![]() Please refer to Section B.2 in Supplementary Material B for detailed explanation and to Supplementary Figure B.2 for the equivalent figure for the Cesare Cesariano Vitruvian man.įour values of w were used to simulate different shape sizes. h is a parametrization of shape A on the positive half plane, in the same direction as α. Here α is a parametrization of the circle (shape B) on the positive half plane - π / 2 ≤ α ≤ π / 2. Plots of d a h, d b α (first row) and their probability functions (second row) for w = 10, and 4 different γ = r / w ratios: (1) γ = 5 / 4, (2) γ = 274 / 225, (3) γ = 1.1 (4) γ = 1. Original Cesariano image from original da Vinci image from. d b α is a function of α giving the distance of a point b on B to shape A. d a h is a function of h giving the distance of a point a on A to shape B. Right: partition of B into 7 angular segments to compute d b α, - π 2 ≤ α ≤ π 2, giving the distance of a point b on B to shape A. Each segment is parametrized by 0 ≤ h ≤ l i as indicated by the arrows. Middle: partition of A into 7 segments to compute d a a function of h giving the distance of a point a on A to shape B. Using symmetry, the analysis is restricted to the right half plane. Second row: Leonardo da Vinci Vitruvian man shapes. Using symmetry, the analysis is restricted to 0 ≤ α ≤ π 4 and 0 ≤ h ≤ w. First row: Cesare Cesariano Vitruvian man shapes with two of the three cases to analyze based on the ratio w / r. Schematic representations of required parametrizations for comparing a cube A to a cylinder B. To avoid any ambiguity, the wording shape or structure will be used when referring to 3D object as a whole and the wording contour will refer to a 2D contour on an image slice. Thus, RTSS cannot represent a 3D continuous shape but rather a discrete set of 2D continuous curves representing the intersection of the 3D shape with the image acquisition planes. Vertices are limited to being on an image slice. A 2D contour is a set of 2D closed curves on the image slice (acquisition plane), represented as an irregular polygon with locations for each vertex in real-world coordinates, and therefore can approximate continuous 2D curves with a precision depending on the number of vertices. A structure is a discrete set of 2D contours, defined on a stack of 2D parallel image slices composing the 3D image series. The process of creating a dataset with gold standard values for CSMs consisted of five steps: Mathematical definition of the measures parametric definition of the shapes analytic calculation of the corresponding CSMs creation of the image and contour data for the defined shapes and generation of corresponding numerical values for the CSMs.įirst, it is important to recall how structures are represented by DICOM RTSS. The aim of this study was to develop a synthetic dataset consisting of simple geometric shapes with corresponding analytically calculated ground truth values for a number of mathematically defined CSMs. Such a dataset can be used for the testing and validation of quantitative contouring assessment tools and implementations. This necessitates building a dataset with known CSM values. ![]() It is difficult to assess correctness of implementation/definition because the true values of the measurements are unknown. reported that “the greatest variations in implementation choices were found in the method of conversion from RTSS to a voxel mask, the method of sampling the surface when calculating distance measures and in the definition of distance measures”. However, definition and implementation of CSMs vary between centers, which can greatly influence results and comparisons. Quantitative CSMs may also be used in other Quality Assurance (QA) procedures, such as image registration. ![]() To be done quantitatively, such assessment requires the use of contour similarity measures (CSMs). Therefore the accuracy of contouring is an active area of research, whether for evaluating differences in contouring between observers, or assessing the performance of automatic segmentation approaches (both in development, , and clinical commissioning, ,, , ). Contouring in radiotherapy is essential for treatment planning, identifying regions that require high dose (target volumes) and regions that need sparing (organs at risk).
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