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Given a set of 3D to 2D putative matches, labeling the correspondences as inliers or outliers plays a critical role in a wide range of computer vision applications including the Perspective-n-Point (PnP) and object recognition. In this paper, we study a more generalized problem which allows the matches to belong to multiple objects with distinct poses. We propose a deep architecture to simultaneously label the correspondences as inliers or outliers and classify the inliers into multiple objects. Specifically, we discretize the 3D rotation space into twenty convex cones based on the facets of a regular icosahedron. For each facet, a facet classifier is trained to predict the probability of a correspondence being an inlier for a pose whose rotation normal vector points towards this facet. An efficient RANSAC-based post-processing algorithm is also proposed to further process the prediction results and detect the objects. Experiments demonstrate that our method is very efficient compared to existing methods and is capable of simultaneously labeling and classifying the inliers of multiple objects with high precision. 

In this paper, we consider a general sparse recovery and blind demodulation model. Different from the ones in the literature, in our general model, each dictionary atom undergoes a distinct modulation process; we refer to this as non-stationary modulation. We also assume that the modulation matrices live in a known subspace. Through the lifting technique, the sparse recovery and blind demodulation problem can be reformulated as a column-wise sparse matrix recovery problem, and we are able to recover both the sparse source signal and a cluster of modulation matrices via atomic norm and the induced ` 2,1 norm minimizations. Moreover, we show that the sampling complexity for exact recovery is proportional to the number of degrees of freedom up to log factors in the noiseless case. We also bound the recovery error in terms of the norm of the noise when the observation is noisy. Numerical simulations are conducted to illustrate our results.