Dr. Carlos Brito-Loeza

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Facultad de Matemáticas, Laboratorio de Aprendizaje Automático y Visión, Edificio G

Tel. y Fax: (999) 942-31-40 al 49 ext. 1095

Curriculum vitae - download

Education and Awards

  • PhD Mathematics, University of Liverpool, United Kingdom.
  • MSc. Mathematics, Universidad Autónoma de Yucatán, México.
  • BSc. Eletronic Engineering, Instituto Tecnológico de Mérida, México.
  • Membership to the National System of Researchers since 2010, currently Level I.

Research interests

I am always interested in studying problems where calculus of variations and partial differential equations can be used for modeling the problem and optimization algorithms can be developed to find the solution of the model. Many problems from physics, imaging and analysis of digital data are in this category. In particular, I like to not only designing and studying the properties of the mathematical model but implementing through programming the numerical solution as well.

Some particular topics where I have done some work are:

  • Computer vision and robotics; imaging and digital signal processing algorithms.
  • Variational methods; Nonlinear PDE's; Ill-posed inverse problems.
  • Numerical optimization and numerical analysis; Parallel computation; Multigrid methods.
  • C/C++, Python and Matlab programming.


Below there is a list of projects I am currently involved together with colleagues from CLIR and other institutions. If you are looking for a B.Sc./M.Sc./PhD thesis topic, feel free to approach me to discuss possibilities.  There is plenty of work to do in mathematical modeling, numerical optimization, scientific programming, data analysis and so on.

Imaging problems

Imaging is the process of creating visual representation of objects. In the last years, advances in hardware and software have prompted a very fast growth in the field of imaging science. For instance, in the medical imaging field, high resolution images and new imaging techniques demand new algorithms and mathematical models to tackle new challenges in old processes such as image segmentation, image registration, image denoising and image inpaiting to name a few.


Learning problems

Historically, the problem of supervised classification has been tackled using the neural network approach or with algorithms of a statistical nature. In particular, neural networks, when correctly designed, are capable of delivering efficient solutions to the classification problem. However the analysis of the solution and its properties is very complex and this is why they are commonly referred to as "black box" solutions. In recent years, mathematical models have been proposed based on the calculus of variations for the problem of data classification. This different approach allows us to use powerful mathematical tools such as functional analysis and differential geometry for model analysis. We are interested in developing models and fast algorithms and to tackle the many challenges that appear in doing so.


Comet Assay

Unicellular electrophoresis on gel (comet assay) is a reliable method for measuring DNA damage on cells and evaluating their regenerative capacity. This damaged can be observed through a microscope, where the cells take the form of comets; the stable part of the DNA remains in the head, while the migration of the nucleus, the unstable fraction of DNA, makes up the tail. At CLIR, we are developing image processing tools for an effective segmentation of the head and tail of the DNA molecules processed by the comet assay, and data analytics tools for extracting and understanding patterns to support future research in degenerative diseases.


Fringe pattern analysis

Fringe analysis techniques are very popular to estimate with reasonable accuracy physical quantities such as shape of objects, deformation, refractive index and temperature fields. They achieve these goals by recovering the local phase from one or a collection of interference fringe pattern images. The mathematical model of a fringe pattern is described by the equation


where a is the background illumination, b is the amplitude modulation, ψ is the spatial carrier frequency and φ is the phase map to be recovered. The problem of recovering not only φ but also a and b from the above equation is an ill-posed problem. Recently, variational techniques that aim to reduce uncertainty of the solution by introducing more information into the model by means of regularization of the unknown variables have proved to deliver a feasible solution to this problem. 



Unmanned Aerial System for Remote Data Acquisition and Photogrammetric Sensing

Environmental problems have an obvious impact on virtually every aspect of our daily lives. In particular, the impact of deforestation, erosion and climate change have significantly altered the species population and distribution and have changed the coastal geography. To understand this problem and propose solutions, sensing tools that could enable professionals from various disciplines to have reliable and easily accessible data for the development of models to better understand the problem at hand, are needed. We are interested in developing methodologies for acquiring and merging data from multiple sensors to generate topographical information, with the particular interest in developing the cooperative aspect of the procurement process information across multiple agents.



3D meteoroid trajectories

When a meteoroid enters the Earth's atmosphere, it creates a bright phenomenon called a meteor, reball or bolide (depending on brightness). The interaction of this material with our atmosphere provides us with a unique opportunity to observe and study interplanetary material. Determining the physical state of this material in our atmosphere its strength and mass distribution, and its velocity frequency distribution, provides a unique window on cometary and asteroidal material in the inner solar system. In order to derive that data, we need to model the meteoroid-atmosphere interaction.

Fireball observations from camera networks provide position and time information along the trajectory of a meteoroid that is transiting our atmosphere. The complete dynamical state of the meteoroid at each measured time can be estimated using different techniques techniques.

