Comparative Study on Thresholding

Criterion based thresholding algorithms are simple and effective for two-level thresholding. However, if a multilevel thresholding is needed, the computational complexity will exponentially increase and the performance may become unreliable. In this approach, a novel and more effective method is used for multilevel thresholding by taking hierarchical cluster organization into account. Developing a dendogram of gray levels in the histogram of an image, based on the similarity measure which involves the inter-class variance of the clusters to be merged and the intra-class variance of the new merged cluster . The bottom-up generation of clusters employing a dendogram by the proposed method yields good separation of the clusters and obtains a robust estimate of the threshold. Such cluster organization will yield a clear separation between object and background even for the case of nearly unimodal or multimodal histogram. Since the hierarchical clustering method performs an iterative merging operation, it is extended to multilevel thresholding problem by eliminating grouping of clusters when the pixel values are obtained from the expected numbers of clusters. This paper gives a comparison on Otsu’s & Kwon’s criterion with hierarchical based multi-level thresholding

Gauge-optimal approximate learning for small data classification problems

Small data learning problems are characterized by a significant discrepancy between the limited amount of response variable observations and the large feature space dimension. In this setting, the common learning tools struggle to identify the features important for the classification task from those that bear no relevant information, and cannot derive an appropriate learning rule which allows to discriminate between different classes. As a potential solution to this problem, here we exploit the idea of reducing and rotating the feature space in a lower-dimensional gauge and propose the Gauge-Optimal Approximate Learning (GOAL) algorithm, which provides an analytically tractable joint solution to the dimension reduction, feature segmentation and classification problems for small data learning problems. We prove that the optimal solution of the GOAL algorithm consists in piecewise-linear functions in the Euclidean space, and that it can be approximated through a monotonically convergent algorithm which presents -- under the assumption of a discrete segmentation of the feature space -- a closed-form solution for each optimization substep and an overall linear iteration cost scaling. The GOAL algorithm has been compared to other state-of-the-art machine learning (ML) tools on both synthetic data and challenging real-world applications from climate science and bioinformatics (i.e., prediction of the El Nino Southern Oscillation and inference of epigenetically-induced gene-activity networks from limited experimental data). The experimental results show that the proposed algorithm outperforms the reported best competitors for these problems both in learning performance and computational cost.Comment: 47 pages, 4 figure

Motion Segmentation Aided Super Resolution Image Reconstruction

This dissertation addresses Super Resolution (SR) Image Reconstruction focusing on motion segmentation. The main thrust is Information Complexity guided Gaussian Mixture Models (GMMs) for Statistical Background Modeling. In the process of developing our framework we also focus on two other topics; motion trajectories estimation toward global and local scene change detections and image reconstruction to have high resolution (HR) representations of the moving regions. Such a framework is used for dynamic scene understanding and recognition of individuals and threats with the help of the image sequences recorded with either stationary or non-stationary camera systems. We introduce a new technique called Information Complexity guided Statistical Background Modeling. Thus, we successfully employ GMMs, which are optimal with respect to information complexity criteria. Moving objects are segmented out through background subtraction which utilizes the computed background model. This technique produces superior results to competing background modeling strategies. The state-of-the-art SR Image Reconstruction studies combine the information from a set of unremarkably different low resolution (LR) images of static scene to construct an HR representation. The crucial challenge not handled in these studies is accumulating the corresponding information from highly displaced moving objects. In this aspect, a framework of SR Image Reconstruction of the moving objects with such high level of displacements is developed. Our assumption is that LR images are different from each other due to local motion of the objects and the global motion of the scene imposed by non-stationary imaging system. Contrary to traditional SR approaches, we employed several steps. These steps are; the suppression of the global motion, motion segmentation accompanied by background subtraction to extract moving objects, suppression of the local motion of the segmented out regions, and super-resolving accumulated information coming from moving objects rather than the whole scene. This results in a reliable offline SR Image Reconstruction tool which handles several types of dynamic scene changes, compensates the impacts of camera systems, and provides data redundancy through removing the background. The framework proved to be superior to the state-of-the-art algorithms which put no significant effort toward dynamic scene representation of non-stationary camera systems

