Many studies have assessed breast density in clinical practice. However, calculation of breast density requires segmentation of the mammary gland region, and deep learning has only recently been applied. Thus, the robustness of the deep learning model for different image processing types has not yet been reported. We investigated the accuracy of segmentation of the U-net for mammograms made with variousimage processing types. We used 478 mediolateral oblique view mammograms. The mammograms were divided into 390 training images and 88 testing images. The ground truth of the mammary gland region made by mammary experts was used for the training and testing datasets. Four types of image processing (Types 1–4) were applied to the testing images to compare breast density in the segmented mammary gland regions with that of ground truths. The shape agreement between ground truth and the segmented mammary gland region by U-net of Types 1–4 was assessed using the Dice coefficient, and the equivalence or compatibility of breast density with ground truth was assessed by Bland-Altman analysis. The mean Dice coefficients between the ground truth and U-net were 0.952, 0.948, 0.948, and 0.947 for Types 1, 2, 3, and 4, respectively. By Bland-Altman analysis, the equivalence of breast density between ground truth and U-net was confirmed for Types 1 and 2, and compatibility was confirmed for Types 3 and 4. We concluded that the robustness of the U-net for segmenting the mammary gland region was confirmed for different image processing types.
In individualized screening mammography, a breast density is important to predict potential risks of breast cancer incidence and missing lesions in mammographic diagnosis. Segmentation of the mammary gland region is required when focusing on missing lesions. A deep-learning method was recently developed to segment the mammary gland region. A large amount of ground truth (prepared by mammary experts) is required for highly accurate deep-learning practice; however, this work is time- and labor-intensive. To streamline the ground truth in deep learning, we investigated a difference in acquired mammary gland regions among multiple radiological technologists having various experience and reading levels, who shared the criteria on segmentation. If we can ignore a skill level for image reading, we can increase a number of training images. Three certified radiological technologists segmented the mammary gland region in 195 mammograms. The degree of coincidence among them was assessed with respect to seven factors which indicated the feature of segmented regions including the breast density and mean glandular dose, using Student’s t-test and Bland-Altman analysis. The assessments made by the three radiological technologists were consistent considering all factors, except the mean pixel value. Thus, we concluded that the ground truths prepared by multiple practitioners with different experiences can be accepted for the segmentation of the mammary gland region and they are applicable for training images if they stringently share the criteria on the segmentation.
We develop an automatic smoothing procedure for an estimate of the spectral density of a random process. The procedure is based on smoothing the periodogram with variable bandwidth and a spline interpolation. Effective varying bandwidth is obtained by approximating the log periodogram with a step function whose positions of level changes are determined using a dynamic programming technique. We show that the step function can be obtained by minimizing the cost function D(C||μk) for a given K. The number of partitions K also can be chosen by minimizing another cost function L(K). Some numerical examples show that the resulting estimates are shown to be good representations of the true spectra.
In this paper, we propose a method for tracking of a instantaneous equivalent bandwidth (IEBW) of non-stationary random signals. IEBW is defined on the positve time-frequency distribution of a non-stationary random signal by using Renyi entropy. It is a natural extension of a equivalent bandwidth for stationary random signals. In order to obtain the positive time-frequency satisfying the marginals of a random signal, we have modified a copula-based time-frequency technique slightly. We, then, showed the results of two simple computer simulations. The results show that the method presented here can track the IEBW of the random signals properly. We also applied the method to track the change of the IEBW of the heart sound. The results suggest that tracking the IEBW could be a useful index for automatic diagnostic of heart disease.
In this paper, we present the definition of a the generalized equivalent bandwidth (EBW) of a stochastic process. The generalized EBW is defined by W(α) = exp(H(α))/2, where H(α) is Renyi's entropy H(α) = 1/(1-α)log ( -infinityIntegralinfinity ) pα(f)df, p(f) is the normlized power spectrum and α greater than or equal to 0 is the order of the EWB. The generalized EBW is a new class of EBW which can represent major equivalent bandwidths uniformly. We also argue an interpretation of the generalized EBW from a different perspective. In latter of this article, we examine an estimation property of the generalized EBW. When we obtain an estimated smoothed power spectrum by using the convolution of periodogram and smoothing window, we evaluate how smoothing window length, data length or the variance of an estimated spectrum affect estimation of the generalized EBW. The result indicates that if we increase the data length while keeping the variance constant, the increase rate of the generalized EBW caused by smoothing window will decrease. On the other hand, if we decrease the variance while holding the data length fixed, the generalized EBW of estimated power spectrum will increase.
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Noise and Fluctuations in Photonics, Quantum Optics, and Communications
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