0000000000073042
AUTHOR
Dionisio F. Yáñez
showing 23 related works from this author
Improving the stability bound for the PPH nonlinear subdivision scheme for data coming from strictly convex functions
2021
Abstract Subdivision schemes are widely used in the generation of curves and surfaces, and therefore they are applied in a variety of interesting applications from geological reconstructions of unaccessible regions to cartoon film productions or car and ship manufacturing. In most cases dealing with a convexity preserving subdivision scheme is needed to accurately reproduce the required surfaces. Stability respect to the initial input data is also crucial in applications. The so called PPH nonlinear subdivision scheme is proven to be both convexity preserving and stable. The tighter the stability bound the better controlled is the final output error. In this article a more accurate stabilit…
Learning multiresolution schemes for compression of images
2007
We introduce a new type of multiresolution based on the Harten's framework using learning theory. This changes the point of view of the classical multiresolution analysis and it transforms an approximation problem in a learning problem opening great possibilities. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)
Adaptive rational interpolation for cell-average
2020
Abstract In this paper, we extend the rational interpolation introduced by G. Ramponi et al. (1997, 1998, 1996, 1995) to the cell average setting. We propose a new family of non linear interpolation operator. It consists on constructing new approximations using a non linear weighted combination of polynomials of degree 1 or 2 to obtain new interpolations of degree 2 or 4 respectively. New weights are proposed and analyzed. Gibbs phenomenon is studied and some experiments are performed comparing the new methods with classical linear and non linear interpolation as Weighted Essentially Non-Oscillatory (WENO).
Cell-average multiresolution based on local polynomial regression. Application to image processing
2014
In Harten (1996) [32] presented a general framework about multiresolution representation based on four principal operators: decimation and prediction, discretization and reconstruction. The discretization operator indicates the nature of the data. In this work the pixels of a digital image are obtained as the average of a function in some defined cells. A family of Harten cell-average multiresolution schemes based on local polynomial regression is presented. The stability is ensured by the linearity of the operators obtained and the order is calculated. Some numerical experiments are performed testing the accuracy of the prediction operators in comparison with the classical linear and nonli…
On Multiresolution Transforms Based on Weighted-Least Squares
2014
This work is devoted to construct Harten’s multiresolution transforms using Weighted-Least squares for different discretizations. We establish a relation between the filters obtained using some decimation operators. Some properties and examples of filters are presented.
On the use of generalized harmonic means in image processing using multiresolution algorithms
2019
In this paper we design a family of cell-average nonlinear prediction operators that make use of the generalized harmonic means and we apply the resulting schemes to image processing. The new famil...
The Acquisition of Computational Thinking through Mentoring: An Exploratory Study
2020
Educational robotics are commonly present in kindergarten and primary school classrooms, particularly Bee-bot. Its ease of use allows the introduction of computer programming to young children in educational contexts from a science, technology, engineering, arts, and mathematics (STEAM) perspective. Despite this rise, there are still few investigations that collect evidence on the effectiveness of robotic interventions. Although mentoring experiences with robotics had been carried out in educational contexts, this work explores their effect on the acquisition of computational thinking skills through mentoring. Participants from the second grade, aged seven through eight years, were exposed …
A nonlinear Chaikin-based binary subdivision scheme
2019
Abstract In this work we introduce and analyze a new nonlinear subdivision scheme based on a nonlinear blending between Chaikin’s subdivision rules and the linear 3-cell subdivision scheme. Our scheme seeks to improve the lack of convergence in the uniform metric of the nonlinear scheme proposed in Amat et al. (2012), where the authors define a cell-average version of the PPH subdivision scheme (Amat et al., 2006). The properties of the new scheme are analyzed and its performance is illustrated through numerical examples.