Analytical Imaging for Complex Materials

Systems known as complex materials have key attributes that contribute to their designation as "complex''. For example, evolving dynamical properties add complexity, as is observed in supercooled liquids. Polymers and proteins are structurally complex as they can fold in different conformations, with these different conformations affecting different biological functions or physical properties. Complex materials generally have interesting macroscopic properties that are difficult to predict from their microscopic (molecular) constituents. The connection between microscopic features and macroscopic properties in these materials has been a subject of study for decades, yet the ability to wield strong predictive power in these materials remains elusive. Imaging can provide information in both space and time necessary to understand how the microscopic details in these materials yield the observed macroscopic properties. Moreover, time-sequenced imaging allows one to understand how these properties might evolve. To image these details however, requires high resolution in both time and space. Unfortunately, obtaining images and extracting information from these images becomes quite difficult as the length scales of interest become small, especially when signal-to-background ratios are low. My dissertation work addresses the challenge of extracting such information by developing quantitative methods to circumvent obstacles related to obfuscation from low signal as well as the diffraction limit, with high-throughput and high-resolution. I apply these techniques towards the study of the following complex materials via imaging: (1) single molecules rotating in a supercooled liquid (2) conjugated polymers containing multiple emitters within the diffraction limit (3) solvent vapor annealing mediated conjugated polymer aggregation and (4) collagen gels during their formation and perturbation. The first chapter describes how the local dynamics in a supercooled liquid may be assessed by the rotations of single-molecule probes. To resolve rotations however, requires splitting the fluorescence signal from single-molecules into orthogonal polarizations thereby reducing the already low signal-to-background ratio (SBR) expected from single-molecule experiments. The data is further complicated by instances of photoblinking and out-of-plane rotation, when only background signal is present. A convenient method for excluding background signal was developed via a Monte Carlo simulation for discriminating points in the trajectory composed only of background signal that is robust to SBR. These simulations also showed an SBR dependance for the accuracy of the values extracted from rotational autocorrelation functions. This method was used experimentally to directly demonstrate ergodicity in supercooled liquids. The next chapter focuses on conjugated polymers, which display a complex relationship between chain conformation and photophysics. This conformational complexity exists even at the single-chain level, obscuring the understanding of how excitons behave in the bulk, such as in a device. Understanding this relationship however, is difficult as conformation and photophysics are hard to access in operando not only because a single conjugated polymer chain is smaller than the diffraction limit, but also because a fluorescing conjugated polymer emits light from many locations. The overall conformation is typically assessed using polarization modulation measurements, which only provide mesoscale information about a chain's conformation. A super-resolution method was developed to map the distribution of emitters and trace out single-chain conformation. The extracted radii of gyration for these single-chains matched well with polymer theory. Chapter three describes the development of experimental and image analytical tools to bridge single-chain studies of photophysics in conjugated polymer, to the photophysics that might be observed in a conjugated polymer device where chain-chain contacts and high levels of local ordering may be present. It has been shown previously that solvent vapor annealing can be used to prepare conjugated polymer aggregates of various levels of internal ordering. However, solvent vapor annealing is a process that is difficult to control and difficult to evaluate. Therefore, a first-of-its-kind apparatus was constructed that can generate and deliver solvent vapor in a controlled fashion to swell polymer films while monitoring both film dynamics by fluorescence imaging as well as swelling extent via a quartz crystal microbalance. Fluorescent images acquired during aggregation showed heterogeneous diffusion among aggregates, possibly indicating heterogeneous sizing. Fluorescent characterization of presumably differently sized aggregates indicates a possible emergent quenching phenomenon in a bulk conjugated polymer material. The final chapter of this dissertation describes an effort to characterize dynamics in collagen gels. Collagen gels form through a complex sol-gel process precipitated by nucleation and growth fibrillogenesis. To probe the long length scales of interest here, single-molecule methods were not practical. Instead, an optical flow algorithm was explored to detect key physical events in the evolving system. One effort aims to characterize the dynamics of the early gelation process. In particular, the optical flow measurements provide a high-resolution measure for the moment at which the sol-gel transition occurs. Another application involves the use of optical flow to observe distortions in the collagen network while it is undergoing strain stiffening. Preliminary studies show that at critical strain, local breaks in the gel propagate throughout the gel until the gel completely loses its ability to sustain stress. In general, the ability to quantify details about complex materials from imaging data can be quite a complex endeavor itself, requiring awareness of the physical phenomena of interest, how said phenomena manifests optically, and the use and development of appropriate algorithms. As described in this dissertation, the proper use and/or development of the proper image analysis methods allow for extraction of key information from dense data

