gram_savitzky_golay

C++ Implementation of Savitzky-Golay filtering based on Gram polynomials, as described in

• General Least-Squares Smoothing and Differentiation by the Convolution (Savitzky-Golay) Method

Installation

From Ubunu packages

# Make sure you have required tools
sudo apt install apt-transport-https lsb-release ca-certificates gnupg
# Add our key
sudo apt-key adv --keyserver 'hkp://keyserver.ubuntu.com:80' --recv-key F6D3710D0B5016967A994DFFA650E12EFF6D3EDE
# Add our repository
echo "deb https://dl.bintray.com/arntanguy/ppa-head bionic main" | sudo tee -a /etc/apt/sources.list.d/arntanguy-head.list
# Install packages
sudo apt install libgram-savitzy-golay-dev

From source

mkdir build && cd build
cmake -DCMAKE_BUILD_TYPE=Release ..
make
sudo make install

How to include in your projects?

This package uses a modern cmake approach and exports its targets. To include in your own project, simply use:

cmake_minimum_required(VERSION 3.1)
set(CMAKE_CXX_STANDARD 11)

project(Example LANGUAGES CXX)

# Find the state-observation package and all its dependencies (Eigen)
find_package(gram_savitzky_golay REQUIRED)

# Creates a new executable and link it with the `gram_savitzky_golay` target
add_executable(Example example.cpp)
target_link_libraries(Example PUBLIC gram_savitzky_golay::gram_savitzky_golay)

Example

#include <gram_savitzky_golay/gram_savitzky_golay.h>

// Window size is 2*m+1
const size_t m = 3;
// Polynomial Order
const size_t n = 2;
// Initial Point Smoothing (ie evaluate polynomial at first point in the window)
// Points are defined in range [-m;m]
const size_t t = m;
// Derivation order? 0: no derivation, 1: first derivative, 2: second derivative...
const int d = 0;


// Real-time filter (filtering at latest data point)
gram_sg::SavitzkyGolayFilter filter(m, t, n, d);
// Filter some data
std::vector<double> data = {.1, .7, .9, .7, .8, .5, -.3};
double result = filter.filter(data);


// Real-time derivative filter (filtering at latest data point)
// Use first order derivative
// NOTE that the derivation timestep is assumed to be 1. If this is not the case,
// divide the filter result by the timestep to obtain the correctly scaled derivative
// See Issue #1
d=1;
gram_sg::SavitzkyGolayFilter first_derivative_filter(m, t, n, d);
// Filter some data
std::vector<double> values = {.1, .2, .3, .4, .5, .6, .7};
// Should be =.1
double derivative_result = first_derivative_filter.filter(values);

Filtering Rotations

#include <gram_savitzky_golay/spatial_filters.h>

gram_sg::SavitzkyGolayFilterConfig sg_conf(50, 50, 2, 0);
gram_sg::RotationFilter filter(sg_conf);

filter.reset(Eigen::Matrix3d::Zero());

// Add rotation matrices to the filter
filter.add(Eigen::Matrix3d ...)
filter.add(Eigen::Matrix3d ...)
filter.add(Eigen::Matrix3d ...)

// Filter rotation matrices (weighted average of rotation matrices followed by an orthogonalization)
// See Peter Cork lecture here:
// https://www.cvl.isy.liu.se/education/graduate/geometry2010/lectures/Lecture7b.pdf
const Eigen::Matrix3d res = filter.filter();

This header also contains a filter for homogeneous transformations defined as Eigen::Affine3d, and a generic filter for eigen vectors.