Techniques for dense semantic correspondence have provided limited ability to deal with the geometric variations that commonly exist between semantically similar images. While variations due to scale and rotation have been examined, there lack practical solutions for more complex deformations such as affine transformations because of the tremendous size of the associated solution space. To address this problem, we present a discrete-continuous transformation matching (DCTM) framework where dense affine transformation fields are inferred through a discrete label optimization in which the labels are iteratively updated via continuous regularization. In this way, our approach draws solutions from the continuous space of affine transformations in a manner that can be computed efficiently through constant-time edge-aware filtering and a proposed affine-varying CNN-based descriptor. Experimental results show that this model outperforms the state-of-the-art methods for dense semantic correspondence on various benchmarks.
More related to our work is the method of Lin @cite_31 , which jointly estimates correspondence and relative patch orientation for descriptors. However, it is formulated with pre-computed sparse correspondences and also requires considerable computation to solve a complex non-linear optimization. By contrast, our method adopts dense descriptors that can be evaluated efficiently for any affine transformation, and employs quadratic continuous optimization to rapidly infer dense affine transformation fields.
@cite_31
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Aligning image pairs with significant appearance change is a long standing computer vision challenge. Much of this problem stems from the local patch descriptors' instability to appearance variation. In this paper we suggest this instability is due less to descriptor corruption and more the difficulty in utilizing local information to canoni-cally define the orientation (scale and rotation) at which a patch's descriptor should be computed. We address this issue by jointly estimating correspondence and relative patch orientation, within a hierarchical algorithm that utilizes a smoothly varying parameterization of geometric transformations. By collectively estimating the correspondence and orientation of all the features, we can align and orient features that cannot be stably matched with only local information. At the price of smoothing over motion discontinuities (due to independent motion or parallax), this approach can align image pairs that display significant inter-image appearance variations.