A potential crack region method to detect crack using image processing of multiple thresholding

In this paper, a potential crack region method is proposed to detect road pavement cracks by using the adaptive threshold. To reduce the noises of the image, the pre-treatment algorithm was applied according to the following steps: grayscale processing, histogram equalization, filtering traffic lane. From the image segmentation methods, the algorithm combines the global threshold and the local threshold to segment the image. According to the grayscale distribution characteristics of the crack image, the sliding window is used to obtain the window deviation, and then, the deviation image is segmented based on the maximum inter-class deviation. Obtain a potential crack region and then perform a local threshold-based segmentation algorithm. Real images of pavement surface were used at the Su Tong Li road in Suzhou, China. It was found that the proposed approach could give a more explicit description of pavement cracks in images. The method was tested on 509 images of the German asphalt pavement distress (Gap) dataset: The test results were found to be promising (precision = 0.82, recall = 0.81, F1 score = 0.83).

A Riemannian Newton trust-region method for fitting Gaussian mixture models

Gaussian Mixture Models are a powerful tool in Data Science and Statistics that are mainly used for clustering and density approximation. The task of estimating the model parameters is in practice often solved by the expectation maximization (EM) algorithm which has its benefits in its simplicity and low per-iteration costs. However, the EM converges slowly if there is a large share of hidden information or overlapping clusters. Recent advances in Manifold Optimization for Gaussian Mixture Models have gained increasing interest. We introduce an explicit formula for the Riemannian Hessian for Gaussian Mixture Models. On top, we propose a new Riemannian Newton Trust-Region method which outperforms current approaches both in terms of runtime and number of iterations. We apply our method on clustering problems and density approximation tasks. Our method is very powerful for data with a large share of hidden information compared to existing methods.