Metrics for comparing neuronal tree shapes based on persistent homology

As more and more neuroanatomical data are made available through efforts such as NeuroMorpho.Org and FlyCircuit.org, the need to develop computational tools to facilitate automatic knowledge discovery from such large datasets becomes more urgent. One fundamental question is how best to compare neuron structures, for instance to organize and classify large collection of neurons. We aim to develop a flexible yet powerful framework to support comparison and classification of large collection of neuron structures efficiently. Specifically we propose to use a topological persistence-based feature vectorization framework. Existing methods to vectorize a neuron (i.e, convert a neuron to a feature vector so as to support efficient comparison and/or searching) typically rely on statistics or summaries of morphometric information, such as the average or maximum local torque angle or partition asymmetry. These simple summaries have limited power in encoding global tree structures. Based on the concept of topological persistence recently developed in the field of computational topology, we vectorize each neuron structure into a simple yet informative summary. In particular, each type of information of interest can be represented as a descriptor function defined on the neuron tree, which is then mapped to a simple persistence-signature. Our framework can encode both local and global tree structure, as well as other information of interest (electrophysiological or dynamical measures), by considering multiple descriptor functions on the neuron. The resulting persistence-based signature is potentially more informative than simple statistical summaries (such as average/mean/max) of morphometric quantities-Indeed, we show that using a certain descriptor function will give a persistence-based signature containing strictly more information than the classical Sholl analysis. At the same time, our framework retains the efficiency associated with treating neurons as points in a simple Euclidean feature space, which would be important for constructing efficient searching or indexing structures over them. We present preliminary experimental results to demonstrate the effectiveness of our persistence-based neuronal feature vectorization framework

The Panchromatic Hubble Andromeda Treasury

The Panchromatic Hubble Andromeda Treasury (PHAT) is an on-going HST Multicycle Treasury program to image ~1/3 of M31's star forming disk in 6 filters, from the UV to the NIR. The full survey will resolve the galaxy into more than 100 million stars with projected radii from 0-20 kpc over a contiguous 0.5 square degree area in 828 orbits, producing imaging in the F275W and F336W filters with WFC3/UVIS, F475W and F814W with ACS/WFC, and F110W and F160W with WFC3/IR. The resulting wavelength coverage gives excellent constraints on stellar temperature, bolometric luminosity, and extinction for most spectral types. The photometry reaches SNR=4 at F275W=25.1, F336W=24.9, F475W=27.9, F814W=27.1, F110W=25.5, and F160W=24.6 for single pointings in the uncrowded outer disk; however, the optical and NIR data are crowding limited, and the deepest reliable magnitudes are up to 5 magnitudes brighter in the inner bulge. All pointings are dithered and produce Nyquist-sampled images in F475W, F814W, and F160W. We describe the observing strategy, photometry, astrometry, and data products, along with extensive tests of photometric stability, crowding errors, spatially-dependent photometric biases, and telescope pointing control. We report on initial fits to the structure of M31's disk, derived from the density of RGB stars, in a way that is independent of the assumed M/L and is robust to variations in dust extinction. These fits also show that the 10 kpc ring is not just a region of enhanced recent star formation, but is instead a dynamical structure containing a significant overdensity of stars with ages >1 Gyr. (Abridged)Comment: 48 pages including 22 pages of figures. Accepted to the Astrophysical Journal Supplements. Some figures slightly degraded to reduce submission siz

Graph-based Data Modeling and Analysis for Data Fusion in Remote Sensing

Hyperspectral imaging provides the capability of increased sensitivity and discrimination over traditional imaging methods by combining standard digital imaging with spectroscopic methods. For each individual pixel in a hyperspectral image (HSI), a continuous spectrum is sampled as the spectral reflectance/radiance signature to facilitate identification of ground cover and surface material. The abundant spectrum knowledge allows all available information from the data to be mined. The superior qualities within hyperspectral imaging allow wide applications such as mineral exploration, agriculture monitoring, and ecological surveillance, etc. The processing of massive high-dimensional HSI datasets is a challenge since many data processing techniques have a computational complexity that grows exponentially with the dimension. Besides, a HSI dataset may contain a limited number of degrees of freedom due to the high correlations between data points and among the spectra. On the other hand, merely taking advantage of the sampled spectrum of individual HSI data point may produce inaccurate results due to the mixed nature of raw HSI data, such as mixed pixels, optical interferences and etc. Fusion strategies are widely adopted in data processing to achieve better performance, especially in the field of classification and clustering. There are mainly three types of fusion strategies, namely low-level data fusion, intermediate-level feature fusion, and high-level decision fusion. Low-level data fusion combines multi-source data that is expected to be complementary or cooperative. Intermediate-level feature fusion aims at selection and combination of features to remove redundant information. Decision level fusion exploits a set of classifiers to provide more accurate results. The fusion strategies have wide applications including HSI data processing. With the fast development of multiple remote sensing modalities, e.g. Very High Resolution (VHR) optical sensors, LiDAR, etc., fusion of multi-source data can in principal produce more detailed information than each single source. On the other hand, besides the abundant spectral information contained in HSI data, features such as texture and shape may be employed to represent data points from a spatial perspective. Furthermore, feature fusion also includes the strategy of removing redundant and noisy features in the dataset. One of the major problems in machine learning and pattern recognition is to develop appropriate representations for complex nonlinear data. In HSI processing, a particular data point is usually described as a vector with coordinates corresponding to the intensities measured in the spectral bands. This vector representation permits the application of linear and nonlinear transformations with linear algebra to find an alternative representation of the data. More generally, HSI is multi-dimensional in nature and the vector representation may lose the contextual correlations. Tensor representation provides a more sophisticated modeling technique and a higher-order generalization to linear subspace analysis. In graph theory, data points can be generalized as nodes with connectivities measured from the proximity of a local neighborhood. The graph-based framework efficiently characterizes the relationships among the data and allows for convenient mathematical manipulation in many applications, such as data clustering, feature extraction, feature selection and data alignment. In this thesis, graph-based approaches applied in the field of multi-source feature and data fusion in remote sensing area are explored. We will mainly investigate the fusion of spatial, spectral and LiDAR information with linear and multilinear algebra under graph-based framework for data clustering and classification problems