Fast computation of the difference of low-pass transform

Area of Science:

• Image processing
• Signal analysis

Background:

• The Difference of Low-Pass (DOLP) transform converts images into bandpass representations.
• Standard DOLP computation is resource-intensive, requiring O(N^2) multiplies for an N-sample image.

Purpose of the Study:

• To define the DOLP transform and present a computationally efficient algorithm for its calculation.
• To explore the application of Gaussian low-pass filters within the DOLP framework, resulting in Difference of Gaussian (DOG) filtered images.

Main Methods:

• Development of a fast DOLP transform algorithm utilizing a 'resampling' technique.
• Introduction of a 'cascaded convolution with expansion' method to further optimize computation.
• Integration of both techniques for a highly efficient DOLP transform algorithm.

Main Results:

• The 'resampling' method reduces DOLP transform complexity to O(N log(N)) multiplies and O(N) storage.
• The 'cascaded convolution with expansion' method also achieves O(N log(N)) multiplies.
• The combined algorithm achieves O(N) storage and O(N) multiplies for the DOLP transform.

Conclusions:

• A novel and efficient algorithm for the Difference of Low-Pass transform has been developed.
• The optimized DOLP transform significantly reduces computational and storage requirements.
• This advancement facilitates practical applications of DOLP transforms in image processing.