Integrative approaches in fragment-based drug discovery

This thesis combines experimental and computational methods to investigate aspects of fragment identification and elaboration in fragment-based ligand design, a promising approach for identifying small molecule drugs, to target the pharmacologically relevant bromodomain PHIP(2). The research covers various aspects of the process, from initial crystallographic fragment screening to validation of follow-up compounds. Chapters 1 and 2 provide an overview of relevant perspectives and methodologies in fragment-based drug discovery. Chapter 3 reports a crystallographic fragment screening against PHIP(2), resolving 47 fragments at the acetylated-lysine binding site, and evaluates the abilities of crowdsourced computational methods to replicate fragment binding and crystallographic poses. This chapter highlights the challenges associated with using computational methods for reproducing crystallographic fragment screening results with submissions performing relatively weakly. Chapter 4 demonstrates the advantages of X-ray crystallographic screening of crude reaction mixtures generated robotically, showcasing reduced time, solvent, and hardware requirements. Soaking crude reaction mixtures maintains crystal integrity which led to the identification of 22 binders, 3 with an alternate pose caused by a single methyl addition to the core fragment and 1 hit in assays. It demonstrates how affordable methods can generate large amounts of crystallographic data of fragment elaborations. Chapter 5 develops an algorithmic approach to extract features associated with crystallographic binding, deriving simple binding scores using data from Chapter 4. The method identifies 26 false negatives with binding scores enriching binders over non-binders. Employing these scores prospectively in a virtual screening demonstrated how binding features can be exploited to select further follow-up compounds leading to low micromolar potencies. Chapter 6 attempts to integrate more computationally intensive methods to identify fragment follow-up compounds with increased potency through virtual screening enhanced with free energy calculations. Only two out of six synthesised follow-up compounds showed weak binding in assays, and none were resolved in crystal structures. This thesis tackles critical challenges in follow-up design, synthesis, and dataset analysis, underlining the limitations of existing methods in advancing fragment-based drug discovery. It emphasises the necessity of integrative approaches for an optimised “design, make, test” cycle in fragment-based drug discovery

Essays on the nonlinear and nonstochastic nature of stock market data

The nature and structure of stock-market price dynamics is an area of ongoing and rigourous scientific debate. For almost three decades, most emphasis has been given on upholding the concepts of Market Efficiency and rational investment behaviour. Such an approach has favoured the development of numerous linear and nonlinear models mainly of stochastic foundations. Advances in mathematics have shown that nonlinear deterministic processes i.e. "chaos" can produce sequences that appear random to linear statistical techniques. Till recently, investment finance has been a science based on linearity and stochasticity. Hence it is important that studies of Market Efficiency include investigations of chaotic determinism and power laws. As far as chaos is concerned, there are rather mixed or inconclusive research results, prone with controversy. This inconclusiveness is attributed to two things: the nature of stock market time series, which are highly volatile and contaminated with a substantial amount of noise of largely unknown structure, and the lack of appropriate robust statistical testing procedures. In order to overcome such difficulties, within this thesis it is shown empirically and for the first time how one can combine novel techniques from recent chaotic and signal analysis literature, under a univariate time series analysis framework. Three basic methodologies are investigated: Recurrence analysis, Surrogate Data and Wavelet transforms. Recurrence Analysis is used to reveal qualitative and quantitative evidence of nonlinearity and nonstochasticity for a number of stock markets. It is then demonstrated how Surrogate Data, under a statistical hypothesis testing framework, can be simulated to provide similar evidence. Finally, it is shown how wavelet transforms can be applied in order to reveal various salient features of the market data and provide a platform for nonparametric regression and denoising. The results indicate that without the invocation of any parametric model-based assumptions, one can easily deduce that there is more to linearity and stochastic randomness in the data. Moreover, substantial evidence of recurrent patterns and aperiodicities is discovered which can be attributed to chaotic dynamics. These results are therefore very consistent with existing research indicating some types of nonlinear dependence in financial data. Concluding, the value of this thesis lies in its contribution to the overall evidence on Market Efficiency and chaotic determinism in financial markets. The main implication here is that the theory of equilibrium pricing in financial markets may need reconsideration in order to accommodate for the structures revealed