequential kernel density estimation in video data comprising frames, the method steps comprising:
- finding a gradient ascent direction in at least one density function using a mean-shift vector, wherein the density function determines a plurality of modes in each frame of the video data, the modes corresponding to potential visual features to be tracked between frames, and reducing the number of modes located in each frame of the video data, wherein each mode location is a visual feature to be tracked;
- generating at least one Hessian corresponding to the mode location of the visual feature in each frame of the video data;
- determining a covariance of the modes using the Hessian matrix;
- and
- approximating density to determine an update to the density function at each of the mode locations using the Hessian matrix and the covariance, wherein the update tracks the visual feature in the video data between frames.
A method for sequential kernel density estimation in video data for a first sub-space, the method comprising:
- determining a matrix of eigen vectors of the covariance of multi-dimensional data corresponding to at least one visual feature in video data to be tracked between frames of the video data, wherein a plurality of modes is determined in the first sub-space corresponding to a plurality of potential visual features and the number of modes located in the first sub-space is reduced to locate the at least one visual feature;
- selecting a first set of eigen values corresponding to a first set of eigen vectors;
- projecting data from the first sub-space on to a second sub-space;
- and
- performing mode finding in the second sub-space, wherein the mode finding tracks the at least one visual feature in the video data between frames.
A method for background modeling for an image sequence, the method comprising:
- (a) receiving an image frame;
- (b) approximating density for each pixel of the image frame to determine a background;
- (c) creating a background model using the approximated density;
- (d) receiving another image frame wherein the image frames constitute a sequence of images;
- (e) subtracting background from the another image frame according to the background model;
- (f) determining the validity of background classification for the another image frame;
- (g) updating the background using sequential kernel density approximation;
- (h) repeating steps (d) through (g) until all frames of the image sequence have been processed;
- and
- (i) outputting the image sequence with the background subtracted.
Dependencies are inferred from the claim text.