Fine-Scale Singularity Detection in Multi-Dimensional Imaging with Regular, Orientable, Symmetric, Frame Atoms with Small Support

生命的本质特征之一是运动。无论是柴可夫斯基的《天鹅湖》中完美无瑕的白色天鹅优美壮观的舞蹈，还是蹒跚学步的孩子早期尝试使用双手，运动的神经学对所有动物和人类来说都是独一无二的：学习运动技能和必要的肌肉协调。通过实践，技能得到完善。最后，对这种体验式学习过程的保留是对这种学习过程的总结。该项目的最终目标是为神经科学家提供新的工具，他们使用活体动物在细胞水平上研究学习的生物学基础。神经细胞的细胞质结构中的许多解剖学变化促进了这种功能，例如形成称为轴突和树突的长分支，以及细尺度的树突棘和轴突按钮。后者是在这些细胞质延伸的表面上产生的解剖学上不太永久的结构。树突棘和轴突按钮形成突触，这是神经元之间的通信网关。该研究小组将开发数学和计算工具，用于自动化研究活神经元中的脊柱种群及其在学习过程中的时间演变。预期的结果将为神经科学家提供许多软件工具，这些工具将自动分析突触强度及其随着学习的演变。这些发现将有助于更好地理解自闭症和药物成瘾的生物学机制。该项目的研究人员将开发用于树突表面（包括棘）的3D数字分割的算法，该算法来自某种类型的显微镜获得的3D图像，该显微镜使用激光并通过利用神经元的天然荧光能力作为扫描仪工作。他们的目标是生成精确的二进制重建的树枝状乔木，包括它的刺。该项目的主要挑战是活神经元的图像采集具有提供有限的脊柱细节的分辨率。通常，图像包含噪声，这进一步使提取显示棘细节的树突表面的准确的二进制3D重建复杂化。克服这个问题是该项目的核心目标，因为脊柱体积估计量化了突触强度。这些独特的挑战导致研究人员开发新的数学工具进行精细尺度分析。他们将建立一个小尺寸的3D成像，3D方向选择，基于帧的过滤器，适用于在嘈杂的图像中感测曲线和表面。这些滤波器将被设计为响应图像平滑度的局部变化。从这些滤波器在不同尺度上获得的信息将被用作多层深度学习启发的神经网络的输入，该神经网络将确定图像中哪些体素属于脊柱表面。进一步的算法工具将被开发，以跟踪每个树突棘单独随着时间的推移。相同的滤波工具将用于不同的应用领域，即实时生成照明中性图像。这将有助于快速、高吞吐量地去除图像中的不均匀照明的影响，该不均匀照明的影响抑制通过软件或裸眼对与场景中的形状或纹理相关联的轮廓的检测。研究人员将发展的数学理论的照明中和使用的概念，从分形和微观局部分析。照明中和算法的设想工作的实时视频分析，并与人脸验证算法的潜力，可用于人脸识别，激光显微镜和遥感应用。

One of life's essential characteristic is movement. Whether it is the spectacular, delicate dance of the unblemished, white swan in Tchaikovsky's Swan Lake, or the early attempts of a toddler to use his or her hands, the neurology of movement is uniquely common for all animals and humans: learning a motor skill, and the necessary muscle coordination. With practice the skill is perfected. Finally, the retainment of this experience-based learning process is the conclusion of this learning process. The ultimate goal of this project is to provide new tools to neuroscientists who study the biological basis of learning at the cell level using live animals. This function is facilitated by a number of anatomical changes in the structure of the cytoplasm of neural cells, such as the formation of lengthy branches known as axons and dendrites, and at a fine scale of dendritic spines and axonal buttons. The latter are less anatomically permanent structures arising on the surface of these cytoplasmic extensions. Dendritic spines and axonal buttons form synapses, which are the communication gateways between neurons. The research team will develop mathematical and computational tools for automatizing the study of spine populations in live neurons, and of their time-evolution during learning. The anticipated outcomes will provide neuroscientists with a number of software tools which will automatize the analysis of synaptic strength and its evolution with learning. These findings will contributed to the better understanding the biological mechanisms of autism and drug addictions.The investigators on this project will develop algorithms for the 3D digital segmentations of dendritic surfaces including spines from 3D images acquired with a certain type of microscope, which uses laser light and works as a scanner by exploiting the natural ability of neurons to fluoresce. They aim to generate accurate binary reconstructions of a dendritic arbor including its spines. The primary challenge in this project is that image acquisition of live neurons has a resolution which provides limited detail of the spines. Often, images contain noise which further complicates the extraction of accurate, binary 3D reconstructions of dendritic surfaces showing spine details. Overcoming this problem is a core goal of the project because spine volume estimation quantifies synaptic strength. These unique challenges lead the investigators to the development of novel mathematical tools for fine scale analysis. They will build ensembles of short in size 3D imaging, 3D-orientation selective, frame-based filters, suitable for sensing curves and surfaces in noisy images. These filters will be designed to respond to local changes of image smoothness. Information obtained from these filters at various scales, will be utilized as input for multilayer, deep-learning inspired neural networks which will determine in an image which voxels belong to spine surfaces. Further algorithmic tools will be developed to track every spine of a dendrite individually over time. The same filtering tools will be used in a different application domain, the generation of illumination neutral images, in real-time. This will help the fast, high throughput removal of the effects of uneven illumination in images inhibiting the detection, by software or the naked eye of contours associated with shapes or textures in a scene. The investigators will develop the mathematical theory of illumination neutralization using concepts from fractal and microlocal analysis. The illumination neutralization algorithm is envisioned to work for real-time video analysis and in conjunction with face verification algorithms with the potential to be used in face recognition, laser microscopy and remote sensing applications.