Formal description, compression and transformation of digital pictures II. Picture algebra and geometry

In an earlier paper (Part I) we described the construction of Hermite code for multiple grey-level pictures using the concepts of vector spaces over Galois Fields. In this paper a new algebra is worked out for Hermite codes to devise algorithms for various transformations such as translation, reflection, rotation, expansion and replication of the original picture. Also other operations such as concatenation, complementation, superposition, Jordan-sum and selective segmentation are considered. It is shown that the Hermite code of a picture is very powerful and serves as a mathematical signature of the picture. The Hermite code will have extensive applications in picture processing, pattern recognition and artificial intelligence.

Formal description, compression and transformation of digital pictures

This paper describes the application of vector spaces over Galois fields, for obtaining a formal description of a picture in the form of a very compact, non-redundant, unique syntactic code. Two different methods of encoding are described. Both these methods consist in identifying the given picture as a matrix (called picture matrix) over a finite field. In the first method, the eigenvalues and eigenvectors of this matrix are obtained. The eigenvector expansion theorem is then used to reconstruct the original matrix. If several of the eigenvalues happen to be zero this scheme results in a considerable compression. In the second method, the picture matrix is reduced to a primitive diagonal form (Hermite canonical form) by elementary row and column transformations. These sequences of elementary transformations constitute a unique and unambiguous syntactic code-called Hermite code—for reconstructing the picture from the primitive diagonal matrix. A good compression of the picture results, if the rank of the matrix is considerably lower than its order. An important aspect of this code is that it preserves the neighbourhood relations in the picture and the primitive remains invariant under translation, rotation, reflection, enlargement and replication. It is also possible to derive the codes for these transformed pictures from the Hermite code of the original picture by simple algebraic manipulation. This code will find extensive applications in picture compression, storage, retrieval, transmission and in designing pattern recognition and artificial intelligence systems.

MRT Letter: Light Sheet Based Imaging Flow Cytometry on a Microfluidic Platform

We propose a light sheet based imaging flow cytometry technique for simultaneous counting and imaging of cells on a microfluidic platform. Light sheet covers the entire microfluidic channel and thus omits the necessity of flow focusing and point scanning based technology. Another advantage lies in the orthogonal detection geometry that totally cuts-off the incident light, thereby substantially reducing the background in the detection. Compared to the existing state-of-art techniques the proposed technique shows marked improvement. Using fluorescently-coated Saccharomyces cerevisiae cells we have recorded cell counting with throughput as high as 2,090 cells/min in the low flow rate regime and were able to image the individual cells on-the-go. Overall, the proposed system is cost-effective and simple in channel geometry with the advantage of efficient counting in operational regime of low laminar flow. This technique may advance the emerging field of microfluidic based cytometry for applications in nanomedicine and point of care diagnostics. Microsc. Res. Tech. 76:1101-1107, 2013. (c) 2013 Wiley Periodicals, Inc.

MRT Letter: Experimental Verification of Vectorial Theory to Determine Field at the Geometrical Focus of a Cylindrical Lens

We provide experimental evidence supporting the vectorial theory for determining electric field at and near the geometrical focus of a cylindrical lens. This theory provides precise distribution of field and its polarization effects. Experimental results show a close match (approximate to 95% using (2)-test) with the simulation results (obtained using vectorial theory). Light-sheet generated both at low and high NA cylindrical lens shows the importance of vectorial theory for further development of light-sheet techniques. Potential applications are in planar imaging systems (such as, SPIM, IML-SPIM, imaging cytometry) and spectroscopy. Microsc. Res. Tech. 77:105-109, 2014. (c) 2014 Wiley Periodicals, Inc.

MRT Letter: Two-Photon Excitation-Based 2pi Light-Sheet System for Nano-Lithography

We propose two-photon excitation-based light-sheet technique for nano-lithography. The system consists of 2 -configured cylindrical lens system with a common geometrical focus. Upon superposition, the phase-matched counter-propagating light-sheets result in the generation of identical and equi spaced nano-bump pattern. Study shows a feature size of as small as few tens of nanometers with a inter-bump distance of few hundred nanometers. This technique overcomes some of the limitations of existing nano-lithography techniques, thereby, may pave the way for mass-production of nano-structures. Potential applications can also be found in optical microscopy, plasmonics, and nano-electronics. Microsc. Res. Tech. 78:1-7, 2015. (c) 2014 Wiley Periodicals, Inc.

MRT Letter: A Unified Accelerated Maximum Likelihood Technique for Widefield, Confocal, and Super-Resolution 4Pi Microscopy

We propose an algorithmic technique for accelerating maximum likelihood (ML) algorithm for image reconstruction in fluorescence microscopy. This is made possible by integrating Biggs-Andrews (BA) method with ML approach. The results on widefield, confocal, and super-resolution 4Pi microscopy reveal substantial improvement in the speed of 3D image reconstruction (the number of iterations has reduced by approximately one-half). Moreover, the quality of reconstruction obtained using accelerated ML closely resembles with nonaccelerated ML method. The proposed technique is a step closer to realize real-time reconstruction in 3D fluorescence microscopy. Microsc. Res. Tech. 78:331-335, 2015. (c) 2015 Wiley Periodicals, Inc.