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Shape Classification
Shape classification is a classification problem where the studied subjects are shapes. The classification could be binary classification or multi-class classification. Examples of the first case is ; examples of the second cases are hand written digits recognition, MPEG shape recognition.
Even though shape classification is a kind of classification problem, it has some special properties. First, shapes are usually complicated to describe and
the similarity measurement (distance) among them are even harder to
compute. Second, shapes usually don't reside in a Euclidean space, sometimes shapes distances are not even metric. Therefore, many metric-based machine learning algorithms (e.g. Support Vector Machine using common kernals) can't be applied directly for shape classification. Designing a good classification algorithm to recognition shapes usually involves defining the similarity measurement between two shapes and/or a learning algorithm based on the defined similarity measurement.
Previous researches on shape classification are mostly focused on two independent components, improving similarity measurement of two shapes and improving the learning algorithms with given similarity measurement. We embed both shape matching and classification in a unified learning framework, so that the alignment of two shapes is parametrized to produce matching scores with good discriminative power. In order to accomplish this task, as part of our training set, we need not only have shapes with labeled classes, but also labeled matches between shapes of the same class.
Shape classification through structured learning
Shape classification through feature-matching scores has been an active research area in recent years. Approaches
in this category typically solve the shape classification problem by determining scores based on point correspondences between an input shape and a set of stored shape exemplars. The matching scores obtained are then used for classification in a second stage, which may involve learning. However, the matching objective function is typically handcrafted or engineered in a non data-driven manner.
The key contribution of our method is to show how the matching criterion itself can be optimized so that the final classification error delivered by matching scores is minimized. In other words, instead of performing learning only after matching scores have been obtained, we learn the matching scores themselves so that the classification loss is small. Figure 1 illustrates the comparison between traditional methods (top) and our proposed learning scheme (bottom). We embed both matching and classification in a
unified learning framework, so that the alignment of two shapes is parametrized to produce matching scores with good discriminative power.
 Figure 1. (a) Existing methods; learning happens after the matching scores have been obtained.
(b) Our approach; both matching and classification are optimized within a unified learning scheme.
In order to accomplish this task, as part of our training set, we need not only have shapes with labeled classes, but also labeled matches between shapes of the same class. Our setting is similar to the some recently introduced algorithm, but differs in that here we are concerned with minimizing the classification error, not the matching error per se. In our experiments, we will show how the expensive step of manually labeling matches can be avoided. We will show that the problem of learning matching scores for classification leads to a non-convex optimization problem, which is very hard to solve. Our strategy is to make use of recent methods related to structured prediction, enabling us to solve the problem in an elegant way, with good empirical results.
Codes
The codes (cpp and python codes) are available at
http://code.google.com/p/shapematching/
If you want to contribute to the codes, please feel free to contact me.
References
[1] Longbin. Chen, J. J. McAuley, R. S. Feris, T.
S. Caetano, and M. Turk. "Shape Classification Through Structured Learning of Matching Measures", IEEE Conference on Computer Vision and
Pattern Recognition (CVPR 2009), Miami, Florida, June 22-24, 2009. (pdf)
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