Shape Interaction Matrix Revisited and Robustified: Efficient Subspace Clustering with Corrupted and Incomplete Data

The Shape Interaction Matrix (SIM) is one of the earliest approaches to performing subspace clustering (i.e., separating points drawn from a union of subspaces). In this paper, we revisit the SIM and reveal its connections to several recent subspace clustering methods. Our analysis lets us derive a simple, yet effective algorithm to robustify the SIM and make it applicable to realistic scenarios where the data is corrupted by noise. We justify our method by intuitive examples and the matrix perturbation theory. We then show how this approach can be extended to handle missing data, thus yielding an efficient and general subspace clustering algorithm. We demonstrate the benefits of our approach over state-of-the-art subspace clustering methods on several challenging motion segmentation and face clustering problems, where the data includes corrupted and missing measurements.Comment: This is an extended version of our iccv15 pape

Vessel tractography using an intensity based tensor model

In this paper, we propose a novel tubular structure segmen- tation method, which is based on an intensity-based tensor that fits to a vessel. Our model is initialized with a single seed point and it is ca- pable of capturing whole vessel tree by an automatic branch detection algorithm. The centerline of the vessel as well as its thickness is extracted. We demonstrated the performance of our algorithm on 3 complex contrast varying tubular structured synthetic datasets for quantitative validation. Additionally, extracted arteries from 10 CTA (Computed Tomography An- giography) volumes are qualitatively evaluated by a cardiologist expert’s visual scores

Vessel tractography using an intensity based tensor model with branch detection

In this paper, we present a tubular structure seg- mentation method that utilizes a second order tensor constructed from directional intensity measurements, which is inspired from diffusion tensor image (DTI) modeling. The constructed anisotropic tensor which is fit inside a vessel drives the segmen- tation analogously to a tractography approach in DTI. Our model is initialized at a single seed point and is capable of capturing whole vessel trees by an automatic branch detection algorithm developed in the same framework. The centerline of the vessel as well as its thickness is extracted. Performance results within the Rotterdam Coronary Artery Algorithm Evaluation framework are provided for comparison with existing techniques. 96.4% average overlap with ground truth delineated by experts is obtained in addition to other measures reported in the paper. Moreover, we demonstrate further quantitative results over synthetic vascular datasets, and we provide quantitative experiments for branch detection on patient Computed Tomography Angiography (CTA) volumes, as well as qualitative evaluations on the same CTA datasets, from visual scores by a cardiologist expert

Innovation Pursuit: A New Approach to Subspace Clustering

In subspace clustering, a group of data points belonging to a union of subspaces are assigned membership to their respective subspaces. This paper presents a new approach dubbed Innovation Pursuit (iPursuit) to the problem of subspace clustering using a new geometrical idea whereby subspaces are identified based on their relative novelties. We present two frameworks in which the idea of innovation pursuit is used to distinguish the subspaces. Underlying the first framework is an iterative method that finds the subspaces consecutively by solving a series of simple linear optimization problems, each searching for a direction of innovation in the span of the data potentially orthogonal to all subspaces except for the one to be identified in one step of the algorithm. A detailed mathematical analysis is provided establishing sufficient conditions for iPursuit to correctly cluster the data. The proposed approach can provably yield exact clustering even when the subspaces have significant intersections. It is shown that the complexity of the iterative approach scales only linearly in the number of data points and subspaces, and quadratically in the dimension of the subspaces. The second framework integrates iPursuit with spectral clustering to yield a new variant of spectral-clustering-based algorithms. The numerical simulations with both real and synthetic data demonstrate that iPursuit can often outperform the state-of-the-art subspace clustering algorithms, more so for subspaces with significant intersections, and that it significantly improves the state-of-the-art result for subspace-segmentation-based face clustering

A discrete Reeb graph approach for the segmentation of human body scans

Segmentation of 3D human body (HB) scan is a very challenging problem in applications exploiting human scan data. To tackle this problem, we propose a topological approach based on discrete Reeb graph (DRG) which is an extension of the classical Reeb graph to unorganized cloud of 3D points. The essence of the approach is detecting critical nodes in the DRG thus permitting the extraction of branches that represent the body parts. Because the human body shape representation is built upon global topological features that are preserved so long as the whole structure of the human body does not change, our approach is quite robust against noise, holes, irregular sampling, moderate reference change and posture variation. Experimental results performed on real scan data demonstrate the validity of our method

Cavlectometry: Towards Holistic Reconstruction of Large Mirror Objects

We introduce a method based on the deflectometry principle for the reconstruction of specular objects exhibiting significant size and geometric complexity. A key feature of our approach is the deployment of an Automatic Virtual Environment (CAVE) as pattern generator. To unfold the full power of this extraordinary experimental setup, an optical encoding scheme is developed which accounts for the distinctive topology of the CAVE. Furthermore, we devise an algorithm for detecting the object of interest in raw deflectometric images. The segmented foreground is used for single-view reconstruction, the background for estimation of the camera pose, necessary for calibrating the sensor system. Experiments suggest a significant gain of coverage in single measurements compared to previous methods. To facilitate research on specular surface reconstruction, we will make our data set publicly available

The use of the Kalman filter in the automated segmentation of EIT lung images

In this paper, we present a new pipeline for the fast and accurate segmentation of impedance images of the lungs using electrical impedance tomography (EIT). EIT is an emerging, promising, non-invasive imaging modality that produces real-time, low spatial but high temporal resolution images of impedance inside a body. Recovering impedance itself constitutes a nonlinear ill-posed inverse problem, therefore the problem is usually linearized, which produces impedance-change images, rather than static impedance ones. Such images are highly blurry and fuzzy along object boundaries. We provide a mathematical reasoning behind the high suitability of the Kalman filter when it comes to segmenting and tracking conductivity changes in EIT lung images. Next, we use a two-fold approach to tackle the segmentation problem. First, we construct a global lung shape to restrict the search region of the Kalman filter. Next, we proceed with augmenting the Kalman filter by incorporating an adaptive foreground detection system to provide the boundary contours for the Kalman filter to carry out the tracking of the conductivity changes as the lungs undergo deformation in a respiratory cycle. The proposed method has been validated by using performance statistics such as misclassified area, and false positive rate, and compared to previous approaches. The results show that the proposed automated method can be a fast and reliable segmentation tool for EIT imaging

Segment Anything Meets Universal Adversarial Perturbation

As Segment Anything Model (SAM) becomes a popular foundation model in computer vision, its adversarial robustness has become a concern that cannot be ignored. This works investigates whether it is possible to attack SAM with image-agnostic Universal Adversarial Perturbation (UAP). In other words, we seek a single perturbation that can fool the SAM to predict invalid masks for most (if not all) images. We demonstrate convetional image-centric attack framework is effective for image-independent attacks but fails for universal adversarial attack. To this end, we propose a novel perturbation-centric framework that results in a UAP generation method based on self-supervised contrastive learning (CL), where the UAP is set to the anchor sample and the positive sample is augmented from the UAP. The representations of negative samples are obtained from the image encoder in advance and saved in a memory bank. The effectiveness of our proposed CL-based UAP generation method is validated by both quantitative and qualitative results. On top of the ablation study to understand various components in our proposed method, we shed light on the roles of positive and negative samples in making the generated UAP effective for attacking SAM