Skeletonization and Partitioning of Digital Images Using Discrete Morse Theory

We show how discrete Morse theory provides a rigorous and unifying foundation for defining skeletons and partitions of grayscale digital images. We model a grayscale image as a cubical complex with a real-valued function defined on its vertices (the voxel values). This function is extended to a discrete gradient vector field using the algorithm presented in Robins, Wood, Sheppard TPAMI 33:1646 (2011). In the current paper we define basins (the building blocks of a partition) and segments of the skeleton using the stable and unstable sets associated with critical cells. The natural connection between Morse theory and homology allows us to prove the topological validity of these constructions; for example, that the skeleton is homotopic to the initial object. We simplify the basins and skeletons via Morse-theoretic cancellation of critical cells in the discrete gradient vector field using a strategy informed by persistent homology. Simple working Python code for our algorithms for efficient vector field traversal is included. Example data are taken from micro-CT images of porous materials, an application area where accurate topological models of pore connectivity are vital for fluid-flow modelling

Disconnected Skeleton: Shape at its Absolute Scale

We present a new skeletal representation along with a matching framework to address the deformable shape recognition problem. The disconnectedness arises as a result of excessive regularization that we use to describe a shape at an attainably coarse scale. Our motivation is to rely on the stable properties of the shape instead of inaccurately measured secondary details. The new representation does not suffer from the common instability problems of traditional connected skeletons, and the matching process gives quite successful results on a diverse database of 2D shapes. An important difference of our approach from the conventional use of the skeleton is that we replace the local coordinate frame with a global Euclidean frame supported by additional mechanisms to handle articulations and local boundary deformations. As a result, we can produce descriptions that are sensitive to any combination of changes in scale, position, orientation and articulation, as well as invariant ones.Comment: The work excluding {\S}V and {\S}VI has first appeared in 2005 ICCV: Aslan, C., Tari, S.: An Axis-Based Representation for Recognition. In ICCV(2005) 1339- 1346.; Aslan, C., : Disconnected Skeletons for Shape Recognition. Masters thesis, Department of Computer Engineering, Middle East Technical University, May 200

Geometric Approaches for 3D Shape Denoising and Retrieval

A key issue in developing an accurate 3D shape recognition system is to design an efficient shape descriptor for which an index can be built, and similarity queries can be answered efficiently. While the overwhelming majority of prior work on 3D shape analysis has concentrated primarily on rigid shape retrieval, many real objects such as articulated motions of humans are nonrigid and hence can exhibit a variety of poses and deformations. Motivated by the recent surge of interest in content-based analysis of 3D objects in computeraided design and multimedia computing, we develop in this thesis a unified theoretical and computational framework for 3D shape denoising and retrieval by incorporating insights gained from algebraic graph theory and spectral geometry. We first present a regularized kernel diffusion for 3D shape denoising by solving partial differential equations in the weighted graph-theoretic framework. Then, we introduce a computationally fast approach for surface denoising using the vertexcentered finite volume method coupled with the mesh covariance fractional anisotropy. Additionally, we propose a spectral-geometric shape skeleton for 3D object recognition based on the second eigenfunction of the Laplace-Beltrami operator in a bid to capture the global and local geometry of 3D shapes. To further enhance the 3D shape retrieval accuracy, we introduce a graph matching approach by assigning geometric features to each endpoint of the shape skeleton. Extensive experiments are carried out on two 3D shape benchmarks to assess the performance of the proposed shape retrieval framework in comparison with state-of-the-art methods. The experimental results show that the proposed shape descriptor delivers best-in-class shape retrieval performance

Effect of space conditions on neuronal plasticity and connectivity

Looking for opportunities to explore new frontiers and developing new technologies have always been in the nature of mankind. In 1957, the first rocket in space opened a new era for space traveling towards other planets. Concomitantly, a wide range of concerns related to human health risks that could occur during spaceflight was raised. Up to now, a large number of experiments has been performed to determine the biological effects of space conditions on human health, in order to develop appropriate countermeasures. However, extensive investigations still need to be performed before considering long-term spaceflight towards other planets such as Mars. Since the first human space flight, it has been observed that in weightlessness conditions, equilibrium sense organs can send misleading inputs to the central nervous system which is forced to develop new strategies and adapt to adequately translate these messages. Furthermore, cosmic radiations are known to induce oxidative stress as well as genomic damages. In this thesis, we studied concomitant microgravity and radiation exposures as models for space conditions and developed various methods to analyse their specific and combined effects on in vitro neuronal network models. In vitro primary neuronal network cultures were established and exposed to simulated space conditions to investigate neuronal network remodelling (plasticity and connectivity) as well as genomic damage/repair dynamics. This work was performed to address questions on neuronal network disorders occurring during spaceflights and, in the future, to develop strategies against these effects

