Low-complexity topological derivative-based segmentation.

Area of Science:

• Computer Vision
• Image Processing
• Computational Mathematics

Background:

• Topological derivative methods are used for image segmentation and restoration.
• Existing methods suffer from high computational complexity due to large sparse matrices, especially with increasing image size.

Purpose of the Study:

• To propose an effective scheme for fast and accurate image segmentation with low computational complexity.
• To maintain the segmentation performance of the original topological derivative-based approach.

Main Methods:

• Developed a scheme to reduce the computational cost of sparse matrix generation and multiplication by converting it into convolution filtering using 2D filters.
• Designed and implemented a parallel processing structure on a graphics processing unit (GPU) by dividing images into blocks for parallel processing.

Main Results:

• Achieved a computational complexity reduction of approximately 908 times compared to the original method.
• Further reduced complexity by approximately 17 times using the parallel GPU structure.
• Demonstrated that the proposed scheme's efficiency is independent of image size, offering significant advantages for large images.
• Obtained segmentation results nearly identical to the original sparse matrix-based approach.

Conclusions:

• The proposed scheme offers a significant reduction in computational complexity for topological derivative-based image segmentation.
• The parallel GPU implementation further enhances efficiency, making it suitable for large-scale image processing tasks.
• This method provides a valuable tool for efficient and accurate image segmentation without compromising performance.