Image Analysis Applications of the Maximum Mean Discrepancy Distance Measure

Abstract

The need to quantify distance between two groups of objects is prevalent throughout the signal processing world. The difference of group means computed using the Euclidean, or L2 distance, is one of the predominant distance measures used to compare feature vectors and groups of vectors, but many problems arise with it when high data dimensionality is present. Maximum mean discrepancy (MMD) is a recent unsupervised kernel-based pattern recognition method which may improve differentiation between two distinct populations over many commonly used methods such as the difference of means, when paired with the proper feature representations and kernels. MMD-based distance computation combines many powerful concepts from the machine learning literature, such as data distribution-leveraging similarity measures and kernel methods for machine learning.

Due to this heritage, we posit that dissimilarity-based classification and changepoint detection using MMD can lead to enhanced separation between different populations. To test this hypothesis, we conduct studies comparing MMD and the difference of means in two subareas of image analysis and understanding: first, to detect scene changes in video in an unsupervised manner, and secondly, in the biomedical imaging field, using clinical ultrasound to assess tumor response to treatment. We leverage effective computer vision data descriptors, such as the bag-of-visual-words and sparse combinations of SIFT descriptors, and choose from an assessment of several similarity kernels (e.g. Histogram Intersection, Radial Basis Function) in order to engineer useful systems using MMD. Promising improvements over the difference of means, measured primarily using precision/recall for scene change detection, and k-nearest neighbour classification accuracy for tumor response assessment, are obtained in both applications.