Evaluation of Segmentation Quality in Magnetic Resonance Images Using Singular Value Decomposition: A Feasibility Study

In the present research work, the use of Singular Value Decomposition is investigated as part of an evaluation metric for the segmentation quality of regions of interest in magnetic resonance imaging used in an experiment of High-Intensity Focused Ultrasound therapy. Accurate segmentation is essential for clinical and research applications in computer vision. However, current evaluation methods have limitations in sensitivity to the shape of segmented objects, highlighting the need for a quantitative shape-sensitive metric. SVD is a promising tool for assessing segmentation similarity to ground truths in therapy planning images through component comparison. The proposed <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$S_{F}$</tex> metric shows strong positive correlations with Global Consistency Error scores across transverse and sagittal images. In the air region, correlations range from 0.66 (transverse) to 0.75 (sagittal), in the gel-pad from 0.72 to 0.91, in tissue from 0.87 to 0.91, in the transducer from 0.78 to 0.91, and in water from 0.93 to 0.94, indicating that S<inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">F</inf> can capture structural similarities and segmentation consistency as GCE evaluates alignment with the ground truth, focusing on boundary accuracy and region continuity. The findings suggest that this tool could enhance sensitivity to object shapes in medical image analysis, improving segmentation quality assessments, clinical diagnostics, and treatment planning.