A Stochastic Approach to Diffeomorphic Point Set Registration with Landmark Constraints.

This work presents a deformable point set registration algorithm that seeks an optimal set of radial basis functions to describe the registration. A novel, global optimization approach is introduced composed of simulated annealing with a particle filter based generator function to perform the registration. It is shown how constraints can be incorporated into this framework. A constraint on the deformation is enforced whose role is to ensure physically meaningful fields (i.e., invertible). Further, examples in which landmark constraints serve to guide the registration are shown. Results on 2D and 3D data demonstrate the algorithm's robustness to noise and missing information.

Graph Curvature for Differentiating Cancer Networks.

Cellular interactions can be modeled as complex dynamical systems represented by weighted graphs. The functionality of such networks, including measures of robustness, reliability, performance, and efficiency, are intrinsically tied to the topology and geometry of the underlying graph. Utilizing recently proposed geometric notions of curvature on weighted graphs, we investigate the features of gene co-expression networks derived from large-scale genomic studies of cancer. We find that the curvature of these networks reliably distinguishes between cancer and normal samples, with cancer networks exhibiting higher curvature than their normal counterparts. We establish a quantitative relationship between our findings and prior investigations of network entropy. Furthermore, we demonstrate how our approach yields additional, non-trivial pair-wise (i.e. gene-gene) interactions which may be disrupted in cancer samples. The mathematical formulation of our approach yields an exact solution to calculating pair-wise changes in curvature which was computationally infeasible using prior methods. As such, our findings lay the foundation for an analytical approach to studying complex biological networks.

Interactive Image Segmentation Framework Based On Control Theory.

Segmentation of anatomical structures in medical imagery is a key step in a variety of clinical applications. Designing a generic, automated method that works for various structures and imaging modalities is a daunting task. Instead of proposing a new specific segmentation algorithm, in this paper, we present a general design principle on how to integrate user interactions from the perspective of control theory. In this formulation, Lyapunov stability analysis is employed to design and analyze an interactive segmentation system. The effectiveness and robustness of the proposed method are demonstrated.

Optimal-mass-transfer-based estimation of glymphatic transport in living brain.

It was recently shown that the brain-wide cerebrospinal fluid (CSF) and interstitial fluid exchange system designated the 'glymphatic pathway' plays a key role in removing waste products from the brain, similarly to the lymphatic system in other body organs1,2. It is therefore important to study the flow patterns of glymphatic transport through the live brain in order to better understand its functionality in normal and pathological states. Unlike blood, the CSF does not flow rapidly through a network of dedicated vessels, but rather through para-vascular channels and brain parenchyma in a slower time-domain, and thus conventional fMRI or other blood-flow sensitive MRI sequences do not provide much useful information about the desired flow patterns. We have accordingly analyzed a series of MRI images, taken at different times, of the brain of a live rat, which was injected with a paramagnetic tracer into the CSF via the lumbar intrathecal space of the spine. Our goal is twofold: (a) find glymphatic (tracer) flow directions in the live rodent brain; and (b) provide a model of a (healthy) brain that will allow the prediction of tracer concentrations given initial conditions. We model the liquid flow through the brain by the diffusion equation. We then use the Optimal Mass Transfer (OMT) approach3 to derive the glymphatic flow vector field, and estimate the diffusion tensors by analyzing the (changes in the) flow. Simulations show that the resulting model successfully reproduces the dominant features of the experimental data.

Stochastic Image Registration with User Constraints.

Constrained registration is an active area of research and is the focus of this work. This note describes a non-rigid image registration framework for incorporating landmark constraints. Points that must remain stationary are selected, the user chooses the spatial extent of the inputs, and an automatic step computes the deformable registration, respecting the constraints. Parametrization of the deformation field is by an additive composition of a similarity transformation and a set of Gaussian radial basis functions. The bases' centers, variances, and weights are determined with a global optimization approach that is introduced. This approach is based on the particle filter for performing constrained optimization; it explores a series of states defining a deformation field that is physically meaningful (i.e., invertible) and prevents chosen points from moving. Results on synthetic two dimensional images are presented.

Interactive medical image segmentation using PDE control of active contours.

