Ryszard Kozera

• Warsaw University of Life Sciences

The aim of this research is to create an automated system for identifying soil microorganisms at the genera level based on raw microscopic images of monocultural colonies grown in laboratory environment. The examined genera are: Fusarium, Trichoderma, Verticillium, Purpureolicillium and Phytophthora. The proposed pipeline deals with unprocessed mic...

TfELM introduces an innovative Python framework leveraging TensorFlow for Extreme Learning Machines (ELMs), offering a comprehensive suite for diverse machine learning (ML) tasks. Existing solutions in the ELM landscape lack comprehensive implementations. TfELM fills this gap by consolidating 18 ELM variants (including 14 so-far unimplemented in Py...

The identification of soil microorganisms plays a crucial role in agriculture and horticulture, as it enables the monitoring of beneficial species and early detection of pathogens. In this study, we propose a system that utilizes machine vision and machine learning techniques, specifically Convolutional Neural Networks, to automate the identificati...

The visual analysis of microscopic images is often used for soil bacteria recognition in microbiology. Such task can be automated with the aid of machine learning and digital image processing techniques. The best results for soil microorganism identification usually rely on extracting features based on color. However, accommodating in the latter an...

This research investigates the integration of Metaheuristic Algorithms (MAs) with the Extreme Learning Machine (ELM) model to optimize parameters of activation function. While MAs have traditionally been employed for weights selection, a methodology that utilizes MA for the selection of activation function parameters was proposed. The performance o...

This work presents a research on Nature Inspired Metaheuristic Algorithms (MA) used as optimizers in training process of Machine Learning method called Extreme Learning Machine (ELM). We tested 19 MA optimizers measuring their performance directly on sample datasets. The impact of input parameters such as number of hidden layer units, optimization...

The problem of fitting a given ordered sample of data points in arbitrary Euclidean space is addressed. The corresponding interpolation knots remain unknown and as such must be first somehow found. The latter leads to a highly non-linear multivariate optimization task, equally non-trivial for theoretical analysis and for derivation of a computation...

Extreme Learning Machine (ELM) is a feed-forward neural network with one hidden layer. In its modification called ELM Radial Basis Function the input data is a priori clustered into a number of sets represented by their centroids. The matrix of distances between each sample and centroid is calculated and applied as input data to the neural network....

The main goal of this paper is to construct automated system for accurate identification of soil microorganisms on a genera level based on microscopic images of the monocultural colonies. The microorganisms in question belong to one of the following genera: Fusarium, Trichoderma, Verticillium or Phytophthora. Proposed classification system is fully...

This study investigates the performance of 36 different activation functions applied in Extreme Learning Machine on 10 distinct datasets. Results show that Mish and Sexp activation functions exhibit outstanding generalization abilities and consistently perform well across most datasets, while other functions are more dependent on the characteristic...

Soil bacteria have a significant impact on agriculture and horticulture. These bacteria can be distinguished by the microbiologists based on their microscopic images. In our project this approach is performed with the aid of machine learning and image processing techniques. The implemented fully automated recognition system identifies five bacteria...

In this paper we investigate groups which admit the existence of weighted consistent approximations for pairwise comparisons matrices. These approximations are defined by extending the classical matrix projection for R_{+} to abstract weighted projections on the non-linear sets of transitive group-valued matrices. It is of interest that all of them...

The problem of fitting multidimensional reduced data is analyzed here . The missing interpolation knots T are substituted by T^ which minimize a non-linear multivariate function J0. One of numerical schemes designed to compute such optimal knots relies on iterative scheme called Leap-Frog Algorithm. The latter is based on merging the respective gen...

Soil bacteria play a fundamental role in plant growth. This paper focuses on developing and testing some techniques designed to identify automatically such microorganisms. More specifically, the recognition performed here deals with the specific five genera of soil bacteria. Their microscopic images are classified with machine learning methods usin...

The problem of fitting multidimensional reduced data \(\mathcal{M}_n\) is discussed here. The unknown interpolation knots \(\mathcal{T}\) are replaced by optimal knots which minimize a highly non-linear multivariable function \(\mathcal{J}_0\). The numerical scheme called Leap-Frog Algorithm is used to compute such optimal knots for \(\mathcal{J}_0...

