Papers by Dimiter Prodanov
Cybernetics and Information Technologies, 2015
Image segmentation methods can be classified broadly into two classes: intensity-based and geomet... more Image segmentation methods can be classified broadly into two classes: intensity-based and geometry-based. Edge detection is the base of many geometry-based segmentation approaches. Scale space theory represents a systematic treatment of the issues of spatially uncorrelated noise with its main application being the detection of edges, using multiple resolution scales, which can be used for subsequent segmentation, classification or encoding. The present paper will give an overview of some recent applications of scale spaces into problems of microscopic image analysis. Particular overviews will be given to Gaussian and alpha-scale spaces. Some applications in the analysis of biomedical images will be presented. The implementation of filters will be demonstrated.
Lab on a chip, Jan 21, 2015
A compelling clinical need exists for inexpensive, portable haematology analyzers that can be uti... more A compelling clinical need exists for inexpensive, portable haematology analyzers that can be utilized at the point-of-care in emergency settings or in resource-limited settings. Development of a label-free, microfluidic blood analysis platform is the first step towards such a miniaturized, cost-effective system. Here we assemble a compact lens-free in-line holographic microscope and employ it to image blood cells flowing in a microfluidic chip, using a high-speed camera and stroboscopic illumination. Numerical reconstruction of the captured holograms allows classification of unlabeled leukocytes into three main subtypes: lymphocytes, monocytes and granulocytes. A scale-space recognition analysis to evaluate cellular size and internal complexity is also developed and used to build a 3-part leukocyte differential. The lens-free image-based classification is compared to the 3-part white blood cell differential generated by using a conventional analyzer on the same blood sample and is ...
Frontiers in Neuroinformatics, 2011
Image acquisition, processing, and quantification of objects (morphometry) require the integratio... more Image acquisition, processing, and quantification of objects (morphometry) require the integration of data inputs and outputs originating from heterogeneous sources. Management of the data exchange along this workflow in a systematic manner poses several challenges, notably the description of the heterogeneous meta-data and the interoperability between the software used. The use of integrated software solutions for morphometry and management of imaging data in combination with ontologies can reduce meta-data loss and greatly facilitate subsequent data analysis. This paper presents an integrated information system, called LabIS. The system has the objectives to automate (i) the process of storage, annotation, and querying of image measurements and (ii) to provide means for data sharing with third party applications consuming measurement data using open standard communication protocols. LabIS implements 3-tier architecture with a relational database back-end and an application logic middle tier realizing web-based user interface for reporting and annotation and a web-service communication layer.The image processing and morphometry functionality is backed by interoperability with ImageJ, a public domain image processing software, via integrated clients. Instrumental for the latter feat was the construction of a data ontology representing the common measurement data model. LabIS supports user profiling and can store arbitrary types of measurements, regions of interest, calibrations, and ImageJ settings. Interpretation of the stored measurements is facilitated by atlas mapping and ontology-based markup. The system can be used as an experimental workflow management tool allowing for description and reporting of the performed experiments. LabIS can be also used as a measurements repository that can be transparently accessed by computational environments, such as Matlab. Finally, the system can be used as a data sharing tool.
The brainstar project: Towards a miniaturized microsystem for wireless brain stimulation and recording in rodents
Chaos, Solitons & Fractals, 2021
The present work demonstrates the connections between the Burgers, diffusion, and Schrödinger's e... more The present work demonstrates the connections between the Burgers, diffusion, and Schrödinger's equations. The starting point is a formulation of the stochastic mechanics, which is modelled along the lines of the scale relativity theory. The resulting statistical description obeys the Fokker-Planck equation. This paper further demonstrates the connection between the two approaches, embodied by the study of the Burgers equation, which from this perspective appears as a stochastic geodesic equation. The main result of the article is the transparent derivation of the Born rule from the starting point of a complex stochastic process, based on a complex Fokker-Planck formalism.
