An efficient iterative thresholding method for image segmentation (1608.01431v2)

Abstract: We proposed an efficient iterative thresholding method for multi-phase image segmentation. The algorithm is based on minimizing piecewise constant Mumford-Shah functional in which the contour length (or perimeter) is approximated by a non-local multi-phase energy. The minimization problem is solved by an iterative method. Each iteration consists of computing simple convolutions followed by a thresholding step. The algorithm is easy to implement and has the optimal complexity $O(N \log N)$ per iteration. We also show that the iterative algorithm has the total energy decaying property. We present some numerical results to show the efficiency of our method.

• The paper introduces an efficient iterative thresholding method for image segmentation based on minimizing a piecewise constant Mumford-Shah functional.
• The key methodology uses non-local energy approximation and leverages FFT for O(N log N) computational efficiency and guaranteed energy decay.
• Numerical results show the method converges rapidly in few iterations, demonstrating stability and potential for real-time applications.

An Efficient Iterative Thresholding Method for Image Segmentation

The paper "An Efficient Iterative Thresholding Method for Image Segmentation" addresses the significant problem of image segmentation, a fundamental aspect of computer vision crucial for applications such as machine vision, medical imaging, and object detection. The authors introduce an efficient algorithm driven by the minimization of the piecewise constant Mumford-Shah functional, demonstrating substantial improvement in computational efficiency compared to prior methods.

Overview

The paper presents a novel iterative thresholding algorithm based on the piecewise constant Mumford-Shah functional, approximating the contour length using non-local multi-phase energy. This energy is derived from convolution involving heat kernels, followed by solving a minimization problem through iterative methods. The authors claim that their method has optimal complexity of $O(N \log N)$ per iteration and guarantees the energy decaying property, leading to convergence.

Numerical Results and Claims

The authors provide robust numerical results verifying the efficiency of their approach. In various test scenarios, including synthetic images and more complex natural scenes, the iterative method reached convergence in relatively few iterations (typically less than 20) and demonstrated stability across different spatial resolutions, supporting their efficiency claim.

Methodological Contributions

What distinguishes this paper is its use of non-local energy representing the perimeter term. By utilizing convolutions of the heat kernel with characteristic functions of image regions, the algorithm exploits fast Fourier transform (FFT) for computational acceleration. This reformulation facilitates a novel, relaxed minimization problem that transitions from convex to concave space, enabling faster calculations than traditional solutions.

Practical and Theoretical Implications

Practically, this development allows for real-time applications in various fields requiring fast and accurate image segmentation. From a theoretical standpoint, the paper's approach aligns with ongoing efforts to enhance segmentation efficiency by leveraging non-local functional approximations.

Future Directions

Given the demonstrated efficiency and applicability across different image types, future advancements might focus on expanding the algorithm's functionality for more complex segmentations and real-time video processing. Further research could also refine parameter selections for diverse image conditions, potentially incorporating adaptive strategies.

Conclusion

Overall, this paper enriches the image segmentation landscape with a computationally efficient approach that promises broad applicability and robustness. Its theoretical underpinnings and numerical validations position it as a substantive contribution to both the practical and academic exploration of image segmentation methodologies.