Todor Georgiev

Adobe · Emerging Products Group

John's differential equation and its canonical form, the ultrahyperbolic equation, plays important role in lightfield imaging. The equation describes a local constraint on the lightfield, that was first observed as a "dimensionality gap" in the frequency representation. Related to the ultrahyperbolic equation, Asgeirsson's theorems describe global...

This paper explores possibilities for new uses of the Radon transform for imaging and analysis of lightfields. We show that the previously reported Dimansionality Gap can be derived from an ultrahyperbolic PDE, first proposed by F. John, which is satisfied by lightfields. Based on inverse John transform we demonstrate rigorous Focal Stack rendering...

Accurate measurement of image-sensor frequency response over a wide range of spatial frequencies is very important for analyzing pixel array characteristics, such as modulation transfer function (MTF), crosstalk, and active pixel shape. Such analysis is especially significant in computational photography for the purposes of deconvolution, multi-ima...

The plenoptic function was originally defined as a complete record of the 3D structure of radiance in a scene and its dependence on a number of different parameters including position, angle, wavelength, polarization, etc. Recently-developed plenoptic cameras typically capture only the geometric aspects of the plenoptic function. Using this informa...

We introduce a novel plenoptic function that can be directly captured or generated after the fact in plenoptic cameras. Whereas previous approaches represent the plenoptic function over a 4D ray space (as radiance or light field), we introduce the representation of the plenoptic function over a 3D plane space. Our approach uses the Radon plenoptic...

To resolve the low resolution problem of Plenoptic cameras we analyze optical signal sampling at frequencies above Nyquist. The resultant aliased signal is superresolved interleaving the array of microimages, thus cancelling the aliasing components. The rendered image can reach full sensor resolution.

Methods, apparatus, and computer-readable storage media for rendering focused plenoptic camera data. A depth-based rendering technique is described that estimates depth at each microimage and then applies that depth to determine a position in the input flat from which to read a value to be assigned to a given point in the output image. The techniqu...

Methods, apparatus, and computer-readable storage media for calibrating focused plenoptic camera data. A calibration technique that does not modify the image data may be applied to raw plenoptic images. Calibration parameters, including but not limited to tilt angle, corner crops, main lens distance from the microlens array, sensor distance from th...

Various methods and apparatus for removing artifacts in frequency domain processing of light-field images are described. Methods for the reduction or removal of the artifacts are described that include methods that may be applied during frequency domain processing and a method that may be applied during post-processing of resultant angular views. T...

Method and apparatus for radiance processing by demultiplexing in the frequency domain. A frequency domain demultiplexing module obtains a radiance image captured with a lens-based radiance camera. The image includes optically mixed spatial and angular frequency components of light from a scene. The module performs frequency domain demultiplexing o...

A method and apparatus for the block-based compression of light-field images. Light-field images may be preprocessed by a preprocessing module into a format that is compatible with the blocking scheme of a block-based compression technique, for example JPEG. The compression technique is then used to compress the preprocessed light-field images. The...

The Lytro camera is the first implementation of a plenoptic camera for the consumer market. We consider it a successful example of the miniaturization aided by the increase in computational power characterizing mobile computational photography. The plenoptic camera approach to radiance capture uses a microlens array as an imaging system focused on...

Recent realizations of hand-held plenoptic cameras have given rise to previously unexplored effects in photography. Designing a mobile phone plenoptic camera is becoming feasible with the significant increase of computing power of mobile devices and the introduction of System on a Chip. However, capturing high numbers of views is still impractical...

A special section of the Journal of Electronic Imaging (JEI) will replace the conference proceedings for papers presented at the SPIE conference on Mobile Computational Photography (SPIE Conference 8667D). The papers will be published early in 2013 and can be viewed at http://electronicimaging.spiedigitallibrary.org, Vol. 22 (2013).

A plenoptic camera captures the 4D radiance about a scene. Recent practical solutions mount a microlens array on top of a commodity SLR to directly acquire these rays. However, they suffer from low resolution as hundreds of thousands of views need to be captured in a single shot. In this paper, we develop a simple but effective technique for improv...

The focused plenoptic camera is based on the Lippmann sensor: an array of microlenses focused on the pixels of a conventional image sensor. This device samples the radiance, or plenoptic function, as an array of cameras with large depth of field, focused at a certain plane in front of the microlenses. For the purpose of digital refocusing (which is...

