A New Variational Model And Its Application In Brain Imaging Dataset

Brain is one of the most complex systems in nature, which governs the human mind and behavior. The research of the structure and function of brain is of great significance to describe the generation mechanism of intelligence, thinking and consciousness and to uncover the working principle of the brain, which can further promote us to understand some advanced function and the formation mechanism of nervous and mental diseases. The cross and integration development of multidisciplinary such as life science, optics, mechanics and information science makes imaging the whole mouse brain dataset at high spatial resolution possible. Translate the brain imaging dataset into biology knowledge has become bottleneck problem in brain research.Shape reconstruction in brain imaging dataset, as an important part of the brain research, plays an important role in digital reconstruction the neuron, registration the brain dataset, qualitative and quantitative analysis, etc. It can help the study of neurons morphology and quantitative analysis the projection of neurons, and lay a foundation for exploring the formation mechanism of brain disease. However, as the large size and high complexity of dataset, shape reconstruction in brain imaging dataset faces great challenges.To meet the needs of translating brain imaging dataset into biology knowledge, aim at the specific problem of shape reconstruction, this thesis structures a new variational model to slove the shape reconstruction problems in brain imaging dataset. The main contributions of this thesis are as following:(1)Construct a new variational model. On the basis of the ordinary variational model, this thesis structures a new variational model by building an energy equation in the resampling dataset. The new variational model can control the movement directions of the boundary elements and overcome the problem of sensitive in selecting the initial boundary curve. At the same time, in combination with the adding of smooth constraint item, the model can overcome the challenge of noise interference.(2) Base on spherical-coordinated variational model, we construct a method for reconstructing the neuron soma morphology. This method translates the 3D image stack into the spherical coordinate system and constructs a variational model for reconstructing the neuron soma morphology in spherical coordinate system. We test some image stacks and verify spherical-coordinated variational model has ability to reconstruct the neuron soma morphology with dense neural circuits and thick dendrite trucks interference.(3)Base on resampling-based variational model, we construct a method for reconstructing the mouse brain surface. This method obtains the local signal around the boundary area and constructs a variational model for reconstructing the mouse brain surface in the resampling dataset. We test some mouse brain datasets and verify resampling-based variational model has ability to reconstruct the mouse brain surface with large volume and significantly variable signals at the brain surface.Methods in this thesis all have practical application in neuron tracing, image pre-processing, mouse brain registration, etc. The method for reconstructing the neuron soma morphology has been used in tracing neuronal populations with dense neurites and sparse neurons. With the soma morphology, we can get the information of the dendrites and axons which directly connected to the soma, which can provide a priori information for the tracking of the neural network and the distribution of nerve fibers. The method for reconstructing the mouse brain surface has been used in image pre-processing, mouse brain registration, etc. With the mouse brain surface, we can remove the interference signals outside the mouse surface and make image pre-processing and mouse brain registration more accurate.