DISCRIMINATIVELY WEIGHTED MULTI-SCALE LOCAL BINARY PATTERNS: APPLICATIONS IN PROSTATE CANCER DIAGNOSIS ON T2W MRI Haibo Wang, Satish Viswanath and Anant Madabuhshi * Department of Biomedical Engineering Case Western Reserve University {haibo.wang3, satish.viswanath, anant.madabhushi}@case.edu ABSTRACT In this paper, we present discriminatively weighted Local Binary Patterns (DWLBP), a new similarity metric to match Multi-scale LBP (MsLBP) in Hamming space. While MsLBP is widely used in image processing on account of its ex- tremely fast bitwise operations on modern CPU, identifying a good metric that measures the dissimilarity of MsLBP remains an open problem. The Hamming score is typically computed at each individual scale and the scores across scales are summed up. This approach however often results in un- derestimating salient patterns. In this paper we seek to learn a vector obtained by optimally weighing the contribution of each individual scale when performing MsLBP based match- ing. Inspired by supervised learning, our methodology aims to learn the multi-scale, weight vector by minimizing the Hamming scores between positive class samples and jointly maximizing the scores between positive and negative class samples. This objective function leads to a convex formula- tion with equality and inequality constraints, which can then be solved via the interior-point optimization method. In this paper we evaluate the efficacy of the DWLBP scheme in de- tecting prostate cancer from T2w MRI and demonstrate that the approach statistically significantly outperforms MsLBP. Index Terms— Prostate Cancer, MRI, Image Processing, Local Binary Patterns, multi-scale 1. INTRODUCTION Pixelwise template matching is often utilized to perform an exhaustive search of an entire image to find pixels similar to a query pixel. A major challenge to overcome when matching a pair of pixels lies in the conflict between matching speed and accuracy. To address the challenge, pixel representation should be distinctive and compact, and computing its dissim- ilarity metric should be achievable quickly. Local Binary Pattern (LBP) [1] has been shown to be pow- erful to match a local pixel feature to another. The LBP de- * This work was made possible by grants from the National Institute of Health (R01CA136535, R01CA140772, R43EB015199, R21CA167811), National Science Foundation (IIP-1248316), and the QED award from the University City Science Center and Rutgers University. scriptor of a pixel is a string of binary bits, each of which is obtained by comparing the gray value of the pixel with a number of others sampled on a ring centered on the pixel. The Hamming distance of LBP refers to the number of bits that are different. This only requires carrying out bitwise XOR oper- ations, which can be computed extremely quickly on modern CPUs. Finding a distinctive ring radius is critical to extract salient LBP descriptions. However, the existing approach that detects local Laplacian extrema [2, 3] is computationally costly, hence, largely negating the benefit of LBP. Sampling multiple radii can statistically guarantee measuring textual content at the salient scale. By assuming independent sam- pling, measuring this multi-scale LBP is defined as the sum of the Hamming scores across individual scales (MsLBP) [1]. Nevertheless, salient patterns are under-emphasized while in- significant patterns are over-emphasized during the process. It is necessary to define a weight vector so as to account for the statistical significance of information at the salient scale by measuring the dissimilarity between a pair of multi-scale LBPs. We anticipate that this strategy will significantly im- prove the matching quality and hence detection accuracy. Recent work shows that learned binary projections are a powerful way to index large image collections based on content [4]. Unsupervised hashing [5, 6] leads to binary codes that can be as poor as random binarization. With su- pervised learning imposed, supervised hashing [4] explicitly learns a mapping that maximizes the distances among dif- ferent classes. However, due to the non-differentiable sign function, one has to relax the objective function, resulting in a suboptimal solution. In this paper, we present a new method, discriminatively weighted Local Binary Patterns (DWLBP), to tackle the prob- lem of combining the multi-scale Hamming scores for match- ing MsLBP. Inspired by supervised hashing, we seek to learn a weight vector by minimizing the squares of Hamming dis- tances between positive class samples and jointly maximizing the Hamming distances between positive and negative class samples. Since each element of the vector must be normal- ized and their sum equals one, we get a final objective func- tion that is convex and constrained by linear equality and in-