arXiv: Tissues and Organs, 2015
Implantation of neuroprosthetic electrodes induces a stereotypical state of neuroinflammation, wh... more Implantation of neuroprosthetic electrodes induces a stereotypical state of neuroinflammation, which is thought to be detrimental for the neurons surrounding the electrode. Mechanisms of this type of neuroinflammation are still not understood well. Recent experimental and theoretical results point out possible role of the diffusion species in this process. The paper considers a model of anomalous diffusion occurring in the glial scar around a chronic implant in two simple geometries -- a separable rectilinear electrode and a cylindrical electrode, which are solvable exactly. We describe a hypothetical extended source of diffusing species and study its concentration profile in steady-state conditions. Diffusion transport is assumed to obey a fractional-order Fick law, which is derived from physically realistic assumptions using a fractional calculus approach. The derived fractional-order distribution morphs into regular order diffusion in the case of integer fractional exponents. The...
3D-map of the motor end-plate regions in the rat gastrocnemic muscle as an aid for localized application of retrograde tracers
Distribution of the motor nerve fibers in the ventral lumbosacral roots: significance for functional electrical stimulation
Chaos, Solitons & Fractals, 2017
Hölder functions represent mathematical models of nonlinear physical phenomena. This work investi... more Hölder functions represent mathematical models of nonlinear physical phenomena. This work investigates the general conditions of existence of fractional velocity as a localized generalization of ordinary derivative with regard to the exponent order. Fractional velocity is defined as the limit of the difference quotient of the function's increment and the difference of its argument raised to a fractional power. A relationship to the point-wise Hölder exponent of a function, its point-wise oscillation and the existence of fractional velocity is established. It is demonstrated that wherever the fractional velocity of non-integral order is continuous then it vanishes. The work further demonstrates the use of fractional velocity as a tool for characterization of the discontinuity set of the derivatives of functions thus providing a natural characterization of strongly non-linear local behavior. A link to fractional Taylor expansions using Caputo derivatives is demonstrated.
PLoS ONE, 2013
The establishment of neuronal connectivity depends on the correct initial polarization of the you... more The establishment of neuronal connectivity depends on the correct initial polarization of the young neurons. In vivo, developing neurons sense a multitude of inputs and a great number of molecules are described that affect their outgrowth. In vitro, many studies have shown the possibility to influence neuronal morphology and growth by biophysical, i.e. topographic, signaling. In this work we have taken this approach one step further and investigated the impact of substrate topography in the very early differentiation stages of developing neurons, i.e. when the cell is still at the round stage and when the first neurite is forming. For this purpose we fabricated micron sized pillar structures with highly reproducible feature sizes, and analyzed neurons on the interface of flat and topographic surfaces. We found that topographic signaling was able to attract the polarization markers of mouse embryonic neurons-N-cadherin, Golgi-centrosome complex and the first bud were oriented towards topographic stimuli. Consecutively, the axon was also preferentially extending along the pillars. These events seemed to occur regardless of pillar dimensions in the range we examined. However, we found differences in neurite length that depended on pillar dimensions. This study is one of the first to describe in detail the very early response of hippocampal neurons to topographic stimuli.
New Developments in Biomedical Engineering, 2010
Preprints, Jul 5, 2021
Image segmentation and classification still represent an active area of research since no univers... more Image segmentation and classification still represent an active area of research since no universal solution can be identified. Established segmentation algorithms like thresholding are problem specific, treat well the easy cases and mostly relied on single parameter i.e intensity. Machine learning approaches offer alternatives where predefined features are combined into different classifiers. On the other hand, the outcome of machine learning is only as good as the underlying feature space. Differential geometry can substantially improve the outcome of machine learning since it can enrich the underlying feature space with new geometrical objects, called invariants. In this way, the geometrical features form a high-dimensional feature space for each pixel, where original objects can be resolved. Alternatives based on the geometry of the image scale-invariant interest points have been exploited successfully in the field of computer vision. Here, we integrate geometrical feature extraction based on signal processing, machine learning and input relying on domain knowledge. The approach is exemplified on the ISBI 2012 image segmentation challenge data set. As a second application we demonstrate powerful image classification functionality based on the same principles, which was applied to the HeLa and HEp-2 data sets. Obtained results demonstrate that feature space enrichment properly balanced with feature selection functionality can achieve performance comparable to deep learning approaches.
