A method to improve the computational efficiency of the Chan-Vese model for the segmentation of ultrasound images

Purpose
Advanced image segmentation techniques like the Chan-Vese (CV) models transform the segmentation problem into a minimization problem which is then solved using the gradient descent (GD) optimization algorithm. This study explores whether the computational efficiency of CV can be improved when GD is replaced by a different optimization method.

Methods
Two GD variants from the literature (Nesterov accelerated, Barzilai-Borwein) and a newly developed hybrid variant of GD were used to improve the computational efficiency of CV by making GD insensitive to local minima. One more variant of GD from the literature (projected GD) was used to address the issue of maintaining the constraint on boundary evolution in CV which also increases computational cost. A novel modified projected GD (Barzilai-Borwein projected GD) was also used to overcome both problems at the same time. The effect of optimization method selection on processing time and the quality of the output was assessed for 25 musculoskeletal ultrasound images (five anatomical areas).

Results
The Barzilai-Borwein projected GD method was able to significantly reduce computational time (average(±std.dev.) reduction 95.82 % (±3.60 %)) with the least structural distortion in the delineated output relative to the conventional GD (average(±std.dev.) structural similarity index: 0.91(±0.06)).

Conclusion
The use of an appropriate optimization method can substantially improve the computational efficiency of CV models. This can open the way for real-time delimitation of anatomical structures to aid the interpretation of clinical ultrasound. Further research on the effect of the optimization method on the accuracy of segmentation is needed.