JHU Johns Hopkins Computer Vision Machine Learning

Diffusion Tensor Imaging is a new 3-D imaging technique that measures the diffusion of water molecules in human and animal tissues. As the space of diffusion tensors is not Euclidean, there is a need to consider its Riemannian structure in image analysis techniques. Our goal is to develop DTI algorithms that are computationally simple and requiring no initialization. Specifically, we are looking into the problems of DTI registration and fiber segmentation and tracking.

Cardiac Motion Segmentation

Several methods are known nowadays for treating cardiac arrhythmias -irregularities in the heartbeat-, the least invasive of which is radiofrequency ablation. The objective of this project is to solve the segmentation problem in order to develop a 3-D model of the heart using real time MR images, and to help the physician during the ablation process. We use segmentation methods based on intensity and dynamic textures framework for segmenting the heart from the chest and the background. We then perform rigid and non-rigid registration to register upcoming low resolution images to the previous high resolution followed by level set methods, which integrates prior information on shape, intensity and cardiac dynamics for segmenting different regions within the heart.

Cardiac Fiber Extraction & Tracing

Orientation extraction and tracing of tubular structures in medical images are important quantitative tools for developing models of the heart both at the histological and cytological levels. The problems of detecting orientation and tracing tubular structures are closely related to a primal problem in processing: edge detection. This has motivated several efforts in the image processing and computer vision communities to introduce fast and robust algorithms. However, those algorithms have to deal with not only the image noise but also the complexity (intersection, bifurcation) of the structure. In this project, we consider the problem of extracting spatial orientation and tracing 2-D and 3-D tubular structures in medical images. Specifically, we aim at developing algorithms to analyze myofiber array orientation and track the 3-D Purkinje network in cardiac data.

Motion Segmentation in Dynamic Scenes

Motion segmentation forms a quintessential part of analyzing dynamic scenes that contain multiple rigid objects in motion. It deals with separating visual features extracted from the scene into different groups, such that each group has a characteristic motion different from that of the other groups. Since we can extract a vast bag of visual features from a scene, we explore different approaches for segmenting the motions in the scene by using these features.

Dynamic Textures

Textures such as grass fluttering in the wind, waves on the ocean exhibit specific dynamics and thus can be modelled as a linear dynamical system. The classical Brightness Constancy Constraint does not hold good for such sequences as they are not rigid and lambertian. We explore methods to exploit the dynamical model and achieve segmentation and estimation of motion of a camera viewing such sequences.

Omnidirectional Motion Estimation and Segmentation

Omnidirectional motion estimating and segmentation involves the analysis of a scene observed from multiple central panoramic views in order to identify the different motion patterns present in the scene. The previous research mainly focuses on sequences captured by perspective or affine cameras. The panoramic camera model is mathematically more complex due to the uneven warping in the scene. We propose methods to estimate and segment the motion models associated with multiple moving objects captured by panoramic cameras.

Multiple view geometry

Multiple view geometry deals with the characterization of the geometric relationships of multiple images of points and lines. Such characterization can be used for structure and motion recovery, feature matching and image transfer. The previous work in multiple view geometry is mainly restricted to a maximum of four views. We propose a unifying geometric representation of the constraints generated by multiple views of a scene by imposing a rank constraint on the so-called multiple view matrix for arbitrarily combined point and line features across multiple views. We demonstrate that all previously known multilinear constraints become simple instantiations of the new condition and that quadrilinear constraints are algebraically redundant.

Recognition of Visual Dynamical Processes

Phenomena like motion of lips in videos, human gaits as well as dynamic textures are examples of processes that can be modeled by linear dynamical systems. Clearly, a sequence of video frames with a person walking or running allude to the particular gait much more accurately than just an intermediate snapshot taken during the gait cycle. On the other hand there might be instances when a snapshot of a person running might look exactly like that of a person walking. If we have a video sequence of the two actions, we clearly see a huge difference. Motivated by this example, we study various methods of doing classification and recognition of visual dynamical processes. We define a number of metrics on the space of linear dynamical systems and using standard system identification techniques and classification methods from the machine learning literature, develop a pipeline for recognition and classification of Linear Dynamical Systems.

Observability of Hybrid Systems

A system is considered to be hybrid if its dynamics can be described as both continuous and discrete. We characterize the observability properties of certain classes of hybrid systems called Jump Linear Systems. We consider both autonomous and non-autonomous linear hybrid systems in our research and derive conditions on the structural parameters of the constituent linear systems in order to uniquely recover continuous/discrete states of the system.

Identification of Hybrid Systems

Given the input-output data generated by a hybrid system, we propose algorithms to identify the number of discrete states, the hybrid state (continuous and discrete) and the model parameters associated with each state. Our research considers batch identification and recursive identification of linear Switched ARX systems (SARX). In contrast to most of the existing methods, we consider the challenging problem where neither the number of models nor the orders are known.

Generalized PCA

Generalized Principal Component Analysis (GPCA) is an algebraic-geometric approach to segmenting data lying in multiple linear subspaces. GPCA is a non-iterative method that operates by fitting the data with a polynomial and then differentiating that polynomial in order to segment the data. This segmentation can be used to initialize iterative methods, such as Expected Maximization.

Manifold Learning

Manifold learning deals with the characterization of high dimensional data for the goals of dimensionality reduction, classification and segmentation. Most of nonlinear dimensionality reduction methods deal with one manifold. We propose methods to simultaneously perform nonlinear dimensionality reduction and clustering of multiple linear and nonlinear manifolds.