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就是运动。无论是柴可夫斯基的《天鹅湖》中完美无瑕的白天鹅的壮观而精致的舞蹈，还是幼儿早期尝试用手的动作，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。通过练习，这项技能就会变得更加完善。最后，保留这个以经验为基础的学习过程是这个学习过程的结论。该项目的最终目标是为神经科学家提供新的工具，他们使用活动物在细胞水平上研究学习的生物学基础。神经细胞细胞质结构的一些解剖学变化促进了这一功能，例如形成了称为轴突和树突的长分支，以及树突和轴突纽扣的细小尺度。后者在解剖学上是出现在这些细胞质延伸表面的不太永久的结构。树突棘和轴突按钮形成突触，突触是神经元之间的通信网关。研究小组将开发数学和计算工具，以自动化研究活神经元中的脊椎群体，以及它们在学习过程中的时间演化。预期的结果将为神经科学家提供一些软件工具，这些工具将自动分析突触强度及其随着学习而演变的过程。这些发现将有助于更好地理解自闭症和吸毒成瘾的生物学机制。该项目的研究人员将开发算法，对树突表面进行3D数字分割，包括用某种类型的显微镜获取的3D图像中的脊椎，这种显微镜使用激光，通过利用神经元的天然荧光能力作为扫描仪工作。他们的目标是生成包括树枝在内的树枝的准确二进制重建。这个项目的主要挑战是，获取活神经元的图像的分辨率只能提供有限的脊椎细节。通常，图像包含噪声，这使得提取显示脊椎细节的树枝状表面的准确、二进制3D重建变得更加复杂。克服这一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来进行精细分析。他们将构建尺寸较短的3D成像、3D方向选择性、基于帧的滤光片，适合在噪声图像中感测曲线和表面。这些滤镜将被设计为响应图像平滑的局部变化。从这些不同尺度的过滤器获得的信息将被用作多层、受深度学习启发的神经网络的输入，该网络将在图像中确定哪些体素属于脊柱表面。随着时间的推移，将开发更多的算法工具来单独跟踪树枝状晶体的每一根刺。相同的过滤工具将用于不同的应用领域，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，该效果抑制了通过软件或肉眼检测与场景中的形状或纹理相关联的轮廓。研究人员将使用分形和微局部分析的概念来发展照明中和的数学理论。照明中和算法被设想用于实时视频分析，并与人脸验证算法结合使用，具有在人脸识别、激光显微镜和遥感应用中的潜力。

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.