This paper discusses the topic of interpolating data points Qm in arbitrary Euclidean space with Lagrange cubics γ^L and exponential parameterization which is governed by a single parameter λ ∈ [0, 1] and replaces a discrete set of unknown knots {ti}i=0m (ti ∈ I) with new values {t^i}i=0m (t^i∈I^). To compare γ with γ^L specific mapping ϕ:I→I^ must...

This book constitutes the refereed proceedings of the International Conference on Computer Vision and Graphics, ICCVG 2020, held in Warsaw, Poland, in September 2020. The 20 full papers were selected from 49 submissions. The contributions cover topics such as: modelling of human visual perception; computational geometry; geometrical models of objec...

This paper discusses the issue of interpolating data points in arbitrary Euclidean space with the aid of Lagrange cubics \(\hat{\gamma }^L\) and exponential parameterization. The latter is commonly used to either fit the so-called reduced data \(Q_m=\{q_i\}_{i=0}^m\) for which the associated exact interpolation knots remain unknown or to model the...

We discuss the problem of fitting a smooth regular curve γ:[0,T]→En based on reduced dataQm={qi}i=0m in arbitrary Euclidean space En. The respective interpolation knots T={ti}i=0m satisfying qi=γ(ti) are assumed to be unknown. In our setting the substitutes Tλ={t^i}i=0m of T are selected according to the so-called exponential parameterization gover...

This work discusses the problem of fitting a regular curve (Formula presented.) based on reduced data points(Formula presented.) in arbitrary Euclidean space. The corresponding interpolation knots (Formula presented.) are assumed to be unknown. In this paper the missing knots are estimated by (Formula presented.) in accordance with the so-called ex...

A real square matrix is generalized doubly stochastic (g.d.s.) if all of its row sums and column sums equal one. We propose efficient numerical algorithms for generating such matrices having possibly orthogonality property or/and satisfying Yang-Baxter equation (YBE). Additionally, an inverse eigenvalue problem for finding orthogonal generalized do...

The potential use of a novel multichannel optical system towards fast and non-destructive bacteria identification and its application for environmental bacteria characterisation on the strain level is presented. It is the first attempt to use the proposed optical method to study various bacteria species (Gram-negative, Gram-positive) commonly prese...

This paper discusses the problem of estimating the trajectory of the unknown curve γ from the sequence of m+1 interpolation points in arbitrary Euclidean space En . The respective knots (in ascending order) are assumed to be unknown. Such Qm is coined reduced data. In our setting, a piecewise-cubic Lagrange interpolation is applied to fit Qm. Here,...

This paper addresses the topic of fitting reduced data represented by the sequence of interpolation points \(\mathcal{M}=\{q_i\}_{i=0}^n\) in arbitrary Euclidean space \(\mathbb {E}^m\). The parametric curve \(\gamma \) together with its knots \(\mathcal{T}=\{t_i\}_{i=0}^n\) (for which \(\gamma (t_i)=q_i\)) are both assumed to be unknown. We look a...

This paper addresses the problem of reconstructing the shape of an unknown Lambertian surface given in the 3D space by a continuously differentiable function \(z = u(x,y)\). The surface is reconstructed from its photometric images obtained by its successive illumination with three different remote light sources. Using computer algebra methods, we s...

This work deals with some properties of synthetic measures designed to differentiate objects in a multidimensional analysis. The aggregate synthetic measures are discussed here to rank the objects including those validating the concentration spread. The paper shows that currently used various measures (based either on a single or a multiple model o...

A real quadratic matrix is generalized doubly stochastic (g.d.s.) if all of its row sums and column sums equal one. We propose numerically stable methods for generating such matrices having possibly orthogonality property or/and satisfying Yang-Baxter equation (YBE). Additionally, an inverse eigenvalue problem for finding orthogonal generalized dou...

This paper discusses the special case of reconstructing the unknown Lambertian surface from two-image photometric stereo. Both images are assumed here to be formed by a genuine second-order algebraic surface. The corresponding uniqueness issue is discussed for different pairs of image irradiance equations under various illumination settings. Illust...

This paper presents a comparison of two Cholesky-like algorithms for solving symmetric quasi-definite system Mz = f. This pair of methods computes the block factorization M = RTDR, where R is upper triangular and D is a diagonal matrix.

