Image Recognition in Context: Application to Microscopic Urinalysis

We propose a new and efficient technique for incorporating contextual information into object classification. Most of the current techniques face the problem of exponential computation cost. In this paper, we propose a new general framework that incorporates partial context at a linear cost. This technique is applied to microscopic urinalysis image recognition, resulting in a significant improvement of recognition rate over the context free approach. This gain would have been impossible using conventional context incorporation techniques. 1 BACKGROUND: RECOGNITION IN CONTEXT There are a number of pattern recognition problem domains where the classification of an object should be based on more than simply the appearance of the object itself. In remote sensing image classification, where each pixel is part of ground cover, a pixel is more likely to be a glacier if it is in a mountainous area, than if surrounded by pixels of residential areas. In text analysis, one can expect to find certain letters occurring regularly in particular arrangement with other letters(qu, ee,est, tion, etc.). The information conveyed by the accompanying entities is referred to as contextual information. Human experts apply contextual information in their decision making [2][ 6]. It makes sense to design techniques and algorithms to make computers aggregate and utilize a more complete set of information in their decision making the way human experts do. In pattern recognition systems, however, *Author for correspondence 964 X B. Song, J Sill, Y. Abu-Mostafa and H. Kasdan the primary (and often only) source of information used to identify an object is the set of measurements, or features , associated with the object itself. Augmenting this information by incorporating context into the classification process can yield significant benefits. Consider a set of N objects Ti , i = 1, ... N. With each object we associate a class label Ci that is a member of a label set n = {1 , ... , D} . Each object Ti is characterized by a set of measurements Xi E R P, which we call a feature vector. Many techniques [1][2][4J[6} incorporate context by conditioning the posterior probability of objects ' identities on the joint features of all accompanying objects. i.e .• P(Cl, C2,··· , cNlxl , . . . , XN). and then maximizing it with respectto Cl, C2, . .. , CN . It can be shown thatp(cl,c2, . . . ,cNlxl, . . . ,xN) ex p(cllxl) ... p(CNlxN) (~ci ""'(N\ given p 1 •.. p CN certain reasonable assumptions. Once the context-free posterior probabilities p( Ci IXi) are known. e.g. through the use of a standard machine learning model such as a neural network, computing P(Cl, ... ,CNlxl, . . . ,XN) for all possible Cl, ... ,CN would entail (2N + 1)DN multiplications. and finding the maximum has complexity of DN. which is intractable for large Nand D. [2J Another problem with this formulation is the estimation of the high dimensional joint distribution p( Cl, ... , CN), which is ill-posed and data hungry. One way of dealing with these problems is to limit context to local regions. With this approach, only the pixels in a close neighborhood. or letters immediately adjacent are considered [4][6][7J. Such techniques may be ignoring useful information, and will not apply to situations where context doesn't have such locality, as in the case of microscopic urinalysis image recognition. Another way is to simplify the problem using specific domain knowledge [1], but this is only possible in certain domains. These difficulties motivate the efficient incorporation of partial context as a general framework, formulated in section 2. In section 3, we discuss microscopic urinalysis image recognition. and address the importance of using context for this application. Also in section 3, techniques are proposed to identify relevant context. Empirical results are shown in section 4. followed by discussions in section 5. 2 FORMULATION FOR INCORPORATION OF PARTIAL CONTEXT To avoid the exponential computational cost of using the identities of all accompanying objects directly as context, we use "partial context". denoted by A. It is called "partial" because it is derived from the class labels. as opposed to consisting of an explicit labelling of all objects. The physical definition of A depends on the problem at hand. In our application. A represents the presence or absence of certain classes. Then the posterior probability of an object Ti having class label Ci conditioned on its feature vector and the relevant context A is p(XiICi, A)P(Ci ; A) P(Xi ; A) We assume that the feature distribution of an object depends only on its own class. i.e., p(xilci, A) = p(xi lci) . This assumption is roughly true for most real world problems. Then. Image Recognition in Context: Application to Microscopic Urinalysis 965 ( .1 . A) p(xilci)p(Ci; A) _ ( .1 .)p(ciIA ) p(A)p(Xi) pC~Xt, -pCtXt p(xijJ~IIA) p(Ci) P(Xi; A) ()( p(cilxi) () = p(cilxi)P(Ci, A) P Ci where p(Ci, A) = p~(~j~) is called the context ratio, through which context plays its role. The context-sensitive posterior probability p( Ci lXi, A) is obtained through the context-free posterior probability p(cilxi) modified by the context ratio P(Ci, A) . The partial-context maximum likelihood decision rule chooses class label Ci for element i such that Ci = argmaxp(cilxi, A) (I) Cj A systematic approach to identify relevant context A is addressed in section 3.3. The partial-context approach treats each element in a set individually, but with additional information from the context-bearing factor A. Once p(cilxi) are known for all i = 1, ... , N, and the context A is obtained, to maximize p(cilxi, A) from D possible values that Ci can take on and for all i, the total number of multiplications is 2N, and the complexity for finding the maximum is N D. Both are linear in N. The density estimation part is also trivial since it is very easy to estimate p(cIA). 3 MICROSCOPIC URINALYSIS