Plenoptic cameras are intended to fully capture the light rays in a scene. Using this information, optical elements can be applied to a scene computationally rather than physically-allowing an infinite variety of pictures to be rendered after the fact from the same plenoptic data. Practical plenoptic cameras necessarily capture discrete samples of...

Processing and rendering of plenoptic camera data requires significant computational power and memory bandwidth. At the same time, real-time rendering performance is highly desirable so that users can interactively explore the infinite variety of images that can be rendered from a single plenoptic image. In this paper we describe a GPU-based approa...

We show that the plenoptic camera is optically equivalent to an array of cameras. We compute the parameters that establish that equivalence and show where the plenoptic camera is more useful than the camera array.

Edward Adelson and James Bergen defined the plenoptic function as a record of the 3D distribution of light rays and their dependence on parameters such as wavelength and polarization. Most research on these ideas has emphasized the 3D aspect of plenoptic-function capture and manipulation, paying less attention to other parameters. A new approach le...

Digital images from a CCD or CMOS sensor with a color filter array must undergo a demosaicing process to combine the separate color samples into a single color image. This interpolation process can interfere with the subsequent superresolution process. Plenoptic superresolution, which relies on precise sub-pixel sampling across captured microimages...

Depth estimation in focused plenoptic camera is a critical step for most applications of this technology and poses interesting challenges, as this estimation is content based. We present an iterative algorithm, content adaptive, that exploits the redundancy found in focused plenoptic camera captured images. Our algorithm determines for each point i...

Computational photography is based on capturing and processing discrete representations of all the light rays in the 3D space of a scene. Compared to conventional photography, which captures 2D images, computational photography captures the entire 4D 'lightfield', (the full 4D radiance). To multiplex the 4D radiance onto conventional 2D sensors, li...

Camera Technology has evolved tremendously in the last 10 years, the proliferation of camera-phones fueling unprecedented advancements on CMOS image sensors. As an emerging field, some of the problems are justified while others are bi-products of the chosen silicon technology and are not fundamental to advancement of image technology. This paper wi...

The focused plenoptic camera differs from the traditional plenoptic camera in that its microlenses are focused on the photographed object rather than at infinity. The spatio-angular tradeoffs available with this approach enable rendering of final images that have significantly higher resolution than those from traditional plenoptic cameras. Unfortu...

The plenoptic function was originally defined as a record of both the 3D structure of the lightfield and of its dependence on parameters such as wavelength, polarization, etc. Still, most work on these ideas has emphasized the 3D aspect of lightfield capture and manipulation, with less attention paid to other parameters. In this paper, we leverage...

Plenoptic cameras, constructed with internal microlens arrays, capture both spatial and angular information, i.e., the full 4-D radiance, of a scene. The design of traditional plenoptic cameras assumes that each microlens image is completely defocused with respect to the image created by the main camera lens. As a result, only a single pixel in the...

The Plenoptic camera, a digital realization of Lippmann's ¿Integral Photography¿ ideas, was introduced in 1992 by Adelson as an approach to solve computer vision problems. Recently, an improved version called Plenoptic 2.0 camera has been independently proposed by Ng, Fife, Lumsdaine, and others. The important part about it is the much higher spa...

This article deals with modelling of branched chained amino acids production. One of important branched chained amino acid is L-valine. The aim of the article is synthesis of dynamic unstructured model of fed-batch fermentation process with intensive droppings for L-valine production. The presented approach of the investigation includes the followi...

We demonstrate high dynamic range (HDR) imaging with the Plenoptic 2.0 camera. Multiple exposure capture is achieved with a single shot using microimages created by microlens array that has an interleaved set of different apertures.

We demonstrate working superresolution with Plenoptic 2.0 camera without need for traditional image registration in software. This paper describes our method, based only on the camera geometry and microlens parameters.

Derivation and analysis of sampling patterns of traditional and focused plenoptic cameras show the former rotates pixels p=2 in phase space, while the latter does not. These results are interpreted regarding the cameras' spatial resolution. A main practical consequence of the difference between the two plenoptic cameras is in the resolution of the...

The article presents a method for synthesis of sinusoidal oscillators based on the modified Van der Pol equation. The synthesis applies the Melnikov theory, which allows obtaining a differential equation with amplitude and frequency assigned in advance. Formulas for determination of basic parameters of the oscillations are presented. The modified V...

