This paper presents an efficient technique for performing a spatially inhomogeneous edge-preserving image smoothing, called fast global smoother. Focusing on sparse Laplacian matrices consisting of a data term and a prior term (typically defined using four or eight neighbors for 2D image), our approach efficiently solves such global objective functions. In particular, we approximate the solution of the memory-and computation-intensive large linear system, defined over a d-dimensional spatial domain, by solving a sequence of 1D subsystems. Our separable implementation enables applying a linear-time tridiagonal matrix algorithm to solve d three-point Laplacian matrices iteratively. Our approach combines the best of two paradigms, i.e., efficient edge-preserving filters and optimization-based smoothing. Our method has a comparable runtime to the fast edge-preserving filters, but its global optimization formulation overcomes many limitations of the local filtering approaches. Our method also achieves high-quality results as the state-of-the-art optimization-based techniques, but runs ∼10-30 times faster. Besides, considering the flexibility in defining an objective function, we further propose generalized fast algorithms that perform Lγ norm smoothing (0 < γ < 2) and support an aggregated (robust) data term for handling imprecise data constraints. We demonstrate the effectiveness and efficiency of our techniques in a range of image processing and computer graphics applications.

We present a descriptor, called fully convolutional selfsimilarity (FCSS), for dense semantic correspondence. To robustly match points among different instances within the same object class, we formulate FCSS using local selfsimilarity (LSS) within a fully convolutional network. In contrast to existing CNN-based descriptors, FCSS is inherently insensitive to intra-class appearance variations because of its LSS-based structure, while maintaining the precise localization ability of deep neural networks. The sampling patterns of local structure and the self-similarity measure are jointly learned within the proposed network in an end-to-end and multi-scale manner. As training data for semantic correspondence is rather limited, we propose to leverage object candidate priors provided in existing image datasets and also correspondence consistency between object pairs to enable weakly-supervised learning. Experiments demonstrate that FCSS outperforms conventional handcrafted descriptors and CNN-based descriptors on various benchmarks.

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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 affinevarying CNN-based descriptor. Experimental results show that this model outperforms the state-of-the-art methods for dense semantic correspondence on various benchmarks.

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