incfbelgiannode/ACTIVESEGMENTATION: Special issue
Active Segmentation platform v 1.2.1. This is a reference release for the Neuroinformatics specia... more Active Segmentation platform v 1.2.1. This is a reference release for the Neuroinformatics special issue in Brain Sciences.
arXiv: Classical Analysis and ODEs, 2016
H\"older functions represent mathematical models of nonlinear physical phenomena. This work ... more H\"older functions represent mathematical models of nonlinear physical phenomena. This work investigates the general conditions of existence of fractional velocity as a localized generalization of ordinary derivative with regard to the exponent order. Fractional velocity is defined as the limit of the difference quotient of the function's increment and the difference of its argument raised to a fractional power. A relationship to the point-wise H\"older exponent of a function, its point-wise oscillation and the existence of fractional velocity is established. It is demonstrated that wherever the fractional velocity of non-integral order is continuous then it vanishes. The work further demonstrates the use of fractional velocity as a tool for characterization of the discontinuity set of the derivatives of functions thus providing a natural characterization of strongly non-linear local behavior. Finally the equivalence with the Kolwankar-Gangal local fractional derivativ...
Quantification of local and regional orientation of outgrowing neurites
arXiv: Rings and Algebras, 2019
Clifford algebras are an active area of mathematical research. The main objective of the paper is... more Clifford algebras are an active area of mathematical research. The main objective of the paper is to exhibit a construction of a matrix algebra isomorphic to a Clifford algebra of signature (p,q), which can be automatically implemented using general purpose linear algebra software. While this is not the most economical way of implementation for lower-dimensional algebras it offers a transparent mechanism of translation between a Clifford algebra and its isomorphic faithful real matrix representation. Examples of lower dimensional Clifford algebras are presented.
Many physical phenomena give rise to mathematical models in terms of fractal, non-differentiable ... more Many physical phenomena give rise to mathematical models in terms of fractal, non-differentiable functions. The paper introduces a broad generalization of the derivative in terms of the maximal modulus of continuity of the primitive function. These derivatives are called indicial derivatives. As an application, the indicial derivatives are used to characterize the nowhere monotonous functions. Furthermore, the non-differentiability set of such derivatives is proven to be of measure zero. As a second application, the indicial derivative is used in the proof of the Lebesgue differentiation theorem. Finally, the connection with the fractional velocities is demonstrated.
arXiv: Classical Analysis and ODEs, 2015
Holderian functions have strong non-linearities, which result in singularities in the derivatives... more Holderian functions have strong non-linearities, which result in singularities in the derivatives. This manuscript presents several fractional-order Taylor expansions of H\"olderian functions around points of non- differentiability. These expansions are derived using the concept of a fractional velocity, which can be used to describe the singular behavior of derivatives and non-differentiable functions. Fractional velocity is defined as the limit of the difference quotient of the increment of a function and the difference of its argument raised to a fractional power. Fractional velocity can be used to regularize ordinary derivatives. To this end, it is possible to define regularized Taylor series and compound differential rules. In particular a compound differential rule for Holder 1/2 functions is demonstrated. The expansion is presented using the auxiliary concept of fractional co-variation of functions.
The chapter introduces multiscale methods for image analysis and their applications to segmentati... more The chapter introduces multiscale methods for image analysis and their applications to segmentation of microscopic images. Specifically, it presents mathematical morphology and linear scale-space theories as overarching signal processing frameworks without excessive mathematical formalization. The chapter introduces several differential invariants, which are computed from parametrized Gaussian kernels and their derivatives. The main application of this approach is to build a multidimensional multiscale feature space, which can be subsequently used to learn characteristic fingerprints of the objects of interests. More specialized applications, such as anisotropic diffusion and detection of blob-like and fiber-like structures, are introduced for two-dimensional images, and extensions to three-dimensional images are discussed. Presented approaches are generic and thus have broad applicability to time-varying signals and to twoand three-dimensional signals, such as microscopic images. T...
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Papers by Dimiter Prodanov