This paper addresses the problem of reconstructing the shape of an unknown Lambertian surface from its two photometric images obtained by successive illumination of the surface with two different remote light sources. Using computer algebra methods, we investigate the conditions of existence and uniqueness of a solution to a system of algebraic equ...

The problem of fitting sparse reduced data in arbitrary Euclidean space is discussed in this work. In our setting, the unknown interpolation knots are determined upon solving the corresponding optimization task. This paper outlines the non-linearity and non-convexity of the resulting optimization problem and illustrates the latter in examples. Symb...

We describe the problem of estimating a length of a regular parameterized curve from an ordered sample of interpolation points in arbitrary Euclidean space by modified complete spline. The corresponding tabular parameters are assumed to be unknown and are approximated by the exponential parameterization (controlled by the parameter λ ∈ [0, 1]). In...

This paper discusses the ambiguous shape recovery in two-image photometric stereo for a Lambertian surface. The current uniqueness analysis refers to linearly independent light-source directions p = (0, 0, −1) and q arbitrary. For this case necessary and sufficient condition determining ambiguous reconstruction is governed by a second-order linear...

This paper tackles the problem of estimating a length of a regular parameterized curve γ from an ordered sample of interpolation points in arbitrary Euclidean space by a natural spline. The corresponding tabular parameters are not given and are approximated by the so-called exponential parameterization (depending on λ ∈ [0, 1]). The respective conv...

Biochar is a solid material of biological origin obtained from biomass carbonization, designed as a mean to reduce greenhouse gases emission and carbon sequestration in soils for a long time. Biochar has a wide spectrum of practical utilization and is applied as a promising soil improver or fertilizer in agriculture, or as a medium for soil or wate...

The problem of reconstructing a Lambertian surface from its two photometric stereo images is discussed. Previously, the solution to this problem was only obtained for a special choice of two light source directions. In this paper, using the computer algebra system Mathematica, the necessary and sufficient conditions for the unique reconstruction of...

This paper discusses the reconstruction of a Lambertian surface \(S_L\) in three-image noisy photometric stereo under the assumption that light-sources are not necessarily positioned at infinity. The corresponding multi-variable non-linear optimization task either incorporating or not an image boundary continuity enforcement (to remove outliers) is...

In this paper we investigate the case of ambiguous shape reconstruction from two light-source photometric stereo based on illuminating the unknown Lambertian surface. So-far this problem is merely well-understood for two linearly independent light-source directions with one illumination assumed as overhead. As already established, a necessary and s...

We examine the asymptotics of a piecewise-quartic Lagrange interpolation used to fit reduced data in arbitrary Euclidean space which are sampled more-or-less uniformly. The unknown interpolation knots are guessed here according to the so-called exponential parameterization which depends on a single parameter λ ∈ [0, 1]. In this work we demonstrate...

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We consider here a natural spline interpolation based on reduced data and the so-called exponential parameterization (depending on parameter λ ∈ [0, 1]). In particular, the latter is studied in the context of the trajectory approximation in arbitrary euclidean space. The term reduced data refers to an ordered collection of interpolation points with...

We discuss an interpolation scheme (based on optimization) to fit a given ordered sample of reduced data \(Q_m\) in arbitrary Euclidean space. Here the corresponding knots are not given and need to be first somehow guessed. This is accomplished by solving an appropriate optimization problem, where the missing knots minimize the cost function measur...

In this paper a feasible computational scheme for reconstructing a smooth Lambertian surface \(S_L\) from noisy images is discussed. The noiseless case of Photometric Stereo relies on solving image irradiance equations. In fact, the entire shape recovery consists of gradient computation and gradient integration. The presence of added noise re-trans...

We investigate the length approximation of the unknown regular curve in arbitrary Euclidean space upon applying a piecewise-quadratic interpolation based on ε -uniformly sampled reduced data in combination with the exponential parameterization. As proved in this paper, similarly to the trajectory estimation, there is a discontinuity in the quality...

This paper presents the method of soil microorganisms identification from the microscopic digital images. The proposed approach includes: Segmentation of the image, feature generation, selection of the most important features and the final recognition stage applying five different solutions of classifiers. The paper presents and discusses the resul...

This book constitutes the refereed proceedings of the International Conference on Computer Vision and Graphic, ICCVG 2016, held in Warsaw, Poland, in September 2016. The 68 full papers presented were carefully reviewed and selected from various submissions. They show various opportunities for valuable research at the border of applied information s...

