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<p>This paper presents a novel Hausdorff distance loss function for image segmentation, particularly in the field of medical imaging. The proposed Hausdorff distance loss function, based on the Felzenszwalb distance transform algorithm, addresses the computational complexity associated with previous Hausdorff distance loss function implementations, bringing it closer to the efficiency of the Dice loss function. The new method significantly reduces the computational time, making it only 11.2% slower than the Dice loss function, compared to the 125.9% slower rate of previous implementations. Furthermore, the proposed Hausdorff distance loss function improves the Dice similarity coefficient from 0.918 to 0.925 and reduces the Hausdorff distance from 4.583 to 3.464, demonstrating enhanced segmentation accuracy. The study's findings suggest that the proposed Hausdorff distance loss function can be a valuable tool for medical image segmentation, providing a balance between computational efficiency and segmentation precision. The code for the new Hausdorff distance loss function is publicly available for use.</p>

<p>This paper presents a novel Hausdorff distance loss function for image segmentation, particularly in the field of medical imaging. The proposed Hausdorff distance loss function, based on the Felzenszwalb distance transform algorithm, addresses the computational complexity associated with previous Hausdorff distance loss function implementations, bringing it closer to the efficiency of the Dice loss function. The new method significantly reduces the computational time, making it only 11.2% slower than the Dice loss function, compared to the 125.9% slower rate of previous implementations. Furthermore, the proposed Hausdorff distance loss function improves the Dice similarity coefficient from 0.918 to 0.925 and reduces the Hausdorff distance from 4.583 to 3.464, demonstrating enhanced segmentation accuracy. The study's findings suggest that the proposed Hausdorff distance loss function can be a valuable tool for medical image segmentation, providing a balance between computational efficiency and segmentation precision. The code for the new Hausdorff distance loss function is publicly available for use.</p>

Agatston scoring does not detect all the calcium present in computed tomography scans of the heart. A technique that removes the need for thresholding and quantifies calcium mass more accurately and reproducibly is needed.Approach: Integrated intensity and volume fraction techniques were evaluated for accurate quantification of calcium mass. Integrated intensity calcium mass, volume fraction calcium mass, Agatston scoring, and spatially weighted calcium scoring were compared with known calcium mass in simulated and physical phantoms. The simulation was created to match a 320-slice CT scanner. Fat rings were added to the simulated phantoms, which resulted in small (30 × 20 cm 2 ), medium (35 × 25 cm 2 ), and large (40 × 30 cm 2 ) phantoms. Three calcification inserts of different diameters and hydroxyapatite densities were placed within the phantoms. All the calcium mass measurements were repeated across different beam energies, patient sizes, insert sizes, and densities. Physical phantom images from a previously reported study were then used to evaluate the accuracy and reproducibility of the techniques.Results: Both integrated intensity calcium mass and volume fraction calcium mass yielded lower root mean squared error (RMSE) and deviation (RMSD) values than Agatston scoring in all the measurements in the simulated phantoms. Specifically, integrated calcium mass (RMSE: 0.49 mg, RMSD: 0.49 mg) and volume fraction calcium mass (RMSE: 0.58 mg, RMSD: 0.57 mg) were more accurate for the low-density stationary calcium measurements than Agatston scoring (RMSE: 3.70 mg, RMSD: 2.30 mg). Similarly, integrated calcium mass (15.74%) and volume fraction calcium mass (20.37%) had fewer false-negative (CAC = 0) measurements than Agatston scoring (75.00%) and spatially weighted calcium scoring (26.85%), on the low-density stationary calcium measurements. Conclusion:The integrated calcium mass and volume fraction calcium mass techniques can potentially improve risk stratification for patients undergoing calcium scoring and further improve risk assessment compared with Agatston scoring.

Purpose Agatston scoring does not detect all the calcium present in computed tomography scans of the heart. A technique that removes the need for thresholding and quantifies calcium mass more accurately and reproducibly is needed. Approach Integrated intensity and volume fraction techniques were evaluated for accurate quantification of calcium mass. Integrated intensity calcium mass, volume fraction calcium mass, Agatston scoring and spatially weighted calcium scoring were compared to known calcium mass in simulated and physical phantoms. The simulation was created to match a 320-slice CT scanner. Fat rings were added to the simulated phantoms, which resulted in small (30x20 cm2), medium (35x25 cm2), and large (40x30 cm2) phantoms. Three calcification inserts of different diameters and hydroxyapatite densities were placed within the phantoms. All the calcium mass measurements were repeated across different beam energies, patient sizes, insert sizes, and densities. Physical phantom images from a previously reported study were then used to evaluate the accuracy and reproducibility of the techniques. Results Both integrated intensity calcium mass and volume fraction calcium mass yielded lower root mean squared error (RMSE) and deviation (RMSD) values than Agatston scoring in all the measurements in the simulated phantoms. Specifically, integrated calcium mass (RMSE: 0.50 mg, RMSD: 0.49 mg) and volume fraction calcium mass (RMSE: 0.59 mg, RMSD: 0.58 mg) were more accurate for the low-density calcium measurements than Agatston scoring (RMSE: 3.5 mg, RMSD: 2.2 mg). Similarly, integrated calcium mass (11.1%) and volume fraction calcium mass (11.1%) had fewer false-negative (CAC=0) measurements than Agatston scoring (38.9%). Conclusion The integrated calcium mass and volume fraction calcium mass techniques can potentially improve risk stratification for patients undergoing calcium scoring and further improve risk assessment compared to Agatston scoring.