Unified Heat Kernel Regression for Diffusion, Kernel Smoothing and Wavelets on Manifolds and Its Application to Mandible Growth Modeling in CT Images

We present a novel kernel regression framework for smoothing scalar surface data using the Laplace-Beltrami eigenfunctions. Starting with the heat kernel constructed from the eigenfunctions, we formulate a new bivariate kernel regression framework as a weighted eigenfunction expansion with the heat kernel as the weights. The new kernel regression is mathematically equivalent to isotropic heat diffusion, kernel smoothing and recently popular diffusion wavelets. Unlike many previous partial differential equation based approaches involving diffusion, our approach represents the solution of diffusion analytically, reducing numerical inaccuracy and slow convergence. The numerical implementation is validated on a unit sphere using spherical harmonics. As an illustration, we have applied the method in characterizing the localized growth pattern of mandible surfaces obtained in CT images from subjects between ages 0 and 20 years by regressing the length of displacement vectors with respect to the template surface.Comment: Accepted in Medical Image Analysi

BRUISE DETECTION IN APPLES USING 3D INFRARED IMAGING AND MACHINE LEARNING TECHNOLOGIES

Bruise detection plays an important role in fruit grading. A bruise detection system capable of finding and removing damaged products on the production lines will distinctly improve the quality of fruits for sale, and consequently improve the fruit economy. This dissertation presents a novel automatic detection system based on surface information obtained from 3D near-infrared imaging technique for bruised apple identification. The proposed 3D bruise detection system is expected to provide better performance in bruise detection than the existing 2D systems. We first propose a mesh denoising filter to reduce noise effect while preserving the geometric features of the meshes. Compared with several existing mesh denoising filters, the proposed filter achieves better performance in reducing noise effect as well as preserving bruised regions in 3D meshes of bruised apples. Next, we investigate two different machine learning techniques for the identification of bruised apples. The first technique is to extract hand-crafted feature from 3D meshes, and train a predictive classifier based on hand-crafted features. It is shown that the predictive model trained on the proposed hand-crafted features outperforms the same models trained on several other local shape descriptors. The second technique is to apply deep learning to learn the feature representation automatically from the mesh data, and then use the deep learning model or a new predictive model for the classification. The optimized deep learning model achieves very high classification accuracy, and it outperforms the performance of the detection system based on the proposed hand-crafted features. At last, we investigate GPU techniques for accelerating the proposed apple bruise detection system. Specifically, the dissertation proposes a GPU framework, implemented in CUDA, for the acceleration of the algorithm that extracts vertex-based local binary patterns. Experimental results show that the proposed GPU program speeds up the process of extracting local binary patterns by 5 times compared to a single-core CPU program

Integrated Segmentation and Interpolation of Sparse Data

This paper addresses the two inherently related problems of segmentation and interpolation of 3D and 4D sparse data by integrating integrate these stages in a level set framework. The method supports any spatial configurations of sets of 2D slices having arbitrary positions and orientations. We introduce a new level set scheme based on the interpolation of the level set function by radial basis functions. The proposed method is validated quantitatively and/or subjectively on artificial data and MRI and CT scans and is compared against the traditional sequential approach

Computerized Analysis of Magnetic Resonance Images to Study Cerebral Anatomy in Developing Neonates

The study of cerebral anatomy in developing neonates is of great importance for the understanding of brain development during the early period of life. This dissertation therefore focuses on three challenges in the modelling of cerebral anatomy in neonates during brain development. The methods that have been developed all use Magnetic Resonance Images (MRI) as source data. To facilitate study of vascular development in the neonatal period, a set of image analysis algorithms are developed to automatically extract and model cerebral vessel trees. The whole process consists of cerebral vessel tracking from automatically placed seed points, vessel tree generation, and vasculature registration and matching. These algorithms have been tested on clinical Time-of- Flight (TOF) MR angiographic datasets. To facilitate study of the neonatal cortex a complete cerebral cortex segmentation and reconstruction pipeline has been developed. Segmentation of the neonatal cortex is not effectively done by existing algorithms designed for the adult brain because the contrast between grey and white matter is reversed. This causes pixels containing tissue mixtures to be incorrectly labelled by conventional methods. The neonatal cortical segmentation method that has been developed is based on a novel expectation-maximization (EM) method with explicit correction for mislabelled partial volume voxels. Based on the resulting cortical segmentation, an implicit surface evolution technique is adopted for the reconstruction of the cortex in neonates. The performance of the method is investigated by performing a detailed landmark study. To facilitate study of cortical development, a cortical surface registration algorithm for aligning the cortical surface is developed. The method first inflates extracted cortical surfaces and then performs a non-rigid surface registration using free-form deformations (FFDs) to remove residual alignment. Validation experiments using data labelled by an expert observer demonstrate that the method can capture local changes and follow the growth of specific sulcus

Extracting 3D parametric curves from 2D images of Helical objects

Helical objects occur in medicine, biology, cosmetics, nanotechnology, and engineering. Extracting a 3D parametric curve from a 2D image of a helical object has many practical applications, in particular being able to extract metrics such as tortuosity, frequency, and pitch. We present a method that is able to straighten the image object and derive a robust 3D helical curve from peaks in the object boundary. The algorithm has a small number of stable parameters that require little tuning, and the curve is validated against both synthetic and real-world data. The results show that the extracted 3D curve comes within close Hausdorff distance to the ground truth, and has near identical tortuosity for helical objects with a circular profile. Parameter insensitivity and robustness against high levels of image noise are demonstrated thoroughly and quantitatively

Integrated Segmentation and Interpolation of Sparse Data

International audienceWe address the two inherently related problems of segmentation and interpolation of 3D and 4D sparse data and propose a new method to integrate these stages in a level set framework. The interpolation process uses segmentation information rather than pixel intensities for increased robustness and accuracy. The method supports any spatial configurations of sets of 2D slices having arbitrary positions and orientations. We achieve this by introducing a new level set scheme based on the interpolation of the level set function by radial basis functions. The proposed method is validated quantitatively and/or subjectively on artificial data and MRI and CT scans, and is compared against the traditional sequential approach which interpolates the images first, using a state-of-the-art image interpolation method, and then segments the interpolated volume in 3D or 4D. In our experiments, the proposed framework yielded similar segmentation results to the sequential approach, but provided a more robust and accurate interpolation. In particular, the interpolation was more satisfactory in cases of large gaps, due to the method taking into account the global shape of the object, and it recovered better topologies at the extremities of the shapes where the objects disappear from the image slices. As a result, the complete integrated framework provided more satisfactory shape reconstructions than the sequential approach