Two neural networks with randomly chosen initial weights may achieve the same weight vectors in the process of their mutual learning. This phenomenon is called a network synchronization, and can be used in cryptography to establish the keys for further communication. The time required to achieve consistent weights of networks depends on the initial...

In this paper a modified complete spline interpolation based on reduced data is examined in the context of trajectory approximation. Reduced data constitute an ordered collection of interpolation points in arbitrary Euclidean space, stripped from the corresponding interpolation knots. The exponential parameterization (controlled by \(\lambda \in [0...

This paper tackles the problem of interpolating reduced data \(Q_m=\{q_i\}_{i=0}^m\) obtained by sampling an unknown curve γ in arbitrary euclidean space. The interpolation knots \({\cal T}_m= \{t_i\}_{i=0}^m\) satisfying γ(t i ) = q i are assumed to be unknown (non-parametric interpolation). Upon selecting a specific numerical scheme \(\hat \gamma...

This paper discusses the problem of fitting non-parametric unordered reduced data (i.e. a collection of interpolation points) with piecewise-quadratic interpolation to estimate an unknown curve \(\gamma \) in Euclidean space \(E^2\). The term reduced data stands for the situation in which the corresponding interpolation knots are unavailable. The c...

It is well-known that artificial neural networks have the ability to learn based on the provisions of new data. A special case of the so-called supervised learning is a mutual learning of two neural networks. This type of learning applied to a specific networks called Tree Parity Machines (abbreviated as TPM networks) leads to achieving consistent...

The paper presents the method of soil microorganisms identification in the microscopic digital images. The solved task includes: segmentation, feature generation, selection of the most important features and the final recognition stage applying 5 different solutions of classifiers. The paper presents and discusses the results concerning the recogn...

This paper discusses the problem of estimating the length of the unknown curve γ in Euclidean space, from ε-uniformly (for ε ≥ 0) sampled reduced data \(Q_m=\{q_i\}_{i=0}^m\), where γ(t i ) = q i . The interpolation knots \(\{t_i\}_{i=0}^m\) are assumed here to be unknown (yielding the so-called non-parametric interpolation). We fit Q m with the pi...

We study the quality of piecewise-Lagrange interpolation for non-parametric data based on ε-uniform samplings and different forms of exponential parameterization. Surprisingly, it turns out that there is a sharp discontinuity in the quality of interpolation: exponential parameterization performs no better than a blind uniform guess, except for the...

In this paper, we prove the difference analogs of the comparison theorems for solutions of the Cauchy problem for a nonlinear ordinary differential equation (ODE). This result is subsequently used to analyze blow-up solution of finite - difference schemes (FDS) approximating the Neumann problem for a parabolic equation with a nonlinear source of po...

Scitation is the online home of leading journals and conference proceedings from AIP Publishing and AIP Member Societies

This paper discusses the problem of fitting non-parametric unordered reduced data (i.e. a collection of interpolation points) with piecewise-quadratic interpolation to estimate an unknown curve γ in Euclidean space E2. The term reduced data stands for the situation in which the corresponding interpolation knots are unavailable. The construction of...

This paper discusses the issue of fitting reduced data \(Q_m=\{q_i\}_{i=0}^m\) with smooth interpolant by piecewise-cubics to estimate an unknown curve γ in arbitrary Euclidean space. The interpolation knots \(\{t_i\}_{i=0}^m\) satisfying γ(t i ) = q i are assumed to be unknown and guessed according to so-called cumulative chords. More specifically...

This paper discusses the problem of fitting non-parametric planar data \(Q_m = \{q_i\}^m_{i=0}\) with four-points piecewise-quadratic interpolant to estimate an unknown convex curve γ in Euclidean space E 2 sampled more-or-less uniformly. The derivation of the interpolant involves non-trivial algebraic and symbolic computations. As it turns out, ex...

This paper discusses the problem of reconstructing the Lambertian surface from noisy three-light source Photometric Stereo. In the continuous image setting the shape recovery process is divided into two steps: an algebraic one (gradient computation) and analytical one (gradient integration). The digitized case with added noise has it discrete analo...