Plenoptic cameras, constructed with internal microlens arrays, focus those microlenses at infinity in order to sam-ple the 4D radiance directly at the microlenses. The con-sequent assumption is that each microlens image is com-pletely defocused with respect to to the image created by the main camera lens and the outside object. As a result, only a...

Lightfield photography is based on capturing discrete representations of all light rays in a volume of 3D space. Compared to conventional photography, which captures 2D images, lightfield photography captures 4D data. To multiplex this 4D radiance onto conventional 2D sensors, lightfield photography demands sophisticated optics and imaging technolo...

This paper presents a theory that encompasses both “plenoptic” (microlens based) and “heterodyning” (mask based) cameras in a single frequency-domain mathematical formalism. Light-field capture has traditionally been analyzed using spatio-angular representation, with the exception of the frequency-domain “heterodyning” work. In this paper we interp...

pij@tu-sofia.bg, 3 dddoychev@tu-sofia.bg, 4 ttodorov@tu-sofia.bg, 5 vstanchev@tu-sofia.bg In this paper we present a specific electronic system for analysis and design of digitally programmable analog circuits. The created electronic system is with module structure and envelops specific circuits such as programmable gain amplifiers (PGAs), attenuat...

Figure 1: Integral view of a seagull This paper introduces the matrix formalism of optics as a useful approach to the area of “light fields”. It is capable of reproducing old results in Integral Photography, as well as generating new ones. Furthermore, we point out the equivalence between radiance density in optical phase space and the light field....

pij@tu-sofia.bg, 3 dddoychev@tu-sofia.bg, 4 ttodorov@tu-sofia.bg, 5 vstanchev@tu-sofia.bg In this paper, practical approaches to design and macromodeling digitally programmable analog circuits are described. The proposed design approaches are based on the design methods for analog circuits, the procedures for performing simulation projects and the...

The most general approach to synthesis of oscillators consists of finding a differential equation satisfying preliminarily assigned properties and then modeling this differential equation by electronic circuit. To this effect the present paper gives a method for synthesis of sinewave oscillator, whereupon the generated sinusoidal oscillations have...

We describe a new theoretical approach to Image Processing and Vision. Expressed in mathemetical terminology, in our formalism image space is a fibre bundle, and the image itself is the graph of a section on it. This mathematical model has advantages to the conventional view of the image as a function on the plane: Based on the new method we are ab...

An integral camera samples the 4D light field of a scene within a single photograph. This paper explores the fundamental tradeoff between spatial resolution and angular resolution that is inherent to integral photography. Based on our analysis we divide previous integral camera designs into two classes depending on how the 4D light field is distrib...

This article deals with modelling of dynamic unstructured model of variable volume fed-batch fermentation process with intensive droppings for L-lysine production. The presented approach of the investigation includes the following main procedures: description of the process by generalized stoichiometric equations; preliminary data processing and ca...

The Healing Brush is a tool introduced for the first time in Adobe Photoshop (2002) that removes defects in images by seamless cloning (gradient domain fusion). The Healing Brush algorithms are built on a new mathematical approach that uses Fibre Bundles and Connections to model the representation of images in the visual system. Our mathematical re...

The Healing Brush is a tool introduced for the first time in Adobe Photoshop (2002) that removes defects in images by seamless cloning (gradient domain fusion). The Healing Brush algorithms are built on a new mathematical approach that uses Fibre Bundles and Connections to model the representation of images in the visual system. Our mathematical re...

This paper describes a method of seamless cloning based on aesthetic theory of lightness perception. Judgment of lightness and color harmony is treated as low level aesthetic judgment made by the human visual system. The equation written based on this consideration is an improvement to Poisson image editing, and produces results that are better tha...

This paper provides a Mathematical model of relighting and adap-tation of human Vision based on the approach of von Kries. It extends Retinex theory into a new image processing formalism using the mathematical concepts of Bundles and Connections, that is well suited for scene relighting applications. Our model generates considerably improved result...

This paper describes an improvement to the Poisson image editing method for seamless cloning. Our approach is based on minimizing an energy expression invariant to relighting. The improved method reconstructs seam-lessly the selected region, matching both pixel values and texture contrast of the surrounding area, while previous algorithms matched p...

