TY - JOUR
T1 - Efficient gamma index calculation using fast Euclidean distance transform
AU - Chen, Mingli
AU - Lu, Weiguo
AU - Chen, Quan
AU - Ruchala, Kenneth
AU - Olivera, Gustavo
PY - 2009
Y1 - 2009
N2 - The gamma index is a tool for dose distribution comparison. It combines both dose difference (DD) and distance to agreement (DTA) into a single quantity. Though it is an effective measure, making up for the inadequacy of DD or DTA alone, its calculation can be very time-consuming. For a k-D space with N quantization levels in each dimension, the complexity of the exhaustive search is O(N2k). In this work, we proposed an efficient method that reduces the complexity from O(N2k) to O(NkM), where M is the number of discretized dose values and is comparable to N. More precisely, by embedding the reference dose distribution in a (k+1)-D spatial-dose space, we can use fast Euclidean distance transform with linear complexity to obtain a table of gamma indices evaluated over a range of the (k+1)-D spatial-dose space. Then, to obtain gamma indices for the test dose distribution, it requires only table lookup with complexity O(Nk). Such a table can also be used for other test dose distributions as long as the reference dose distribution is the same. Simulations demonstrated the efficiency of our proposed method. The speedup for 3D gamma index calculation is expected to be on the order of tens of thousands (from O(N6) to O(N3M)) if N is a few hundreds, which makes clinical usage of the 3D gamma index feasible. A byproduct of the gamma index table is that the gradient of the gamma index with respect to either the spatial or dose dimension can be easily derived. The gradient can be used to identify the main causes of the discrepancy from the reference distribution at any dose point in the test distribution or incorporated in treatment planning and machine parameter optimization.
AB - The gamma index is a tool for dose distribution comparison. It combines both dose difference (DD) and distance to agreement (DTA) into a single quantity. Though it is an effective measure, making up for the inadequacy of DD or DTA alone, its calculation can be very time-consuming. For a k-D space with N quantization levels in each dimension, the complexity of the exhaustive search is O(N2k). In this work, we proposed an efficient method that reduces the complexity from O(N2k) to O(NkM), where M is the number of discretized dose values and is comparable to N. More precisely, by embedding the reference dose distribution in a (k+1)-D spatial-dose space, we can use fast Euclidean distance transform with linear complexity to obtain a table of gamma indices evaluated over a range of the (k+1)-D spatial-dose space. Then, to obtain gamma indices for the test dose distribution, it requires only table lookup with complexity O(Nk). Such a table can also be used for other test dose distributions as long as the reference dose distribution is the same. Simulations demonstrated the efficiency of our proposed method. The speedup for 3D gamma index calculation is expected to be on the order of tens of thousands (from O(N6) to O(N3M)) if N is a few hundreds, which makes clinical usage of the 3D gamma index feasible. A byproduct of the gamma index table is that the gradient of the gamma index with respect to either the spatial or dose dimension can be easily derived. The gradient can be used to identify the main causes of the discrepancy from the reference distribution at any dose point in the test distribution or incorporated in treatment planning and machine parameter optimization.
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U2 - 10.1088/0031-9155/54/7/012
DO - 10.1088/0031-9155/54/7/012
M3 - Article
C2 - 19287084
AN - SCOPUS:63649102975
SN - 0031-9155
VL - 54
SP - 2037
EP - 2047
JO - Physics in medicine and biology
JF - Physics in medicine and biology
IS - 7
ER -