Pattern Theory was initiated by Ulf Grenander about thirty years ago. The aim is to analyze patterns from a statistical point of view in all “signals ” generated by the world, whether they be visual, acoustical, textual, molecular (e.g., DNA strings), neural, etc. Patterns are described using hidden variables, together with their probability distributions, whereas signals, or relevant functions of the signals, are modeled conditionally on the hidden variables. In principle, the detection of patterns in noisy and ambiguous samples can then be achieved by the use of Bayes’s rule. An overview of pattern theory as a mathematical theory of perception was presented during the International Congress of Mathematics in 2002; see [13]. There are enormous difficulties in realizing the pattern theory program. Initially, I was inspired by problems arising in computer vision where the signal is a still image and the pattern is an object. This research is described in Section 2. Recently, I have diversified my research to include applications in natural language modeling and bio-informatics. This work was motivated by questions concerning statistical modeling in the small sample situation and in particular the technique of maximum entropy on the mean. This work is described in

Abstract. We propose an automatic cephalometric X-ray landmark de-tection using a pictorial structure algorithm. We first extract a set of features including: local binary pattern-based features, xy spatially co-ordinates of the points, blobness, tubularness, and Zernike features to compute a likelihood for each of the landmarks, which is learnt using a random forest classifier. As the regularization term, we compute the joint distributions of pairs of landmarks. The final cost function set by the likelihoods and the regularization term is globally optimized using the pictorial structure. We validate the goodness of the detected land-marks on 100 images provided by ISBI 2014 automatic cephalometric X-Ray landmark detection challenge. 1