Non-linear Local Polynomial Regression Multiresolution Methods Using $$\ell ^1$$-norm Minimization with Application to Signal Processing
2015
Harten’s Multiresolution has been developed and used for different applications such as fast algorithms for solving linear equations or compression, denoising and inpainting signals. These schemes are based on two principal operators: decimation and prediction. The goal of this paper is to construct an accurate prediction operator that approximates the real values of the signal by a polynomial and estimates the error using \(\ell ^1\)-norm in each point. The result is a non-linear multiresolution method. The order of the operator is calculated. The stability of the schemes is ensured by using a special error control technique. Some numerical tests are performed comparing the new method with…
Adaptive interpolation with maximum order close to discontinuities
2022
Abstract Adaptive rational interpolation has been designed in the context of image processing as a new nonlinear technique that avoids the Gibbs phenomenon when we approximate a discontinuous function. In this work, we present a generalization to this method giving explicit expressions for all the weights for any order of the algorithm. It has a similar behavior to weighted essentially non oscillatory (WENO) technique but the design of the weights in this case is more simple. Also, we propose a new way to construct them obtaining the maximum order near the discontinuities. Some experiments are performed to demonstrate our results and to compare them with standard methods.
Exploring the development of mental rotation and computational skills in elementary students through educational robotics
2022
Abstract Interest in educational robotics has increased over the last decade. Through various approaches, robots are being used in the teaching and learning of different subjects at distinct education levels. The present study investigates the effects of an educational robotic intervention on the mental rotation and computational thinking assessment in a 3rd grade classroom. To this end, we carried out a quasi-experimental study involving 24 third-grade students. From an embodied approach, we have designed a two-hour intervention providing students with a physical environment to perform tangible programming on Bee-bot. The results revealed that this educational robotic proposal aimed at map…
Cell-average WENO with progressive order of accuracy close to discontinuities with applications to signal processing
2020
In this paper we translate to the cell-average setting the algorithm for the point-value discretization presented in S. Amat, J. Ruiz, C.-W. Shu, D. F. Y\'a\~nez, A new WENO-2r algorithm with progressive order of accuracy close to discontinuities, submitted to SIAM J. Numer. Anal.. This new strategy tries to improve the results of WENO-($2r-1$) algorithm close to the singularities, resulting in an optimal order of accuracy at these zones. The main idea is to modify the optimal weights so that they have a nonlinear expression that depends on the position of the discontinuities. In this paper we study the application of the new algorithm to signal processing using Harten's multiresolution. Se…
Learning-based multiresolution transforms with application to image compression
2013
In Harten's framework, multiresolution transforms are defined by predicting finer resolution levels of information from coarser ones using an operator, called prediction operator, and defining details (or wavelet coefficients) that are the difference between the exact and predicted values. In this paper we use tools of statistical learning in order to design a more accurate prediction operator in this framework based on a training sample, resulting in multiresolution decompositions with enhanced sparsity. In the case of images, we incorporate edge detection techniques in the design of the prediction operator in order to avoid Gibbs phenomenon. Numerical tests are presented showing that the …
On the application of the generalized means to construct multiresolution schemes satisfying certain inequalities proving stability
2021
Multiresolution representations of data are known to be powerful tools in data analysis and processing, and they are particularly interesting for data compression. In order to obtain a proper definition of the edges, a good option is to use nonlinear reconstructions. These nonlinear reconstruction are the heart of the prediction processes which appear in the definition of the nonlinear subdivision and multiresolution schemes. We define and study some nonlinear reconstructions based on the use of nonlinear means, more in concrete the so-called Generalized means. These means have two interesting properties that will allow us to get associated reconstruction operators adapted to the presence o…
Third-order accurate monotone cubic Hermite interpolants
2019
Abstract Monotonicity-preserving interpolants are used in several applications as engineering or computer aided design. In last years some new techniques have been developed. In particular, in Arandiga (2013) some new methods to design monotone cubic Hermite interpolants for uniform and non-uniform grids are presented and analyzed. They consist on calculating the derivative values introducing the weighted harmonic mean and a non-linear variation. With these changes, the methods obtained are third-order accurate, except in extreme situations. In this paper, a new general mean is used and a third-order interpolant for all cases is gained. We perform several experiments comparing the known tec…
Non-separable local polynomial regression cell-average multiresolution operators. Application to compression of images
2016
Abstract Cell-average multiresolution Harten׳s algorithms have been satisfactorily used to compress data. These schemes are based on two operators: decimation and prediction. The accuracy of the method depends on the prediction operator. In order to design a precise function, local polynomial regression has been used in the last years. This paper is devoted to construct a family of non-separable two-dimensional linear prediction operators approximating the real values with this procedure. Some properties are proved as the order of the scheme and the stability. Some numerical experiments are performed comparing the new methods with the classical linear method.