The problem considered in this article involves the construction of evaluation model, which could subsequently be used in the fieldof modeling and risk management. The research work is finalizedby a construction of a new model on the basis of observa-tions of the models used for risk management and knowledge of information theory, machine learning...

Scientific computation is at present one of the most efficient approaches available to researchers and developers for applied mathematics, technical, economical and natural sciences. This book provides practical guidance on how to perform numerical computer simulations using advanced computational and visualization software tools, and the book in part...

This paper discusses the issue of fitting reduced data \(Q_m=\{q_i\}_{i=0}^m\) with piecewise-quadratics to estimate an unknown curve γ in Euclidean space. The interpolation knots \(\{t_i\}_{i=0}^m\) with γ(t i ) = q i are assumed to be unknown. Such non-parametric interpolation commonly appears in computer graphics and vision, engineering and phys...

The phenomenon of neural networks synchronization by mutual learning can be used to construct key exchange protocol on an open channel. For security of this protocol it is important to minimize knowledge about synchronizing networks available to the potential attacker. The method presented herein permits evaluating the level of synchronization befo...

In this paper we discuss the problem of interpolating the so-called reduced data to estimate the unknown curve satisfying . The corresponding interpolation knots for the reduced data are assumed to be unknown. The main issue for such non-parametric data fitting (given selected interpolation scheme) is to complement with somehow guessed , so that th...

Minirhizotron, a non-destructive technique is based on the application of transparent tubes, located in plant’s root zone. This method has been known since the beginning of 20th century and is used for plant root’s observations, especially in forest trees (Scots pine, Norway spruce, silver fir, birch), steppe grasses, vegetables and cereals. Minirh...

Neural networks’ synchronization by mutual learning discovered and described by Kanter et al. [10] can be used to construct relatively secure cryptographic key exchange protocol in the open channel. This phenomenon based on simple mathematical operations, can be performed fast on a computer. The latter makes it competitive to the currently used cry...

In this paper we consider the problem of modeling curves in Rn via interpolation without a priori specified interpolation knots. We discuss two approaches to estimate the missing knots for non-parametric data (i.e. collection of points. The first approach (uniform evaluation) is based on blind guess in which knots are chosen uniformly. The second a...

Purpose: The aim of this research is to determine the construction parameters and the working parameters of the rotors modeled with the aid of the computer simulations. This research is conducted in the context of its application in different systems for sewage rectification. Design/methodology/approach: Modeling and process analysis of the fluid f...

In this paper a 2D Leap Frog Algorithm is applied to solve the so-called noisy Photometric Stereo problem. In 3-source Photometric Stereo (noiseless or noisy) an ideal unknown Lambertian surface is illuminated from distant light-source directions (their directions are assumed to be linearly independent). The subsequent goal, given three images is t...

In this paper we verify sharpness of the theoretical results concerning the asymptotic orders of trajectory approximation of the unknown parametric curve γ in arbitrary Euclidean space. The pertinent interpolation schemes (based on piecewise-quadratics and piecewise-cubics) are here considered for the so-called reduced data. The latter forms an ord...

In this paper we discuss the problem of interpolating the so-called reduced data \(Q_m=\{q_i\}_{i=0}^m\) to estimate the length d(γ) of the unknown curve γ sampled in accordance with γ(t i ) = q i . The main issue for such non-parametric data fitting (given a fixed interpolation scheme) is to complement the unknown knots \(\{t_i\}_{i=0}^m\) with \(...

The restricted correspondence problem is the task of solving the classical stereo correspondence problem when the surface being observed is known to belong to a family of surfaces that vary in a known way with one or more parameters. Under this constraint the surface can be extracted far more robustly than by classical stereo applied to an arbitrar...

Photographic outlines of dimensional solids are robust and rich in information useful for surface reconstruction. This paper studies algebraic surfaces viewed from 2 cameras with known intrinsic and extrinsic parameters. It has been known for some time that for a degree d=2 (quadric) algebraic surface there is a 1-parameter family of surfaces that...

In classical photometric stereo, a Lambertian surface is illuminated from multiple distant point light-sources. In the present paper we consider nearby lightsources instead, so that the unknown surface, is illuminated by non-parallel beams of light. In continuous noiseless cases, the recovery of a Lambertian surface from non-distant illuminations,...

