Subspace clustering has been extensively studied from the hypothesis-and-test, algebraic, and spectral clustering based perspectives. Most assume that only a single type class of subspace is present. Generalizations to multiple types are non-trivial, plagued by challenges such as choice of types and numbers of models, sampling imbalance and parameter tuning. In this work, we formulate the multi-type subspace clustering problem as one of learning non-linear subspace filters via deep multi-layer perceptrons (mlps). The response to the learnt subspace filters serve as the feature embedding that is clustering-friendly, i.e., points of the same clusters will be embedded closer together through the network. For inference, we apply K-means to the network output to cluster the data. Experiments are carried out on both synthetic and real world multi-type fitting problems, producing state-of-the-art results.
: Using deep learning to solve geometric model fitting has received growing considerations. The dense approaches use raw image to model the transformation between image pairs as homography @cite_33 or non-rigid transformation @cite_62 . @cite_41 proposed to estimate the camera pose directly from image sequences. DSAC @cite_42 learns to extract from sparse feature correspondences a geometric model in a manner akin to RANSAC. The ability to learn representations from sparse points was also developed recently @cite_0 @cite_55 . This ability was exploited by @cite_6 to fit essential matrix from noisy correspondences. Despite the promising results, none of the existing works have considered generic model fitting and, more importantly, fitting data drawn from multiple models and even multiple types. In our work, we formulate the generic multi-type fitting problem as one of learning good representations for clustering.
@cite_62 @cite_33 @cite_41 @cite_55 @cite_42 @cite_6 @cite_0
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We address the problem of determining correspondences between two images in agreement with a geometric model such as an affine or thin-plate spline transformation, and estimating its parameters. The contributions of this work are three-fold. First, we propose a convolutional neural network architecture for geometric matching. The architecture is based on three main components that mimic the standard steps of feature extraction, matching and simultaneous inlier detection and model parameter estimation, while being trainable end-to-end. Second, we demonstrate that the network parameters can be trained from synthetically generated imagery without the need for manual annotation and that our matching layer significantly increases generalization capabilities to never seen before images. Finally, we show that the same model can perform both instance-level and category-level matching giving state-of-the-art results on the challenging Proposal Flow dataset. We present a deep convolutional neural network for estimating the relative homography between a pair of images. Our feed-forward network has 10 layers, takes two stacked grayscale images as input, and produces an 8 degree of freedom homography which can be used to map the pixels from the first image to the second. We present two convolutional neural network architectures for HomographyNet: a regression network which directly estimates the real-valued homography parameters, and a classification network which produces a distribution over quantized homographies. We use a 4-point homography parameterization which maps the four corners from one image into the second image. Our networks are trained in an end-to-end fashion using warped MS-COCO images. Our approach works without the need for separate local feature detection and transformation estimation stages. Our deep models are compared to a traditional homography estimator based on ORB features and we highlight the scenarios where HomographyNet outperforms the traditional technique. We also describe a variety of applications powered by deep homography estimation, thus showcasing the flexibility of a deep learning approach. This paper presents a convolutional neural network based approach for estimating the relative pose between two cameras. The proposed network takes RGB images from both cameras as input and directly produces the relative rotation and translation as output. The system is trained in an end-to-end manner utilising transfer learning from a large scale classification dataset. The introduced approach is compared with widely used local feature based methods (SURF, ORB) and the results indicate a clear improvement over the baseline. In addition, a variant of the proposed architecture containing a spatial pyramid pooling (SPP) layer is evaluated and shown to further improve the performance. Few prior works study deep learning on point sets. PointNet is a pioneer in this direction. However, by design PointNet does not capture local structures induced by the metric space points live in, limiting its ability to recognize fine-grained patterns and generalizability to complex scenes. In this work, we introduce a hierarchical neural network that applies PointNet recursively on a nested partitioning of the input point set. By exploiting metric space distances, our network is able to learn local features with increasing contextual scales. With further observation that point sets are usually sampled with varying densities, which results in greatly decreased performance for networks trained on uniform densities, we propose novel set learning layers to adaptively combine features from multiple scales. Experiments show that our network called PointNet++ is able to learn deep point set features efficiently and robustly. In particular, results significantly better than state-of-the-art have been obtained on challenging benchmarks of 3D point clouds. RANSAC is an important algorithm in robust optimization and a central building block for many computer vision applications. In recent years, traditionally hand-crafted pipelines have been replaced by deep learning pipelines, which can be trained in an end-to-end fashion. However, RANSAC has so far not been used as part of such deep learning pipelines, because its hypothesis selection procedure is non-differentiable. In this work, we present two different ways to overcome this limitation. The most promising approach is inspired by reinforcement learning, namely to replace the deterministic hypothesis selection by a probabilistic selection for which we can derive the expected loss w.r.t. to all learnable parameters. We call this approach DSAC, the differentiable counterpart of RANSAC. We apply DSAC to the problem of camera localization, where deep learning has so far failed to improve on traditional approaches. We demonstrate that by directly minimizing the expected loss of the output camera poses, robustly estimated by RANSAC, we achieve an increase in accuracy. In the future, any deep learning pipeline can use DSAC as a robust optimization component. We develop a deep architecture to learn to find good correspondences for wide-baseline stereo. Given a set of putative sparse matches and the camera intrinsics, we train our network in an end-to-end fashion to label the correspondences as inliers or outliers, while simultaneously using them to recover the relative pose, as encoded by the essential matrix. Our architecture is based on a multi-layer perceptron operating on pixel coordinates rather than directly on the image, and is thus simple and small. We introduce a novel normalization technique, called Context Normalization, which allows us to process each data point separately while embedding global information in it, and also makes the network invariant to the order of the correspondences. Our experiments on multiple challenging datasets demonstrate that our method is able to drastically improve the state of the art with little training data. Point cloud is an important type of geometric data structure. Due to its irregular format, most researchers transform such data to regular 3D voxel grids or collections of images. This, however, renders data unnecessarily voluminous and causes issues. In this paper, we design a novel type of neural network that directly consumes point clouds, which well respects the permutation invariance of points in the input. Our network, named PointNet, provides a unified architecture for applications ranging from object classification, part segmentation, to scene semantic parsing. Though simple, PointNet is highly efficient and effective. Empirically, it shows strong performance on par or even better than state of the art. Theoretically, we provide analysis towards understanding of what the network has learnt and why the network is robust with respect to input perturbation and corruption.