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We address the problem of finding deformation between two images for the purpose of recognizing objects. The challenge is that discriminative features are often transformation-variant (e.g. histogram of oriented gradients, texture), while transformation-invariant features (e.g. intensity, color) are often not discriminative. We introduce the concept of attribute flow which explicitly models how image attributes vary with its deformation. We develop a non-parametric method to approximate this using histogram matching, which can be solved efficiently using linear programming. Our method produces dense correspondence between images, and utilizes discriminative, transformation-variant features for simultaneous detection and alignment. Experiments on ETHZ shape categories dataset show that we can accurately recognize highly de-formable objects with few training examples.