This paper shows that a strictly convex solid under observation by two or more cameras with known extrinsic and intrinsic parameters contains points on its surface calculable in terms of multiple photographic images. In the case of a solid with a boundary we can also extract surface orientation at these points, and when the solid has a boundary and...

Existing Photometric Stereo methods provide reasonable surface reconstructions unless the irradiance image is corrupted with noise and effects of digitisation. However, in real world situations the measured image is almost always corrupted, so an efficient method must be formulated to denoise the data. Once noise is added at the level of the images...

Smooth cumulative chord piecewise-cubics, for unparameterised data from regular curves in ℝn, are constructed as follows. In the first step derivatives at given ordered interpolation points are estimated from ordinary (non-C1) cumulative chord piecewise-cubics. Then Hermite interpolation is used to generate a C1 regular (geometrically smooth) piece...

In this paper we consider the problem of extracting the shape of a smooth convex solid, nu subset of R(3), from a set of N photographs. The method begins by extracting the edges of each photograph. These edges are used to form a cone whose apex is the camera centre, which is guaranteed to enclose nu. For a strictly convex solid any two such cones w...

Cumulative chord piecewise-quadratics and piecewise-cubics are examined in detail, and compared with other low degree interpolants for unparameterized data from regular curves in , especially piecewise-4-point quadratics. Or- ders of approximation are calculated and compared with numerical experiments. Good performance of the interpolant is also co...

As the speed, capabilities, and economic advantages of modern digital devices c- tinue to grow, the need for ef?cient information processing, especially in computer - sion and graphics, dramatically increases. Growth in these ?elds stimulated by eme- ing applications has been both in concepts and techniques. New ideas, concepts and techniques are d...

We give a contribution to the representation problem of free-form curves and surfaces. Our proposal is an operational or kinematic approach based on the Lie group SE(3). While in Euclidean space the modelling of shape as orbit of a point under the action of SE(3) is limited, we are embedding our problem into the conformal geometric algebra R4,1 of...

Cumulative chord C 1 piecewise-cubics, for unparameterized data from regular curves in R n, are constructed as follows. In the first step derivatives at given ordered interpolation points are estimated from ordinary (non-C 1) cumulative chord piecewise-cubics. Then Hermite interpolation is used to generate a C 1 piecewise-cubic interpolant. Theoret...

We discuss the problem of estimating the trajectory of a regular curve γ:[0,T]→R n and its length d(γ) from an ordered sample of interpolation points Q m={γ(t 0),γ(t 1),...,γ(t m)}, with tabular points t i's unknown, coined as interpolation of unparameterized data. The respective convergence orders for estimating γ and d(γ) with cumulative chord pi...

From 21.03.04 to 26.03.04, the Dagstuhl Seminar 04131 ``Geometric Properties from Incomplete Data'' was held in the International Conference and Research Center (IBFI), Schloss Dagstuhl. During the seminar, several participants presented their current research, and ongoing work and open problems were discussed. Abstracts of the presentations given...

More-or-less-uniform samples are introduced and used to estimate lengths of smooth regular strictly convex curves in R-2. Quartic convergence is proved and illustrated by examples.

We discuss the problem of estimating an arbitrary regular parameterized curve and its length from an ordered sample of interpolation points in n-dimensional Euclidean space. The corresponding tabular parameters are assumed to be unknown. In this paper the convergence rates for estimating both curve and its length with cumulative chord piecewise-qua...

We show that knowledge-based techniques are as effective as mathematical techniques when satisfying constraints for solving manpower allocation problems. These techniques can be used to fulfill the corresponding local and global constraints based on the dynamic programming algorithm. It uses tools borrowed from genetic and simulated annealing algor...

1-D Leap-Frog (L. Noakes, J. Math. Australian Soc. A, Vol. 64, pp. 37–50, 1999) is an iterative scheme for solving a class of nonquadratic optimization problems. In this paper a 2-D version of Leap-Frog is applied to a non optimization problem in computer vision, namely the recovery (so far as possible) of an unknown surface from 3 noisy camera ima...

Knowledge-based techniques are as effective as mathematical techniques for satisfying constraints in manpower resource allocation (MRA) problems. Our knowledge-based techniques allow direct implementation for logical reasoning, reduce efforts in setting up and interpreting rules of constraints, fair well in giving correct solutions, and are adaptab...