superviseddescent is a C++11 implementation of the supervised descent method, which is a generic algorithm to perform optimisation of arbitrary functions.

There are two main advantages compared to traditional optimisation algorithms like gradient descent, L-BFGS and the like:

• The function doesn't have to be differentiable. It works with arbitrary functions, for example with the HoG operator (which is a non-differentiable function)
• It might be better at reaching a global optimum - give it a try!

The theory is based on the idea of Supervised Descent Method and Its Applications to Face Alignment, from X. Xiong & F. De la Torre, CVPR 2013 (http://ieeexplore.ieee.org/xpl/articleDetails.jsp?tp=&arnumber=6618919)

• Generic implementation, can be used to optimise arbitrary parameters and functions
• Fast, using Eigen for matrix operations
• Modern, clean C++11/14
• Header only (compilation/installation only for the examples and tests)
• Fully cross-platform compatible - learned models can be run even on phones

It is a header only library, and can thus be included directly into your project by just adding superviseddescent/include to your projects include directory and including superviseddescent/superviseddescent.hpp.

• Tested with the following compilers: gcc-4.8.2, clang-3.5, Visual Studio 2013
• Needed dependencies: Boost serialization (1.54.0), OpenCV core (2.4.3), Eigen (3.2). Older versions might work as well.

Define a function:

auto h = [](Mat value, size_t, int) { return std::sin(value.at<float>(0)); };

Generate training data (see examples/simple_function.cpp for the (in this case boring) code):

• training labels y_tr in the interval [-1:0.2:1]
• the inverse function values (the ground truth parameters) x_tr
• fixed starting values of the parameters x0 (a constant value in this case).

Construct and train the model, and (optionally) specify a callback function that prints the residual after each learned regressor:

	vector<LinearRegressor> regressors(10);
	SupervisedDescentOptimiser<LinearRegressor> supervisedDescentModel(regressors);
	auto printResidual = [&x_tr](const Mat& currentPredictions) {
		cout << cv::norm(currentPredictions, x_tr, cv::NORM_L2) / cv::norm(x_tr, cv::NORM_L2) << endl;
	};
	supervisedDescentModel.train(x_tr, x0, y_tr, h, printResidual);

The model can be tested on test data like so:

	Mat predictions = supervisedDescentModel.test(x0_ts, y_ts, h);
	cout << "Test residual: " << cv::norm(predictions, x_ts_gt, cv::NORM_L2) / cv::norm(x_ts_gt, cv::NORM_L2) << endl;

Predictions on new data can similarly be made with:

SupervisedDescentOptimiser::predict(Mat x0, Mat y, H h)

which returns the prediction result.

The SupervisedDescentOptimiser can be used in the same way for landmark detection. In this case,

• h is a feature transform that extracts image features like HoG or SIFT from the image (we thus make it a function object, to store the images)
• we don't use the y values (the so called template) to train, because at testing, the HoG descriptors differ for each person (i.e. each persons face looks different)
• the parameters x are the current 2D landmark locations
• the initial parameters x0 are computed by aligning the mean landmark to a detected face box.

class HogTransform
{
public:
	HogTransform(vector<Mat> images, ...HoG parameters...) { ... };
	
	Mat operator()(Mat parameters, size_t regressorLevel, int trainingIndex = 0)
	{
		// shortened, to get the idea across:
		Mat hogDescriptors = extractHoGFeatures(images[trainingIndex], parameters);
		return hogDescriptors;
	}
private:
	vector<Mat> images;
}

Training the model is the same, except we pass an empty cv::Mat instead of y values:

HogTransform hog(trainingImages, ...HoG parameters...);
supervisedDescentModel.train(trainingLandmarks, x0, Mat(), hog, printResidual);

Testing and prediction work analogous.

For the documented full working example, see examples/landmark_detection.cpp.

Using the SupervisedDescentOptimiser for 3D pose estimation from 2D landmarks works exactly in the same way.

• h is the projection function that projects the 3D model to 2D coordinates, given the current parameters
• y are the 2D landmarks, known (or detected) at training and testing time
• x are the rotation and translation parameters (the 6 DOF of the model)
• the initial parameters x0 are all set to 0, with the exception of t_z being -2000.

class ModelProjection
{
public:
	ModelProjection(Mat model) : model(model) {};

	Mat operator()(Mat parameters, size_t regressorLevel, int trainingIndex = 0)
	{
		// parameters is a vector consisting of [R_x, R_y, R_z, t_x, t_y, t_z]
		projectedPoints = projectModel(parameters);
		return projectedPoints;
	};
private:
	Mat model;
}

ModelProjection projection(facemodel);
supervisedDescentModel.train(x_tr, x0, y_tr, projection, printResidual);

Testing and prediction work analogous.

For the documented full working example, see examples/landmark_detection.cpp.

Building of the examples and tests requires CMake>=2.8.11, OpenCV (core, imgproc, highgui, objdetect) and Boost (system, filesystem, program_options, serialization).

• copy initial_cache.cmake.template to initial_cache.cmake, edit the necessary paths
• create a build directory next to the superviseddescent folder: mkdir build; cd build
• cmake -C ../superviseddescent/initial_cache.cmake -G "<your favourite generator>" ../superviseddescent -DCMAKE_INSTALL_PREFIX=install/
• build using your favourite tools, e.g. make; make install or open the solution in Visual Studio.

Doxygen: http://patrikhuber.github.io/superviseddescent/doc/

The examples and the Class List in doxygen are a good place to start.

This code is licensed under the Apache License, Version 2.0

Contributions are very welcome! (best in the form of pull requests.) Please use Github issues for any bug reports, ideas, and discussions.

If you use this code in your own work, please cite the following paper: Fitting 3D Morphable Models using Local Features, P. Huber, Z. Feng, W. Christmas, J. Kittler, M. Rätsch, IEEE International Conference on Image Processing (ICIP) 2015, Québec City, Canada (http://arxiv.org/abs/1503.02330).