Sainz de Cea Maria V, Nishikawa Robert M, Yang Yongyi
IEEE Trans Med Imaging. 2017 May;36(5):1162-1171. doi: 10.1109/TMI.2017.2654799. Epub 2017 Jan 17.
Computerized detection of clustered microcalcifications (MCs) in mammograms often suffers from the occurrence of false positives (FPs), which can vary greatly from case to case. We investigate how to apply statistical estimation to determine the number of FPs that are present in a detected MC lesion. First, we describe the number of true positives (TPs) by a Poisson-binomial probability distribution, wherein a logistic regression model is trained to determine the probability for an individual detected MC to be a TP based on its detector output. Afterward, we model the spatial occurrence of FPs in a lesion area by a spatial point process (SPP), of which the distribution parameters are estimated from the detections in the lesion and its surrounding region. Furthermore, to improve the estimation accuracy, we incorporate the Poisson-binomial distribution of the number of TPs into the SPP model using maximum a posteriori estimation. In the experiments, we demonstrated the proposed approach on the detection results from a set of 188 full-field digital mammography (FFDM) images (95 cases) by three existing MC detectors. The results showed that there was a strong consistency between the estimated and the actual number of TPs (or FPs) for these detectors. When the fraction of FPs in detection was varied from 20% to 50%, both the mean and median values of the estimation error were within 11% of the total number of detected MCs in a lesion. In particular, when the number of FPs increased to as high as 11.38 in a cluster on average, the error was 2.51 in the estimated number of FPs. In addition, lesions estimated to be more accurate in detection were shown to have better classification accuracy (for being malignant or benign) than those estimated to be less accurate.
乳腺钼靶片中簇状微钙化（MCs）的计算机化检测常常存在假阳性（FPs），且不同病例的假阳性情况差异很大。我们研究如何应用统计估计来确定检测到的MC病变中存在的假阳性数量。首先，我们用泊松二项概率分布来描述真阳性（TPs）的数量，其中训练一个逻辑回归模型，根据单个检测到的MC的探测器输出确定其为TP的概率。之后，我们用空间点过程（SPP）对病变区域中FPs的空间出现情况进行建模，其分布参数根据病变及其周围区域的检测结果进行估计。此外，为提高估计精度，我们使用最大后验估计将TP数量的泊松二项分布纳入SPP模型。在实验中，我们在一组188张全场数字化乳腺钼靶（FFDM）图像（95个病例）的检测结果上，通过三种现有的MC探测器展示了所提出的方法。结果表明，这些探测器的TP（或FP）估计数量与实际数量之间有很强的一致性。当检测中FP的比例从20%变化到50%时，估计误差的均值和中值都在病变中检测到的MC总数的11%以内。特别是，当一个簇中FP的数量平均增加到高达11.38时，FP估计数量的误差为2.51。此外，检测估计更准确的病变在分类准确性（恶性或良性）方面比估计不太准确的病变更好。
