Signal Modeling for Two-Dimensional Image Structures and Scale-Space Based Image Analysis

Model based image representation plays an important role in many computer vision tasks. Consequently, it is of high significance to model image structures with more powerful representation capabilities. In the literature, there exist bulk of researches for intensity based modeling. However, most of them suffer from the illumination variation. On the other hand, phase information, which carries most essential structural information of the original signal, has the advantage of being invariant to the brightness change. Therefore, phase based image analysis is advantageous when compared to purely intensity based approaches. This thesis aims to propose novel image representations for 2D image structures, from which useful local features can be extracted, which are useful for phase based image analysis. The first approach presents a 2D rotationally invariant quadrature filter. This model is able to handle superimposed intrinsically two-dimensional (i2D) patterns with flexible angles of intersection. Hence, it can be regarded as an extension of the structure multivector. The second approach is the monogenic curvature tensor. Coupling methods of differential geometry, tensor algebra, monogenic signal and quadrature filter, we can design a general model for 2D structures as the monogenic extension of a curvature tensor. Based on it, local representations for the intrinsically one-dimensional (i1D) and i2D structures are derived as the monogenic signal and the generalized monogenic curvature signal, respectively. From them, independent features of local amplitude, phase and orientation are simultaneously extracted. Besides, a generalized monogenic curvature scale-space can be built by applying a Poisson kernel to the monogenic curvature tensor. Compared with other related work, the remarkable advantage of our approach lies in the rotationally invariant phase evaluation of 2D structures in a multi-scale framework, which delivers access to phase-based processing in many computer vision tasks. To demonstrate the efficiency and power of the theoretic framework, some computer vision applications are presented, which include the phase based image reconstruction, detecting i2D image structures using local phase and monogenic curvature tensor for optical flow estimation

Breast Cancer: Modelling and Detection

This paper reviews a number of the mathematical models used in cancer modelling and then chooses a specific cancer, breast carcinoma, to illustrate how the modelling can be used in aiding detection. We then discuss mathematical models that underpin mammographic image analysis, which complements models of tumour growth and facilitates diagnosis and treatment of cancer. Mammographic images are notoriously difficult to interpret, and we give an overview of the primary image enhancement technologies that have been introduced, before focusing on a more detailed description of some of our own recent work on the use of physics-based modelling in mammography. This theoretical approach to image analysis yields a wealth of information that could be incorporated into the mathematical models, and we conclude by describing how current mathematical models might be enhanced by use of this information, and how these models in turn will help to meet some of the major challenges in cancer detection

Detection of dark galaxies and circum-galactic filaments fluorescently illuminated by a quasar at z=2.4

A deep narrow-band survey for Ly-alpha emission carried out on the VLT-FORS2 has revealed 98 Ly-alpha candidates down to a flux limit of 4.e-18 erg/s/cm^2 in a volume of 5500 comoving Mpc^3 at z=2.4 centered on the hyperluminous quasar HE0109-3518. The properties of the detected sources in terms of their i) equivalent width distribution, ii) luminosity function, and iii) the average luminosity versus projected distance from the quasar, all suggest that a large fraction of these objects have been fluorescently "illuminated" by HE0109-3518. This conclusion is supported by comparison with detailed radiative transfer simulations of the effects of the quasar illumination. 18 objects have a rest-frame Equivalent Width (EW0) larger than 240A, the expected limit for Ly-alpha emission powered by Population II star formation and 12 sources among these do not have any continuum counterpart in a deep V-band imaging of the same field. For these, a stacking analysis indicates EW0>800A, effectively ruling out Ly-alpha powered by internal star formation. These sources are thus the best candidates so far for proto-galactic clouds or "dark" galaxies at high-redshift, whose existence has recently been suggested by several theoretical studies. Assuming they are mostly ionized by the quasar radiation, we estimate that their gas masses would be about 10^9 Msun implying that their star formation efficiencies (SFE) are less than 1.e-11 yr^-1 several times below the SFE of the most gas-rich dwarf galaxies locally, and five hundred times lower than typical massive star-forming galaxies at z~2. We have also discovered extended, filamentary gas, also likely illuminated by the quasar, around some of the brightest continuum-detected sources with EW0>240A. This emission is compatible with the expectations for circum-galactic cold streams but other origins, including tidal stripping, are also possible.Comment: 26 pages, 16 figures; MNRAS in press (accepted 2012 Jun 15); minor changes from previous version, typos corrected, references adde

A review of some recent developments in polarization-sensitive optical imaging techniques for the study of articular cartilage

This article reviews recent developments in the optical imaging of articular cartilage using polarized-light methods, with an emphasis on tools that could be of use in tissue engineering approaches to treatment. Both second-harmonic generation microscopy and polarization-sensitive optical coherence tomography are described and their potential role in the treatment of cartilage disorders such as osteoarthritis is suggested. Key results are reviewed and future developments are discussed

Background-deflection Brillouin microscopy reveals altered biomechanics of intracellular stress granules by ALS protein FUS

Altered cellular biomechanics have been implicated as key photogenic triggers in age-related diseases. An aberrant liquid-to-solid phase transition, observed in in vitro reconstituted droplets of FUS protein, has been recently proposed as a possible pathogenic mechanism for amyotrophic lateral sclerosis (ALS). Whether such transition occurs in cell environments is currently unknown as a consequence of the limited measuring capability of the existing techniques, which are invasive or lack of subcellular resolution. Here we developed a non-contact and label-free imaging method, named background-deflection Brillouin microscopy, to investigate the three-dimensional intracellular biomechanics at a sub-micron resolution. Our method exploits diffraction to achieve an unprecedented 10,000-fold enhancement in the spectral contrast of single-stage spectrometers, enabling, to the best of our knowledge, the first direct biomechanical analysis on intracellular stress granules containing ALS mutant FUS protein in fixed cells. Our findings provide fundamental insights on the critical aggregation step underlying the neurodegenerative ALS disease