Development of dynamic unstructured model of fed-batch fermentation process with droppings for L-lysine production is the aim of the article. Establishment of the model includes the following main procedures: description of the process by generalized stoichiometric equations; preliminary data processing; identification of the specific rates (growth...

The Healing Brush is a tool first introduced in Photoshop, that achieves seamless removal of defects in images. A similar image pro- cessing algorithm, called Poisson Editing, was later proposed in (8). Our paper presents the theoretical ideas on which Healing is based, as well as some implementational details. Healing is performed by constructing...

Fed-batch fermentations for production of L-lysine and L-valine are carried out using high producing strains. Based on the experimental data, comparative studies of both processes are done, applying different mathematical procedures as follows: preliminary data processing and calculation of different specific rates; development of nonlinear models...

Fed-batch fermentation process using L-lysine producing strain is carried out as an integrated approach for solving an ecological problem. This article deals with applying an approach for modelling and optimisation of the process. Based on previous results, a new set of generalised stoichiometric equations is obtained. The derived stoichiometric eq...

Dynamic experimental data of sorption and desorption phase of L-lysine ion-exchange purification process are investigated. The behaviour of the experimental data is described through non-linear dynamic mathematical models, taking into account the relationship between L-lysine concentration and pH of the culture broth, temperature, flow rate, etc. T...

The paper deals with modelling of the L-valine fermentation process. The modelling problem of biotechnological processes has three aspects: (a) determination of generalised stoichiometric reactions; (b) identification of the underlying reaction network; (c) identification of the kinetics structure and parameters of reaction rates, following an inve...

Herbst and Simon [Phys. Rev. Lett. 41, 67 (1978)] have proven that the complex-scaling method (CSM) is applicable to the Stark effect in atoms. However, their proof is limited to complex scaling with an argument <π/3. Their method makes no statement as to the validity of CSM beyond this region. This article reports on a detailed numerical study of...

Our numerical calculations of the Stark effect in hydrogen suggest a limitation on the range of energies of Stark resonances that can be calculated by the Complex Scaling Method (CSM). We find that CSM can only be used to calculate resonances with energies Im E > &surd;3 Re E. This limitation corresponds precisely to the range of validity of the He...

We propose a new, Affine Space treatment of the theory of Morphing. Instead of the standard approach, where morphing is a transition between two images, we propose a natural way of generalizing the theory to an unlimited number of initial images. Any curve in the Affine Space defined by these images represents, in our approach, a movie. Application...

Performing a variational calculation in the Complex Scaling Method (CSM) gives approximations to the complex eigenvalues of the discrete and continuous spectrum. These eigenvalues are functions of the complex scaling parameter. Varying the argument of this parameter yields "theta-trajectories" in the complex energy plane, while varying the absolute...

The Avron-Herbst-Simon theory of the Stark Effect shows that while the Stark Hamiltonian has only continuous spectrum, there is an appropriately built S-matrix which possesses resonance poles on the second sheet. These can be found with the method of complex scaling. In this work we examine computationally the spectrum of the complex scaled Stark H...

The purpose of ultrawideband /UWB/ amplifier is to amplify the signal with little distortion and little additional noise. The design of efficient UWB amplifiers is a process that requires precise report on conditions and networks of signal propagation. Very important is defining of the amplifier parameter: ratio of the signal-to-noise /SNR/, which...

Lightfield photography enables many new possibilities for digital imaging because it captures both spatial and angular information, i.e., the full four-dimensional radiance, of a scene. Extremely high resolution is required in order to capture four-dimensional data with a two-dimensional sensor. However, images rendered from the lightfield as proje...

In previous works light-field capture has been analyzed in spatio-angular representation. A light-field camera samples the optical signal within a single photograph by multiplexing the 4D radiance onto the physical 2D surface of the sensor. In this paper we develop a theory of multiplexing the radiance in the frequency domain by optically mixing di...

We propose a general mathematical framework for dealing with Light Fields: The Light Field is a 2-form on Light Space (LS). Light Space is the set of all rays in 3D, and is locally isomorphic to the Grassmann manifold G 4 2. The Light Field form is de- fined as the pull-back of the brightness form of the observed surface. It satisfies equations rel...

In this paper we consider cameras as belonging to one of two types: single aperture (conventional) cameras, and multiple aperture (compound eye) cameras. The eyes of insects are well known examples of the second type. Recently Fraunhofer Institute announced the manufacturing of a compound eye camera, which is very thin and has potential application...