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gpufilter stands for GPU Recursive Filtering (paper 1). Additionally, filtering can also be regarded as Prefix Scans or Sums and Summed-area Tables (paper 1) or Integral Images. The main goal of this project is to provide the baseline code in C/C++/CUDA for computing the fastest boundary-aware recursive filtering (paper 3) running on the GPU (graphics processing unit), i.e. a massively-parallel processor The fastest means fastest to date (as the last published paper) and boundary awareness means closed-form exact (i.e. no approximations). The idea of boundary awareness is to compute the exact initial feedbacks needed for recursive filtering infinite input extensions (paper 3). Besides serial interconnection (papers 1 and 3), one can also compute a parallel interconnection of recursive filters (paper 2) and use this parallelism as a new source of performance improvement. Besides 2D images (papers 1, 2 and 3), one can also compute recursive filtering on 1D and 3D input (paper 4).

Please keep in mind that this code is just to check the performance and accuracy of the recursive filtering algorithms on a 2D random image of 32bit floats. Nevertheless, the code can be specialized for 1D or 3D inputs, and for reading any given input and data type.


The project contains the mathematical derivations and algorithms described in the following papers:

  1. GPU-Efficient Recursive Filtering and Summed Area Tables
  2. Efficient finite impulse response filters in massively-parallel recursive systems
  3. Parallel Recursive Filtering of Infinite Input Extensions
  4. GPU efficient 1D and 3D recursive filtering

Getting started

The code is in C/C++/CUDA and has been tested in an NVIDIA GTX Titan X. Jupyter notebooks are included for explanations purposes only. The following sequence of commands assume a working computer environment with CMake and the CUDA SDK (see prerequisites below). It compiles all the algorithms for testing in a range of recursive filter orders. The total compilation time may take tens of minutes to complete.

mkdir build
cd build
cmake ..

It may be the case (depending on your environment) that the cmake command line must be properly configured (for instance to access the proper host compiler):

cmake -DCUDA_HOST_COMPILER=/usr/bin/g++ ..

Or that you need to change the sm_61 (for Pascal) architecture to another target architecture matching your GPU hardware in the root CMakeLists.txt file.

To run the algorithms (paper 1 and 3) after compiling, execute:


replacing N for the desired algorithm (3-6) and R for the desired filter order (1-5). There are also three extra algorithms (paper 1 and 3) that can be called by:


where the first is the algorithm 5 fusioned with 4, the second is the algorithm 5 with varying coefficients, and the third is the summed-area table algorithm.

There are also other algorithms related to parallel interconnection of causal and anticausal filters, extending to both recursive and non-recursive filtering (paper 2). Since they are not fully integrated with the main source code, they are stored here for reference purposes only:



The project has been successfully compiled and tested using the following environment:

  • Ubuntu 16.04
  • CUDA 8.0
  • gcc/g++ 5.4.0
  • CMake 3.5.1
  • Python 2.7.6
  • Pandas 0.18.1

Running the tests

First compile all the algorithms (see getting started above) to then be able to run (this may take hours to finish):

cd ../scripts
mkdir results

The bash scripts use a python script (in scripts/) to compute the average of the performance results. The python script depends on the Pandas library, that can be installed via:

pip install pandas


The authors of this project is listed in the AUTHORS file.


This project is licensed under the MIT License - see the COPYING file for details.


GPU Recursive Filtering







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