Chiu-Yen Kao

Minimization of Region-Scalable Fitting Energy for Image Segmentation

Intensity inhomogeneities often occur in real-world images and may cause considerable difficulties in image segmentation. In order to overcome the difficulties caused by intensity inhomogeneities, we propose a region-based active contour model that draws upon intensity information in local regions at a controllable scale. A data fitting energy is defined in terms of a contour and two fitting functions that locally approximate the image intensities on the two sides of the contour. This energy is then incorporated into a variational level set formulation with a level set regularization term, from which a curve evolution equation is derived for energy minimization. Due to a kernel function in the data fitting term, intensity information in local regions is extracted to guide the motion of the contour, which thereby enables our model to cope with intensity inhomogeneity. In addition, the regularity of the level set function is intrinsically preserved by the level set regularization term to ensure accurate computation and avoids expensive reinitialization of the evolving level set function. Experimental results for synthetic and real images show desirable performances of our method.

Implicit Active Contours Driven by Local Binary Fitting Energy

Local image information is crucial for accurate segmentation of images with intensity inhomogeneity. However, image information in local region is not embedded in popular region-based active contour models, such as the piecewise constant models. In this paper, we propose a region-based active contour model that is able to utilize image information in local regions. The major contribution of this paper is the introduction of a local binary fitting energy with a kernel function, which enables the extraction of accurate local image information. Therefore, our model can be used to segment images with intensity inhomogeneity, which overcomes the limitation of piecewise constant models. Comparisons with other major region-based models, such as the piece-wise smooth model, show the advantages of our method in terms of computational efficiency and accuracy. In addition, the proposed method has promising application to image denoising.

Active contours driven by local and global intensity fitting energy with application to brain MR image segmentation

In this paper, we propose an improved region-based active contour model in a variational level set formulation. We define an energy functional with a local intensity fitting term, which induces a local force to attract the contour and stops it at object boundaries, and an auxiliary global intensity fitting term, which drives the motion of the contour far away from object boundaries. Therefore, the combination of these two forces allows for flexible initialization of the contours. This energy is then incorporated into a level set formulation with a level set regularization term that is necessary for accurate computation in the corresponding level set method. The proposed model is first presented as a two-phase level set formulation and then extended to a multi-phase formulation. Experimental results show the advantages of our method in terms of accuracy and robustness. In particular, our method has been applied to brain MR image segmentation with desirable results.

The development of gyrification in childhood and adolescence

Gyrification is the process by which the brain undergoes changes in surface morphology to create sulcal and gyral regions. The period of greatest development of brain gyrification is during the third trimester of pregnancy, a period of time in which the brain undergoes considerable growth. Little is known about changes in gyrification during childhood and adolescence, although considering the changes in gray matter volume and thickness during this time period, it is conceivable that alterations in the brain surface morphology could also occur during this period of development. The formation of gyri and sulci in the brain allows for compact wiring that promotes and enhances efficient neural processing. If cerebral function and form are linked through the organization of neural connectivity, then alterations in neural connectivity, i.e., synaptic pruning, may also alter the gyral and sulcal patterns of the brain. This paper reviews developmental theories of gyrification, computational techniques for measuring gyrification, and the potential interaction between gyrification and neuronal connectivity. We also present recent findings involving alterations in gyrification during childhood and adolescence.

Fast Sweeping Methods for Static Hamilton--Jacobi Equations

We propose a new sweeping algorithm which discretizes the Legendre transform of the numerical Hamiltonian using an explicit formula. This formula yields the numerical solution at a grid point using only its immediate neighboring grid values and is easy to implement numerically. The minimization that is related to the Legendre transform in our sweeping scheme can either be solved analytically or numerically. We illustrate the efficiency and accuracy approach with several numerical examples in two and three dimensions.

Incorporating topological derivatives into shape derivatives based level set methods

Shape derivatives and topological derivatives have been incorporated into level set methods to investigate shape optimization problems. The shape derivative measures the sensitivity of boundary perturbations while the topological derivative measures the sensitivity of creating a small hole in the interior domain. The combination of these two derivatives yields an efficient algorithm which has more flexibility in shape changing and may escape from a local optimal. Examples on finding the optimal shapes for maximal band gaps in photonic crystal and acoustic drum problems are demonstrated.

