Fast fourier transform correlation tracking algorithm with background correction

A method for tracking an object in an image using Fast Fourier Transforms, comprising:

• determining a background correction for a varying background in the image based on a representation of the background correction that includes a product in the frequency domain of a squared function of the image with a 2-dimension sinc function, wherein the determining a background correction comprises:
• squaring pixel values of a search window and performing a 2-dimension Fast Fourier Transform of the squared pixel values, and
• multiplying the transform of the squared pixel values with the 2-dimension sinc function to obtain the background correction in the frequency domain;
• and
• tracking the object based on the background correction and a cross-correlation between a search window image function and a reference window image function.

A method for tracking an object in an image based on a mean-square-error function having a background correction term and a cross-correlation term, the method comprising the steps of:

• transforming the background correction and cross-correlation terms into the frequency domain;
• computing the background correction term in real time based on a representation of the background correction term that includes a product of a squared function of the image with a 2-dimension sinc function;
• computing the cross-correlation term;
• transforming the computed background correction and cross-correlation terms out of the frequency domain to form a correlation surface;
• and
• determining a minimum of the correlation surface, wherein a location of the minimum corresponds to a location of the object being tracked.

A Fast Fourier Transform correlation tracker for tracking an object in an image, comprising:

• means for determining a background correction for a varying background in the image based on a representation of the background correction that includes a product in the frequency domain of a squared function of the image with a 2-dimension sinc function, wherein the background correction means is configured to:
• square pixel values of a search window and perform a 2-dimension Fast Fourier Transform of the squared pixel values, and
• multiply the transform of the squared pixel values with the 2-dimension sinc function to obtain the background correction in the frequency domain;
• and
• means for tracking the object based on the background correction and a cross-correlation between a search window image function and a reference window image function.