To accurately quantify the local difference between two contour surfaces in two- or three-dimensional space, a new, robust point-to-surface distance measure is developed.Methods:
To evaluate and visualize the local surface differences, point-to-surface distance measures have been utilized. However, previously well-known point-to-surface distance measures have critical shortfalls. Previous distance measures termed “normal distance (ND),” “radial distance,” or “minimum distance (MD)” can report erroneous results at certain points where the surfaces under comparison meet certain conditions. These skewed results are due to the monodirectional characteristics of these methods. ComGrad distance was also proposed to overcome asymmetric characteristics of previous point-to-surface distance measures, but their critical incapability of dealing with a fold or concave contours. In this regard, a new distance measure termed the bidirectional local distance (BLD) is proposed which minimizes errors of the previous methods by taking into account the bidirectional characteristics with the forward and backward directions. BLD measure works through three steps which calculate the maximum value between the forward minimum distance (FMinD) and the backward maximum distance (BMaxD) at each point. The first step calculates the FMinD as the minimum distance to the test surface from a point,p ref on the reference surface. The second step involves calculating the minimum distances at every point on the test surface to the reference surface. During the last step, the BMaxD is calculated as the maximum distance among the minimum distances found at p ref on the reference surface. Tests are performed on two- and three-dimensional artificial contour sets in comparison to MD and ND measure techniques. Three-dimensional tests performed on actual liver and head-and-neck cancer patients.Results:
The proposed BLD measure provides local distances between segmentations, even in situations where ND, MD, or ComGrad measures fail. In particular, the standard deviation measure is not distorted at certain geometries where ND, MD, and ComGrad measures report skewed results.Conclusions:
The proposed measure provides more reliable statistics on contour comparisons. From the statistics, specific local and global distances can be extracted. Bidirectional local distance is a reliable distance measure in comparing two- or three-dimensional organ segmentations.
This work benefited from the use of the Insight Segmentation and Registration Toolkit (ITK) and Visualization Toolkit (VTK), the open source software developed as an initiative of the U.S. National Library of Medicine and available at “www.itk.org” and “www.vtk.org,” respectively. This project is partially supported by the Agency for Healthcare Research and Quality (AHRQ) grant 5R18HS017424. Our developed software for comparison between BLD, ND, MD, and ComGrad in two-dimensional space can be downloaded at “http://rophys.case.edu/bld/distancemeasure.zip.”
I.A. Normal distance measure
I.B. Minimum distance measure
I.C. ComGrad measure
I.D. Bidirectional local distance (BLD), a new measure to compare segmentations
II. MATERIALS AND METHODS
II.A. Theory of bidirectional local distance measure
II.B. Benchmarking bidirectional local distance measure
II.B.1. Measuring rigid-shifted contours
II.B.2. Measuring deformed 2D contours
II.B.3. Application to three-dimensional structures
II.C. Effect of smoothing volumes
II.D. Calculating the standard deviation surface map
III.A. Measuring shifted contours
III.B. Distance measure comparisons for various 2D shapes
III.C. Application to three-dimensional structures
III.D. Effect of smoothing organ volumes on distance measurements
III.E. A standard deviation surface map generated using the BLD measure
IV. DISCUSSIONS AND CONCLUSION
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