Machine Learning to Analyze Images of Shocked Materials for Precise and Accurate Measurements

A supervised machine learning algorithm, called locally adaptive discriminant analysis (LADA), has been developed to locate boundaries between identifiable image features that have varying intensities. LADA is an adaptation of image segmentation, which includes techniques that find the positions of image features (classes) using statistical intensity distributions for each class in the image. In order to place a pixel in the proper class, LADA considers the intensity at that pixel and the distribution of intensities in local (nearby) pixels. This paper presents the use of LADA to provide, with statistical uncertainties, the positions and shapes of features within ultrafast images of shock waves. We demonstrate the ability to locate image features including crystals, density changes associated with shock waves, and material jetting caused by shock waves. This algorithm can analyze images that exhibit a wide range of physical phenomena because it does not rely on comparison to a model. LADA enables analysis of images from shock physics with statistical rigor independent of underlying models or simulations

💡 Research Summary

This paper introduces and demonstrates the application of a novel supervised machine learning algorithm named Locally Adaptive Discriminant Analysis (LADA) for the precise analysis of ultrafast images in shock physics. The core challenge addressed is the difficulty in interpreting such images due to factors like irreproducible measurements, high noise, low contrast, unpredictable material responses (e.g., fracture, jetting), and heterogeneous illumination. Traditional methods like Fourier filtering or model-based comparisons are often inadequate for providing quantitative, statistically rigorous data from these complex images.

LADA is an image segmentation algorithm that classifies pixels into user-defined classes (e.g., unshocked material, shock front, crystals). Its key innovation is its “locally adaptive” nature. Unlike global methods that use intensity histograms from the entire image, LADA makes decisions per pixel based on intensity distributions constructed only from nearby, or “local,” training data. The user provides two critical parameters: d, the radius within which to search for local training pixels, and n, the number of pixels used to build a local histogram for each class. For each pixel, the algorithm gathers up to n training pixels from each class within a distance d, fits Gaussian distributions to these local intensity histograms, and assigns the pixel to the class for which its intensity has the highest probability. This approach makes LADA exceptionally robust to high noise and significant overlap in the global intensity distributions of different classes, which are common in shockwave imagery.

The paper provides a detailed, step-by-step application of LADA to a sequence of images depicting converging shock waves in water. It explains the process of defining training data maps, selecting optimal d and n parameters, and running the segmentation. Crucially, LADA goes beyond simple segmentation by quantifying the uncertainty of its results. It generates two types of statistical maps: an Analysis of Variance (ANOVA) p-value map, which indicates regions where the intensity distributions of local classes overlap heavily and are thus hard to distinguish, and a Maximum Likelihood Estimator (MLE) p-value map (thresholded at 5%), which highlights pixels with low confidence in their class assignment. These uncertainty metrics allow for rigorous error propagation in subsequent calculations.

Using LADA, the authors extract the precise pixel locations of the shock front in each image frame, along with their uncertainties. This data is then used to calculate shock velocities as a function of time, complete with propagated error bars. The paper further illustrates LADA’s versatility by mentioning its successful application to other challenging shock images featuring crystals and material jetting. In conclusion, LADA enables model-independent, statistically rigorous analysis of shock physics images, providing a powerful new tool for extracting precise quantitative measurements—such as feature positions, shapes, and velocities—from data that was previously difficult or impossible to analyze with conventional techniques.