Visual Information Processing Group
Home Members Publications Projects Events Resources Ph. D.

LFGPC: Learning Optimal Filters for Gaussian Process Classification


P. Ruiz, R. Molina, and A.K. Katsaggelos, “Joint Data Filtering and Labeling using Gaussian Processes and Alternating Direction Method of Multipliers”, IEEE Transactions on Image Processing, vol. 25, no. 7, 3059-3072, July 2016. [BibTeX entry][Abstract][ (1614 KB.)]


Sequence labeling aims at assigning a label to every sample of a signal (or pixel of an image) while taking into account the sequentiality (or vicinity) of the samples. To perform this task, many works in the literature first filter and then label the data. Unfortunately, the filtering, which is performed independently from the labeling, is far from optimal and frequently makes the latter task harder. In this work, a novel approach which trains a Gaussian Process (GP) classifier and estimates the coefficients of an optimal filter jointly is presented. The new approach, based on Bayesian modeling and Alternating Direction Method of Multipliers (ADMM) optimization, performs both tasks simultaneously. All unknowns are treated as stochastic variables which are estimated using Variational Inference and filtering and labeling are linked with the use of ADMM. In the experimental section synthetic and real experiments are presented to compare the proposed method with other existing approaches.

Representation of joint filtering and GP classification system


Original Signal Coefficients

Filter Coefficients
Filtered Features

A synthetic example

Our  groundtruth is a checkerboard. We generate the observations adding Gaussian noise of variance 0.16, and means 0.25 and 0.75 for Black and White classes, respectively. Here we show the original groundtruth and the noisy observations:


Applying the proposed method, the following results are obtained:

Filter sizes
3 x 3
5 x 5
7 x 7
9 x 9
Obtained filters
Filtered observations
Classification maps



Matlab Code and Synthetic Dataset

MATLAB code and synthetic dataset can be downloaded here.


The programs are granted free of charge for research and education purposes only. Scientific results produced using the software provided shall acknowledge the use of the GPF implementation provided by us. If you plan to use it for non-scientific purposes, don't hesitate to contact us.

Because the programs are licensed free of charge, there is no warranty for the program, to the extent permitted by applicable law. except when otherwise stated in writing the copyright holders and/or other parties provide the program "as is" without warranty of any kind, either expressed or implied, including, but not limited to, the implied warranties of merchantability and fitness for a particular purpose. The entire risk as to the quality and performance of the program is with you. Should the program prove defective, you assume the cost of all necessary servicing, repair or correction.

In no event unless required by applicable law or agreed to in writing will any copyright holder, or any other party who may modify and/or redistribute the program, be liable to you for damages, including any general, special, incidental or consequential damages arising out of the use or inability to use the program (including but not limited to loss of data or data being rendered inaccurate or losses sustained by you or third parties or a failure of the program to operate with any other programs), even if such holder or other party has been advised of the possibility of such damages.

Visual Image Processing
University of Granada