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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Deep convolutional neural networks (CNN) have seen tremendous success in large-scale generic object recognition. In comparison with generic object recognition, fine-grained image classification (FGIC) is much more challenging because (i) fine-grained labeled data is much more expensive to acquire (usually requiring domain expertise); (ii) there exists large intra-class and small inter-class variance. Most recent work exploiting deep CNN for image recognition with small training data adopts a simple strategy: pre-train a deep CNN on a large-scale external dataset (e.g., ImageNet) and fine-tune on the small-scale target data to fit the specific classification task. In this paper, beyond the fine-tuning strategy, we propose a systematic framework of learning a deep CNN that addresses the challenges from two new perspectives: (i) identifying easily annotated hyper-classes inherent in the fine-grained data and acquiring a large number of hyper-class-labeled images from readily available external sources (e.g., image search engines), and formulating the problem into multitask learning; (ii) a novel learning model by exploiting a regularization between the fine-grained recognition model and the hyper-class recognition model. We demonstrate the success of the proposed framework on two small-scale fine-grained datasets (Stanford Dogs and Stanford Cars) and on a large-scale car dataset that we collected. Many state-of-the-art approaches for object recognition reduce the problem to a 0-1 classification task. This allows one to leverage sophisticated machine learning techniques for training classifiers from labeled examples. However, these models are typically trained independently for each class using positive and negative examples cropped from images. At test-time, various post-processing heuristics such as non-maxima suppression (NMS) are required to reconcile multiple detections within and between different classes for each image. Though crucial to good performance on benchmarks, this post-processing is usually defined heuristically. We introduce a unified model for multi-class object recognition that casts the problem as a structured prediction task. Rather than predicting a binary label for each image window independently, our model simultaneously predicts a structured labeling of the entire image (Fig. 1). Our model learns statistics that capture the spatial arrangements of various object classes in real images, both in terms of which arrangements to suppress through NMS and which arrangements to favor through spatial co-occurrence statistics. We formulate parameter estimation in our model as a max-margin learning problem. Given training images with ground-truth object locations, we show how to formulate learning as a convex optimization problem. We employ the cutting plane algorithm of (Mach. Learn. 2009) to efficiently learn a model from thousands of training images. We show state-of-the-art results on the PASCAL VOC benchmark that indicate the benefits of learning a global model encapsulating the spatial layout of multiple object classes (a preliminary version of this work appeared in ICCV 2009, , IEEE international conference on computer vision, 2009). We present a novel probabilistic approach for fitting a statistical model to an image. A 3D Morphable Model (3DMM) of faces is interpreted as a generative (Top-Down) Bayesian model. Random Forests are used as noisy detectors (Bottom-Up) for the face and facial landmark positions. The Top-Down and Bottom-Up parts are then combined using a Data-Driven Markov Chain Monte Carlo Method (DDMCMC). As core of the integration, we use the Metropolis-Hastings algorithm which has two main advantages. First, the algorithm can handle unreliable detections and therefore does not need the detectors to take an early and possible wrong hard decision before fitting. Second, it is open for integration of various cues to guide the fitting process. Based on the proposed approach, we implemented a completely automatic, pose and illumination invariant face recognition application. We are able to train and test the building blocks of our application on different databases. The system is evaluated on the Multi-PIE database and reaches state of the art performance. We introduce a novel method for 3D object detection and pose estimation from color images only. We first use segmentation to detect the objects of interest in 2D even in presence of partial occlusions and cluttered background. By contrast with recent patch-based methods, we rely on a “holistic” approach: We apply to the detected objects a Convolutional Neural Network (CNN) trained to predict their 3D poses in the form of 2D projections of the corners of their 3D bounding boxes. This, however, is not sufficient for handling objects from the recent T-LESS dataset: These objects exhibit an axis of rotational symmetry, and the similarity of two images of such an object under two different poses makes training the CNN challenging. We solve this problem by restricting the range of poses used for training, and by introducing a classifier to identify the range of a pose at run-time before estimating it. We also use an optional additional step that refines the predicted poses. We improve the state-of-the-art on the LINEMOD dataset from 73.7 [2] to 89.3 of correctly registered RGB frames. We are also the first to report results on the Occlusion dataset [1 ] using color images only. We obtain 54 of frames passing the Pose 6D criterion on average on several sequences of the T-LESS dataset, compared to the 67 of the state-of-the-art [10] on the same sequences which uses both color and depth. The full approach is also scalable, as a single network can be trained for multiple objects simultaneously.