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.
Tliere are a number of important phenom- ena in motion perception involving colicrcnce. Examples include motion capture and motion cooperativity. We propose a theoretical model, called the motion coherence tlieory, that gives a possible explanation for these effects (Yuille and Grzywacz, 1988a,b). In this framework, the aperture problem can also be thought of as a problem of coherence and given a similar explanation. We propose the concept of a velocity field dcfined everywhere in the image, even where there is no explicit motion information available. Through a cost function, tlie model imposes smoothness on the velocity field in a more general way than previous theories. In this paper, we provide a de- tailed theoretical analysis of the motion coherence theory. We discuss its relations with previous theories and show that some of t1ic.m arc approximations to it. A sccorid pa- per (Grzywacz, Smith, and Yuillc, 1088) provides exten- sions and cletnilcd comparisons to psychophysical plienom- cna. Tlic theory applies to both short-range and long- range motion. It places them in the same computational framework aiid provides a way to define interactions be- twcr:11 the two 1)roccsses.  An analysis of moving least squares (m.l.s.) methods for smoothing and interpolating scattered data is presented. In particular, theorems are proved concerning the smoothness of interpolants and the description of m.l.s. processes as projection methods. Some properties of compositions of the m.l.s. projector, with projectors associated with finiteelement schemes, are also considered. The analysis is accompanied by examples of univariate and bivariate problems. This paper introduces a new color transfer method which is a process of transferring color of an image to match the color of another image of the same scene. The color of a scene may vary from image to image because the photographs are taken at different times, with different cameras, and under different camera settings. To solve for a full nonlinear and nonparametric color mapping in the 3D RGB color space, we propose a scattered point interpolation scheme using moving least squares and strengthen it with a probabilistic modeling of the color transfer in the 3D color space to deal with mis-alignments and noise. Experiments show the effectiveness of our method over previous color transfer methods both quantitatively and qualitatively. In addition, our framework can be applied for various instances of color transfer such as transferring color between different camera models, camera settings, and illumination conditions, as well as for video color transfers. We introduce a robust moving least-squares technique for reconstructing a piecewise smooth surface from a potentially noisy point cloud. We use techniques from robust statistics to guide the creation of the neighborhoods used by the moving least squares (MLS) computation. This leads to a conceptually simple approach that provides a unified framework for not only dealing with noise, but also for enabling the modeling of surfaces with sharp features.Our technique is based on a new robust statistics method for outlier detection: the forward-search paradigm. Using this powerful technique, we locally classify regions of a point-set to multiple outlier-free smooth regions. This classification allows us to project points on a locally smooth region rather than a surface that is smooth everywhere, thus defining a piecewise smooth surface and increasing the numerical stability of the projection operator. Furthermore, by treating the points across the discontinuities as outliers, we are able to define sharp features. One of the nice features of our approach is that it automatically disregards outliers during the surface-fitting phase.  We provide an image deformation method based on Moving Least Squares using various classes of linear functions including affine, similarity and rigid transformations. These deformations are realistic and give the user the impression of manipulating real-world objects. We also allow the user to specify the deformations using either sets of points or line segments, the later useful for controlling curves and profiles present in the image. For each of these techniques, we provide simple closed-form solutions that yield fast deformations, which can be performed in real-time.  