An Affordable Portable Obstetric Ultrasound Simulator for Synchronous and Asynchronous Scan Training

The increasing use of Point of Care (POC) ultrasound presents a challenge in providing efficient training to new POC ultrasound users. In response to this need, we have developed an affordable, compact, laptop-based obstetric ultrasound training simulator. It offers freehand ultrasound scan on an abdomen-sized scan surface with a 5 degrees of freedom sham transducer and utilizes 3D ultrasound image volumes as training material. On the simulator user interface is rendered a virtual torso, whose body surface models the abdomen of a particular pregnant scan subject. A virtual transducer scans the virtual torso, by following the sham transducer movements on the scan surface. The obstetric ultrasound training is self-paced and guided by the simulator using a set of tasks, which are focused on three broad areas, referred to as modules: 1) medical ultrasound basics, 2) orientation to obstetric space, and 3) fetal biometry. A learner completes the scan training through the following three steps: (i) watching demonstration videos, (ii) practicing scan skills by sequentially completing the tasks in Modules 2 and 3, with scan evaluation feedback and help functions available, and (iii) a final scan exercise on new image volumes for assessing the acquired competency. After each training task has been completed, the simulator evaluates whether the task has been carried out correctly or not, by comparing anatomical landmarks identified and/or measured by the learner to reference landmark bounds created by algorithms, or pre-inserted by experienced sonographers. Based on the simulator, an ultrasound E-training system has been developed for the medical practitioners for whom ultrasound training is not accessible at local level. The system, composed of a dedicated server and multiple networked simulators, provides synchronous and asynchronous training modes, and is able to operate with a very low bit rate. The synchronous (or group-learning) mode allows all training participants to observe the same 2D image in real-time, such as a demonstration by an instructor or scan ability of a chosen learner. The synchronization of 2D images on the different simulators is achieved by directly transmitting the position and orientation of the sham transducer, rather than the ultrasound image, and results in a system performance independent of network bandwidth. The asynchronous (or self-learning) mode is described in the previous paragraph. However, the E-training system allows all training participants to stay networked to communicate with each other via text channel. To verify the simulator performance and training efficacy, we conducted several performance experiments and clinical evaluations. The performance experiment results indicated that the simulator was able to generate greater than 30 2D ultrasound images per second with acceptable image quality on medium-priced computers. In our initial experiment investigating the simulator training capability and feasibility, three experienced sonographers individually scanned two image volumes on the simulator. They agreed that the simulated images and the scan experience were adequately realistic for ultrasound training; the training procedure followed standard obstetric ultrasound protocol. They further noted that the simulator had the potential for becoming a good supplemental training tool for medical students and resident doctors. A clinic study investigating the simulator training efficacy was integrated into the clerkship program of the Department of Obstetrics and Gynecology, University of Massachusetts Memorial Medical Center. A total of 24 3rd year medical students were recruited and each of them was directed to scan six image volumes on the simulator in two 2.5-hour sessions. The study results showed that the successful scan times for the training tasks significantly decreased as the training progressed. A post-training survey answered by the students found that they considered the simulator-based training useful and suitable for medical students and resident doctors. The experiment to validate the performance of the E-training system showed that the average transmission bit rate was approximately 3-4 kB/s; the data loss was less than 1% and no loss of 2D images was visually detected. The results also showed that the 2D images on all networked simulators could be considered to be synchronous even though inter-continental communication existed

Focus+Context via Snaking Paths

Focus+context visualizations reveal specific structures in high detail while effectively depicting its surroundings, often relying on transitions between the two areas to provide context. We present an approach to generate focus+context visualizations depicting cylindrical structures along snaking paths that enables the structures themselves to become the transitions and focal areas, simultaneously. A method to automatically create a snaking path through space by applying a path finding algorithm is presented. A 3D curve is created based on the 2D snaking path. We describe a process to deform cylindrical structures in segmented volumetric models to match the curve and provide preliminary geometric models as templates for artists to build upon. Structures are discovered using our constrained volumetric sculpting method that enables removal of occluding material while leaving them intact. We find the resulting visualizations effectively mimic a set of motivating illustrations and discuss some limitations of the automatic approach