White matter tractography by anisotropic wavefront evolution and diffusion tensor imaging

Determination of axonal pathways provides an invaluable means to study the connectivity of the human brain and its functional network. Diffusion tensor imaging (DTI) is unique in its ability to capture the restricted diffusion of water molecules which can be used to infer the directionality of tissue components. In this paper, we introduce a white matter tractography method based on anisotropic wavefront propagation in diffusion tensor images. A front propagates in the white matter with a speed profile governed by the isocontour of the diffusion tensor ellipsoid. By using the ellipsoid, we avoid possible misclassification of the principal eigenvector in oblate regions. The wavefront evolution is described by an anisotropic version of the static Hamilton-Jacobi equation, which is solved by a sweeping method in order to obtain correct arrival times. Pathways of connection are determined by tracing minimum-cost trajectories using the characteristic vector field of the resulting partial differential equation. A validity index is described to rate the goodness of the resulting pathways with respect to the directionality of the tensor field. Connectivity results using normal human DTI brain images are illustrated and discussed. We also compared our method with a similar level set-based tractography technique, and found that the anisotropic evolution increased the validity index of the obtained pathways by 18%.

Quantification of age-related and per diopter accommodative changes of the lens and ciliary muscle in the emmetropic human eye.

PURPOSE To calculate age-related and per diopter (D) accommodative changes in crystalline lens and ciliary muscle dimensions in vivo in a single cohort of emmetropic human adults ages 30 to 50 years. METHODS The right eyes of 26 emmetropic adults were examined using ultrasonography, phakometry, anterior segment optical coherence tomography, and high resolution magnetic resonance imaging. Accommodation was measured both subjectively and objectively. RESULTS In agreement with previous research, older age was linearly correlated with a thicker lens, steeper anterior lens curvature, shallower anterior chamber, and lower lens equivalent refractive index (all P < 0.01). Age was not related to ciliary muscle ring diameter (CMRD) or lens equatorial diameter (LED). With accommodation, lens thickness increased (+0.064 mm/D, P < 0.001), LED decreased (-0.075 mm/D, P < 0.001), CMRD decreased (-0.105 mm/D, P < 0.001), and the ciliary muscle thickened anteriorly (+0.013 to +0.026 mm/D, P < 0.001) and thinned posteriorly (-0.011 to -0.015, P < 0.01). The changes per diopter of accommodation in LED, CMRD, and ciliary muscle thickness were not related to subject age. CONCLUSIONS The per diopter ciliary muscle contraction is age independent, even as total accommodative amplitude declines. Quantifying normal biometric dimensions of the accommodative structures and changes with age and accommodative effort will further the development of new IOLs designed to harness ciliary muscle forces.

A Geometric Method for Automatic Extraction of Sulcal Fundi

Sulcal fundi are 3-D curves that lie in the depths of the cerebral cortex and, in addition to their intrinsic value in brain research, are often used as landmarks for downstream computations in brain imaging. In this paper, we present a geometric algorithm that automatically extracts the sulcal fundi from magnetic resonance images and represents them as spline curves lying on the extracted triangular mesh representing the cortical surface. The input to our algorithm is a triangular mesh representation of an extracted cortical surface as computed by one of several available software packages for performing automated and semi-automated cortical surface extraction. Given this input we first compute a geometric depth measure for each triangle on the cortical surface mesh, and based on this information we extract sulcal regions by checking for connected regions exceeding a depth threshold. We then identify endpoints of each region and delineate the fundus by thinning the connected region while keeping the endpoints fixed. The curves, thus, defined are regularized using weighted splines on the surface mesh to yield high-quality representations of the sulcal fundi. We present the geometric framework and validate it with real data from human brains. Comparisons with expert-labeled sulcal fundi are part of this validation process

Mitochondrial Dynamics and Motility Inside Living Vascular Endothelial Cells: Role of Bioenergetics

The mitochondrial network is dynamic with conformations that vary between a tubular continuum and a fragmented state. The equilibrium between mitochondrial fusion/fission, as well as the organelle motility, determine network morphology and ultimately mitochondrial/cell function. Network morphology has been linked with the energy state in different cell types. In this study, we examined how bioenergetic factors affect mitochondrial dynamics/motility in cultured vascular endothelial cells (ECs). ECs were transduced with mitochondria-targeted green fluorescent protein (mito-GFP) and exposed to inhibitors of oxidative phosphorylation (OXPHOS) or ATP synthesis. Time-lapse fluorescence videos were acquired and a mathematical program that calculates size and speed of each mitochondrial object at each time frame was developed. Our data showed that inner mitochondrial membrane potential (ΔΨm), ATP produced by glycolysis, and, to a lesser degree, ATP produced by mitochondria are critical for maintaining the mitochondrial network, and different metabolic stresses induce distinct morphological patterns (e.g., mitochondrial depolarization is necessary for “donut” formation). Mitochondrial movement, characterized by Brownian diffusion with occasional bursts in displacement magnitude, was inhibited under the same conditions that resulted in increased fission. Hence, imaging/mathematical analysis shed light on the relationship between bioenergetics and mitochondrial network morphology; the latter may determine EC survival under metabolic stress.