Design of Multiresolution Operators Using Statistical Learning Tools: Application to Compression of Signals
2012
Using multiresolution based on Harten's framework [J. Appl. Numer. Math., 12 (1993), pp. 153---192.] we introduce an alternative to construct a prediction operator using Learning statistical theory. This integrates two ideas: generalized wavelets and learning methods, and opens several possibilities in the compressed signal context. We obtain theoretical results which prove that this type of schemes (LMR schemes) are equal to or better than the classical schemes. Finally, we compare traditional methods with the algorithm that we present in this paper.
Generalized wavelets design using Kernel methods. Application to signal processing
2013
Abstract Multiresolution representations of data are powerful tools in signal processing. In Harten’s framework, multiresolution transforms are defined by predicting finer resolution levels of information from coarser ones using an operator, called the prediction operator, and defining details (or wavelet coefficients) that are the difference between the exact values and the predicted values. In this paper we present a multiresolution scheme using local polynomial regression theory in order to design a more accurate prediction operator. The stability of the scheme is proved and the order of the method is calculated. Finally, some results are presented comparing our method with the classical…
Relación entre complejidad y dificultad en tareas con patrones lineales reiterativos en estudiantes de 5 años
2018
Una de las finalidades de la enseñanza de las matemáticas en Educación Infantil es fomentar el pensamiento lógico, la creatividad y la capacidad para resolver problemas de los estudiantes. Entre las actividades escolares propias de estas edades es habitual encontrar tareas de identificación y continuación de patrones lineales de repetición. Esta actividad puede ser estudiada desde un contexto de resolución de problemas en el que el estudiante debe discriminar la información superflua de aquella que le permite obtener la regla de generación de la serie y resolver la tarea. Diferentes variables como la longitud del núcleo de repetición, el número de descriptores, su naturaleza o la aparición …
Non-consistent cell-average multiresolution operators with application to image processing
2016
In recent years different techniques to process signal and image have been designed and developed. In particular, multiresolution representations of data have been studied and used successfully for several applications such as compression, denoising or inpainting. A general framework about multiresolution representation has been presented by Harten (1996) 20. Harten's schemes are based on two operators: decimation, D , and prediction, P , that satisfy the consistency property D P = I , where I is the identity operator. Recently, some new classes of multiresolution operators have been designed using learning statistical tools and weighted local polynomial regression methods obtaining filters…
On Augmented Reality for the Learning of 3D-Geometric Contents: A Preliminary Exploratory Study with 6-Grade Primary Students
2019
Nowadays, Augmented Reality (AR) is one of the emerging technologies with a greater impact in the Education field. Research has proved that AR-based activities improve the teaching and learning processes. Also, the use of this type of technology in classroom facilitates the understanding of contents from different areas as Arts, Mathematics or Science. In this work we propose an AR-based instruction in order to explore the benefits in a 6th-grade Primary course related to 3D-geometry shapes. This first experiment, designed from an exploratory approach, will shed light on new study variables to perform new implementations whose conclusions become more consistent. The results obtained allow u…
Monotone cubic spline interpolation for functions with a strong gradient
2021
Abstract Spline interpolation has been used in several applications due to its favorable properties regarding smoothness and accuracy of the interpolant. However, when there exists a discontinuity or a steep gradient in the data, some artifacts can appear due to the Gibbs phenomenon. Also, preservation of data monotonicity is a requirement in some applications, and that property is not automatically verified by the interpolator. Hence, some additional techniques have to be incorporated so as to ensure monotonicity. The final interpolator is not actually a spline as C 2 regularity and monotonicity are not ensured at the same time. In this paper, we study sufficient conditions to obtain monot…
On new means with interesting practical applications: Generalized power means
2021
Means of positive numbers appear in many applications and have been a traditional matter of study. In this work, we focus on defining a new mean of two positive values with some properties which are essential in applications, ranging from subdivision and multiresolution schemes to the numerical solution of conservation laws. In particular, three main properties are crucial—in essence, the ideas of these properties are roughly the following: to stay close to the minimum of the two values when the two arguments are far away from each other, to be quite similar to the arithmetic mean of the two values when they are similar and to satisfy a Lipchitz condition. We present new means with these pr…