 Journal publications

  1. Legarda-Saenz, A Téllez Quiñones, C Brito-Loeza, A Espinosa-Romero, "Variational phase recovering without phase unwrapping in phase-shifting interferometry", International Journal of Computer Mathematics 96 (6), 1217-1229.
  2. Carlos Brito-Loeza, Ricardo Legarda-Sáenz, Arturo Espinosa-Romero, Anabel Martin-Gonzalez, "A Mean Curvature Regularized Based Model for Demodulating Phase Maps from Fringe Patterns", Journal Communications in Computational Physics, 24 (1), 27-43, 2018.
  3. José L Medina-Catzin, Anabel Martin-Gonzalez, Carlos Brito-Loeza, Victor Uc-Cetina, "Body gestures recognition system to control a service robot", Journal Int J Inf Tech Comput Sci, Volume 9, Pages 69-76, 2017.
  4. Brito‐Loeza, Carlos, Ke Chen, and Victor Uc‐Cetina, “Image denoising using the Gaussian curvature of the image surface”, Numerical Methods for Partial Differential Equations, 32(3):1066-1089, 2015.
  5. Ibrahim, Mazlinda, Ke Chen, and Carlos Brito-Loeza, “A novel variational model for image registration using Gaussian curvature”, Geometry, Imaging and Computing, 1(4):417-446, 2014.
  6. Víctor Uc-Cetina, Carlos Brito-Loeza, and Hugo Ruiz-Piña, “Chagas Parasite Detection in Blood Images Using AdaBoost”, Computational and Mathematical Methods in Medicine, Article ID 139681, 13 pages, doi:10.1155/2015/139681, 2015.
  7. César Cobos-May, Víctor Uc-Cetina, Carlos Brito-Loeza, and Anabel Martin-Gonzalez, “A Convex Set Based Algorithm to Automatically Generate Haar-Like Features”, Journal Computer Science, 2(2):64-70, 2014.
  8. Ricardo Legarda-Saenz, Carlos Brito-Loeza  and Arturo Espinosa-Romero, “Variational method for integrating radial gradient field”, Optics and Lasers in Engineering, 63:53-57, 2014.
  9. Ricardo Legarda-Saenz, Carlos Brito-Loeza, and Arturo Espinosa-Romero, “Total variation regularization cost function for demodulating phase discontinuities”, Applied optics 53(11): 2297-2301, 2014.
  10. Martha Varguez-Moo, Victor Uc-Cetina, and Carlos Brito-Loeza, “Clasificación de documentos usando Máquinas de Vectores de Apoyo”, Abstraction and Application Magazine, 2014.
  11. Víctor Uc-Cetina, Carlos Brito-Loeza, and Hugo Ruiz-Piña, “Chagas parasites detection through Gaussian discriminant analysis”, Abstraction and Application Magazine 8, 2014.
  12. Roger Soberanis-Mukul, Víctor Uc-Cetina, Carlos Brito-Loeza, Hugo Ruiz-Piña, “An automatic algorithm for the detection of Trypanosoma cruzi parasites in blood sample images”, Computer methods and programs in biomedicine 112(3):633-639, 2013.
  13. Carlos Brito-Loeza and Ke Chen, “Fast iterative algorithms for solving the minimization of curvature-related functionals in surface fairing”, International Journal of Computer Mathematics, 90(1):92-108, 2013.
  14. Noppadol Chumchob, Ke Chen and Carlos Brito-Loeza, “A new variational model for removal of combined additive and multiplicative noise and a fast algorithm for its numerical approximation”, 90(1):140-161, 2013.
  15. Noppadol Chumchob, Ke Chen and Carlos Brito-Loeza, “A Fourth Order variational Image Registration Model and Its Fast Multigrid Algorithm”, SIAM Multiscale Modeling and Simulation, 9(1):89-128, 2011.
  16. Carlos Brito-Loeza and Ke Chen, “Fast Numerical Algorithms for the Euler’s Elastica Inpainting Model”, International Journal of Modern Mathematics, 5(2):157-182, 2010.
  17. Carlos Brito-Loeza and Ke Chen, “Multigrid Algorithm for High-Order Denoising”, SIAM Journal on Imaging Sciences, 3(3):363-389, 2010.
  18. Carlos Brito-Loeza and Ke Chen, “On High Order Denoising Models and Fast Algorithms for Vector-valued Images”, Image Processing, IEEE Transactions on, 19(6):1518-1527, 2010.
  19. Carlos Brito-Loeza and Ke Chen, “Multigrid Method for a Modified Curvature Driven Diffusion Model for Image Inpainting”, Journal of Computational Mathematics, 26(6): 856-875, 2008.

