基于核密度估计与尺度空间表示的多类直方图阈值化方法
Multiclass histogram-based thresholding using kernel density estimation and scale-space representations
AI总结：
该研究针对模式高度重叠的直方图，提出基于核密度估计与尺度空间表示的多类阈值化方法，经合成直方图与多孔样品CT图像验证，其孔隙率估计精度远优于K-means聚类。
摘要：
我们提出一种针对直方图的多类阈值化方法，该直方图的模式可能重叠得极为紧密，以至于合并为单峰分布。该直方图通过非参数核密度（KD）估计进行近似，这是一种高斯混合模型，每个区间对应一个分量且具有共同带宽，其参数由期望最大化（EM）迭代确定。由于该估计是高斯混合模型，高斯卷积的半群性质可在拟合带宽之外以闭式形式生成其尺度空间表示，包括大于和小于拟合带宽的情况。该算法会增大或减小带宽，直到估计的局部极小值数量等于所需类别数减一，并将这些极小值的位置作为阈值返回。我们在具有已知阈值的合成直方图上验证了该方法，并将其应用于天然多孔样品的X射线计算机断层扫描图像的直方图，其中三相（固相、液相、气相）高度重叠。通过所得分割计算出的孔隙率与直接实验测量值的偏差在4%以内，而K-means聚类对其的估计误差达52%。
英文摘要：
We present a method for multiclass thresholding of histograms whose modes may overlap so strongly that they merge into a unimodal distribution. The histogram is approximated by a nonparametric kernel density (KD) estimate, a mixture of Gaussians with one component per bin and a common bandwidth, whose parameters are determined by Expectation-Maximization (EM) iterations. Because the estimate is a Gaussian mixture, the semigroup property of Gaussian convolution yields its scale-space representation in closed form, at bandwidths both larger and smaller than the fitted one. The algorithm increases or decreases the bandwidth until the number of local minima of the estimate equals the number of requested classes minus one, and returns the positions of those minima as the threshold values. We validate the method on synthetic histograms with known thresholds, and we apply it to the histogram of X-ray computed tomography images of a natural porous sample in which the three phases strongly overlap. The porosity computed from the resulting segmentation agrees with the direct experimental measurement to within 4%, whereas K-means clustering misestimates it by 52%.
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