In Proc. 10th IEEE International Conference of Computer Vision, beijing, October 2005.Efficient Learning of Relational Object Class ModelsAharon Bar Hillel Tomer Hertz Daphna WeinshallSchool of Computer Science and Engineering and the Center for Neural ComputationHebrew university of Jerusalem, Israel 91904{ aharonbh, tomboy, daphna}@cs.huji.ac.ilAbstractWe present an efficient method for learning part-basedobject class models. The models include location and scalerelations between parts, as well as part appearance. Mod-els are learnt from raw object and background images, rep-resented as an unordered set of features extracted using aninterest point detector. The object class is generativelymod-eled using a simple Bayesian network with a central hiddennode containing location and scale information, and nodesdescribing object parts. The model’s parameters, however,are optimized to reduce a loss function which reflects train-ing error, as in discriminative methods. Specifically, theoptimization is done using a boosting-like technique withcomplexity linear in the number of parts and the numberof features per image. This efficiency allows our methodto learn relational models with many parts and features,and leads to improved results when compared with othermethods. Extensive experimental results are described, us-ing some common bench-mark datasets and three sets ofnewly collected data, showing the relative advantage of ourmethod.1 IntroductionOne of the important organization principles of ob-ject recognition is the categorization of objects into objectclasses. Humans learn to categorize objects into classesfrom an early age, and usually beginby learning “basic cate-gories”, such as balls or chairs [14]. Categorization is a hardlearning problem due to the large inner-class variability ofobject classes, in addition to the “common” object recogni-tion problems of varying pose and illumination. Recently,there has been a growing interest in the task of object classrecognition [11, 10, 3, 2] which can be defined as follows:given an image, determine whether the object of interest ap-pears in the image (and perhaps also provide its location).Following previous work [1, 11], in this paper we repre-sent an object using a part-based model (see Fig. 1). Suchmodels can capture the essence of an object class, since theyrepresent both parts’ appearance and invariant relations oflocation and scale between the parts. Part-based models aresomewhat resistant to various sources of variability such aswithin-class variance, partial occlusion and articulation, andthey may be convenientfor indexing in a more complex sys-tem.Figure 1. Dog im-age with our learntmodel drawn on top.Each circle represents apart in the model. Theparts relative locationand scale are relatedto one another througha hidden center (betterviewed in color).Part-based approachesto object class recognitioncan be crudely divided intotwo types: (1) ’generative-model-based’ methods (e.g.,[11]) and (2) ’discriminative-model-free’ methods (e.g.,[2]). In the ’Generative-model based’ approach aprobabilistic model of theobject class is learnt bylikelihood maximization.The likelihood ratio test isused to classify new images.The main advantage of thisapproach is the ability tomodel relations betweenobject parts. In addition, domain knowledge can beincorporated into the model’s structure and priors [9].’Discriminative-model-free’ methods seek a classificationrule which discriminates object images from backgroundimages. The main advantage of discriminative methods isthe direct minimization of a classification-based error func-tion, which typically leads to superior classification results[4]. Additionally since these methods are model-free, theyare usually computationally efficient.In our current work, we try to enjoy the benefits of bothworlds: The modeling power of the generative approach,with the accuracy and efficiency of discriminative optimiza-tion. We present a novel method for object class recogni-tion, based on discriminative optimization of a simple gen-erative object model. Specifically, we use a compact star-like Bayesian network as our generative model, and extendcurrent discriminativeboosting techniques to enable param-1eter optimization of this model. This combination providessome benefits which are not available in the purely genera-tive or discriminative frameworks. Thus, in the frameworkof generative object modeling, our discriminative optimiza-tion allows - for the first time - efficient learning from un-segmented images, with complexity linear in P and Nf, thenumber of model parts and the number of features per im-age respectively. This is in sharp contrast to the O(NPf)complexity of maximum-likelihood estimation [11], whichremains essentially exponential even when a star-like rela-tional model is used [12]. It also improves the behaviorof feature selection during learning. From the discrimina-tive perspective, a classifier based on a generative modelallows for the natural treatment of spatial relations betweenmodel parts, which are not easily incorporated into currentdiscriminative techniques.In an earlier work [1] we considered discriminative op-timization via boosting of a very simple generative model,in which parts were assumed to be independent, and onlythe parts’s appearance was modeled (i.e without consider-ing any relations between the parts). Here we extend thegenerative model to include dependencies between parts,modeling both parts’ location and scale. The model, de-scribed in Section 2.2, includes a hidden variable to repre-sent the object’s center, and the location and scale of eachpart depend only on this hidden variable. Parts are thereforeconditionally independent given the location of the ’hiddencenter’. In section 3 we show how to modify a boosting likealgorithm in order to learn a model in which parts are onlyconditionally independent of one another. Unlike the boost-ing technique used in [1], which views boosting as gradientdescent in function space [8], the modified boosting pre-sented here is based on a new simpler view of boosting asgradient descent. Our final algorithm is a boosting exten-sion with some elements from traditional gradient descenttechniques.In order to compare our algorithm to the previously sug-gested state-of-the-art generative and discriminative meth-ods, we used the benchmark datasets used by both [11] (ourgenerative competitor) and [2] (our
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