Selected talks

  1. A Variational Model for Binary Classification in the Supervised Learning Context, The Fourth International Workshop on Image Processing Techniques and Applications, 22-23 July 2019, CMIT, University of Liverpool, UK.
  2. Una visión diferente de los procesos de segmentación y registro de imágenes médicas, XLI Congreso Nacional de Ingeniería Biomédica CNIB2018 18 al 20 de octubre del 2018 León, Guanajuato, México.
  3. Variational methods for imaging and supervised learning, Zhejiang University of Science and Technology, China, May 12, 2018 - May 20, 2018.
  4. A one week course on mathematical modeling and solutions of different imaging and supervised learning problems using variational techniques,  Nanchang University, ChinaApril 27, 2018 – May 12, 2018.
  5. A Gaussian Curvature Based Denoising Model for Non-Gaussian Noise, SIAM Conference on Imaging Science, May 23-26, Hotel Albuquerque at Old Town, Albuquerque, New Mexico, USA, 2016.
  6. Fringe Analysis Using Curvature Models, SIAM Conference on Imaging Science, May 23-26, Hotel Albuquerque at Old Town, Albuquerque, New Mexico, USA, 2016.
  7. Image Denoising Using the Gaussian Curvature of the Image Surface, SIAM Conference on Imaging Science, May 12-14, Hong Kong Baptist University, Hong Kong, 2014.
  8. High order models and fast algorithms for fairing variational implicit surfaces, SIAM Conference on Imaging Science, May 20-22, Philadelphia, Pennsylvania, USA, 2012.
  9. On numerical algorithms for level set and curvature based models for surface fairing. 24th. Biennial Conference on Numerical Analysis, University of Strathclyde, Glasgow, UK, 2011.
  10. On high order variational models for blind image deblurring, International Workshop on Image Processing Techniques and Applications, 22-23 June, CMIT, Liverpool, UK, 2011.
  11. High-Order Vector-Valued Models for Image Restoration, SIAM Conference on Imaging Science, April 12th - 14th, Chicago, Illinois, USA, 2010.
  12. Multigrid Algorithms for High Order Variational Models with Applications to Digital Image Denoising and Inpainting, 23rd. Biennial Conference on Numerical Analysis, University of Strathclyde, Glasgow, UK, 2009.

Current students

  1. Moises Uc Cetina. Aprendizaje máquina por comparación usando métodos variacionales. (PhD)
  2. Rafael Viana Cámara.  Análisis y procesamiento de imágenes ecocardiográficas en modelo murino. (M.Sc)
  3. Rubén Couoh KuNavegación robótica en interiores utilizando una cámara RGB-D y sensores inerciales  (M.Sc)

Former students

  1. Desarrollo de un Sistema de Visión Computacional para el Vuelo Autónomo de un Vehículo Aéreo no Tripulado, Manuel Poot Chin, 2019. 
  2. Proceso de Ensamblado y Desarrollo de un Entorno de Simulación de un Dron, Carlos Acosta Montalvo, 2019.
  3. A Brief Presentation on the Calculus of Variations with Applications to Supervised Learning, Carlos Brito Pacheco, 2018.
  4. Análisis  Computacional  de  Células  Procesadas  por  Electroforesis  en  Gel  (Ensayo  Cometa), Javier Luna González, 2018.
  5. Diseño de un Sistema Embebido para el Reconocimiento Automático de Actividades Físicas Usando Aprendizaje Supervisado, Geenkel Coss Lara, 2018.
  6. Métodos de conjuntos de nivel para la evolución interactiva de superficies implícitas en entornos virtuales de sistemas hápticos, Josué Tadeo Moreno Vázquez, 2015. 
  7. Algoritmo de segmentación de objetos basado en la forma con aplicación en sistemas de vigilancia, Erberth Jesús Castillo Ceh, 2015.
  8. Clasificación en tiempo real de imágenes hiperespectrales de percepción remota usando múltiples GPUs y un CPU multinúcleo, Felipe de Jesús Solís, 2014.
  9. Algoritmos de segmentación de Trypanosoma cruzi en imágenes de muestras sanguíneas, Roger David Soberanis Mukul, 2014. Currently PhD student at Technische Universität München.
  10. Algoritmos para diseñar plantillas de convolución que determinan características tipo Haar, César Iván Cobos May, 2014. Currently Phd student at Texas A&M University
  11. Modelo de Contornos Activos para la Segmentación de Parásitos en Imágenes de Sangre, Juan Antonio Ríos Briceño, 2013.
  12. Análisis, Construcción y Evaluación de un robot delta, David Felipe Morales Aldana, 2013. Currently Phd student at The University of Manchester, UK.
  13. Método Actor-Critico para tareas de aprendizaje por refuerzo en espacios de estados y una acción con parámetros continuos, Francisco Coral Sabido, 2013. Currently Phd student at Texas A&M University
  14. Detección de Trypanosoma Cruzi en Imágenes obtenidas a partir de muestras sanguíneas, Roger David Soberanis Mukul, 2012.
  15. Paralelización del Método de los Contornos Activos, Juan Antonio Ríos Briceño, 2011.