Segmentation of injured or unusual anatomic structures in medical imagery is a problem that has continued to elude fully automated solutions. In this paper, the goal of easy-to-use and consistent interactive segmentation is transformed into a control synthesis problem. A nominal level set partial differential equation (PDE) is assumed to be given; this open-loop system achieves correct segmentation under ideal conditions, but does not agree with a human expert's ideal boundary for real image data. Perturbing the state and dynamics of a level set PDE via the accumulated user input and an observer-like system leads to desirable closed-loop behavior. The input structure is designed such that a user can stabilize the boundary in some desired state without needing to understand any mathematical parameters. Effectiveness of the technique is illustrated with applications to the challenging segmentations of a patellar tendon in magnetic resonance and a shattered femur in computed tomography.

Anatomic and morphological evaluation of the quadriceps tendon using 3-dimensional magnetic resonance imaging reconstruction: applications for anterior cruciate ligament autograft choice and procurement.

BACKGROUND: The autograft of choice for anterior cruciate ligament (ACL) reconstruction remains controversial. The quadriceps tendon is the least utilized and least studied of the potential autograft options. PURPOSE: To determine if the quadriceps tendon has the anatomic characteristics to produce a graft whose length and volume are adequate, reproducible, and predictable when compared with the other commonly used autografts. STUDY DESIGN: Cross-sectional study; Level of evidence, 3. METHODS: Axial proton density magnetic resonance imaging (MRI) scans of 60 skeletally mature patients (30 male and 30 female) were evaluated. Volumetric analysis of 3-dimensional models of the patellar and quadriceps tendons was performed before and after the removal of a 10 mm-wide graft from both tendons. Length, thickness, and width measurements of the quadriceps tendon were made at predetermined locations. Anthropometric data were collected, and subgroup analysis, sex analysis, and linear regression were performed. RESULTS: The mean percentage of volume remaining after removal of a 10 mm-wide graft from the patellar tendon was 56.6%, compared with 61.3% when harvesting an 80 mm-long graft of the same width from the quadriceps tendon. The intra-articular volume of the proposed quadriceps tendon graft was 87.5% greater than that of the patellar tendon graft. The mean length of the quadriceps tendon was 73.5 ± 12.3 mm in female patients and 81.1 ± 10.6 mm in male patients. These measurements were most highly correlated with patient height. The width of the quadriceps tendon decreased as one proceeded proximally from its insertion, and the thickness of the quadriceps tendon remained relatively constant. CONCLUSION: The quadriceps tendon has the anatomic characteristics to produce a graft whose length and volume are both reproducible and predictable, while yielding a graft with a significantly greater intra-articular volume than a patellar tendon graft with a similar width.

Optical flow estimation for flame detection in videos.

Computational vision-based flame detection has drawn significant attention in the past decade with camera surveillance systems becoming ubiquitous. Whereas many discriminating features, such as color, shape, texture, etc., have been employed in the literature, this paper proposes a set of motion features based on motion estimators. The key idea consists of exploiting the difference between the turbulent, fast, fire motion, and the structured, rigid motion of other objects. Since classical optical flow methods do not model the characteristics of fire motion (e.g., non-smoothness of motion, non-constancy of intensity), two optical flow methods are specifically designed for the fire detection task: optimal mass transport models fire with dynamic texture, while a data-driven optical flow scheme models saturated flames. Then, characteristic features related to the flow magnitudes and directions are computed from the flow fields to discriminate between fire and non-fire motion. The proposed features are tested on a large video database to demonstrate their practical usefulness. Moreover, a novel evaluation method is proposed by fire simulations that allow for a controlled environment to analyze parameter influences, such as flame saturation, spatial resolution, frame rate, and random noise.

Interactive MRI Segmentation with Controlled Active Vision.

Partitioning Magnetic-Resonance-Imaging (MRI) data into salient anatomic structures is a problem in medical imaging that has continued to elude fully automated solutions. Implicit functions are a common way to model the boundaries between structures and are amenable to control-theoretic methods. In this paper, the goal of enabling a human to obtain accurate segmentations in a short amount of time and with little effort is transformed into a control synthesis problem. Perturbing the state and dynamics of an implicit function's driving partial differential equation via the accumulated user inputs and an observer-like system leads to desirable closed-loop behavior. Using a Lyapunov control design, a balance is established between the influence of a data-driven gradient flow and the human's input over time. Automatic segmentation is thus smoothly coupled with interactivity. An application of the mathematical methods to orthopedic segmentation is shown, demonstrating the expected transient and steady state behavior of the implicit segmentation function and auxiliary observer.