Required functionalities

Each group should implement a system with the following functionality:

1. Gold standard F-matrix estimation from known correspondences. (Many of the required functions exist in LAB3, and in OpenCV).
   
2. Computation of an E-matrix from F and known K, and subsequent extraction of R and t from E, and visible-points constraint.
   
3. Robust Perspective-n-point (PnP) estimation for adding a new view and detecting outliers.
4. Bundle adjustment for N cameras (N≥2) using known correspondences, intrinsic camera parameters (K-matrix), and an initial guess for the camera poses.
   
5. Use a sparsity mask for the Jacobian in the Bundle adjustment step (this speedup is absolutely essential if you use scipy.optimize.least_squares). Alternatively, in C++ you can use Ceres Solver, which handles the sparsity in a different way. Yet another option is to use pytorch (Ask your guide for details).
6. Evaluate the robustness to noise in the implemented system, by measuring the camera pose errors of your reconstruction. Details can be found here.

In addition to the above, groups with four students should implement at least one of the following functionalities:

1. Visualisation of the 3D model. Pick one of the following:
   • Use Poisson surface reconstruction (or screened PSR) to obtain a volumetric representation. Try e.g. the version in Meshlab, or Kazhdan's own implementation (has more options). Both require you to estimate colour and surface normals for the 3D-points, and saving these in PLY format. Use visibility in cameras to determine normal signs. See Kazhdan and Hoppe for a theoretical description.
   • Use space carving (as in Fitzgibbon, Cross and Zisserman) to generate a volumetric representation of your object.
   • Use texture patches (e.g. PMVS) or billboards, to represent the texture of the estimated 3D model.
2. Find correspondences between pairs of views, and remove false matches using epipolar geometry and cross-checking. (Allows the implemented system to use any image set with known K)
3. Use your own camera to take images of an object, and reconstruct it. This requires estimation of the K-matrix, and possibly lens distortion, followed by image rectification. Note that this also requires finding your own correspondences (functionality #2), and that you need to carefully plan how to take the images.
4. Densify your initial sparse SfM model, using dense stereo between selected frame pairs. E.g. PatchMatch can be used, or using one of the approaches in the Multiview Stereo tutorial.
5. Use next-best-view selection (e.g. as in Schönberger et al., or some simplified form thereof) to select the order in which cameras are added to SfM.
6. Replace Incremental SfM with Global SfM. Use global estimation of all rotation matrices as an initialisation of Bundle Adjustment (as in Martinec and Pajdla).
7. Write your own non-linear solver, e.g.~Levenberg-Marquardt (see the report by Madsen et al.), and use the Shur-Complement Trick to speed up the computation of the update step (see the IREG compendium).

Groups with five students are required to implement two of the above, and groups with six members should implement three.

Datasets

The Visual Geometry Group at Oxford University has a number of datasets availabe on their web site, e.g., the dinosaur sequence:

• Multiple-views datasets from the Visual Geometry Group at Oxford University

These data sets contain coordinates of image points that are tracked between images, which means that there is both some amount of noise on the image coordinates and that these points are not visible over the entire sequence since they are occluded in some or even most of the images. The data sets contain some type of ground truth in terms of estimated camera matrices for each view.

Notice that the dinosaur sequence is a turn-table sequence that is generated by rotating the object around a fixed axis. The acquisition geometry of this dataset makes it sensitive to the quality of the used point correspondences.

For debugging it is useful to work with a noise free dataset, and for this purpose we have "cleaned" the dinosaur data set from any noise (up to the numerical accuracy of Matlab) and produced a dataset that contains 2D image points, 3D points, and the camera matrices. These are found in the BAdino2.mat file on the local ISY file system:

• /courses/TSBB15/sequences/BAdino/BAdino2.mat

The EPFL multi-view stereo datasets are also highly recommended:

• Multi-view stereo datasets

They all have undistorted high-res images, with ground-truth camera poses and known intrinsic camera parameters. However, you have to find the correspondences yourself here.

Python code

Please look at the utility code for CE3. You can find it at /courses/TSBB15/python/ in the computer labs. Also look at the Extra exercises in the lab sheet, they are meant to help you get started with the projects.

Matlab code

In the case that you use Matlab for solving the tasks in this project there are some software packages, that will spare you from implementing all functionalities yourself:

• The Visual Geometry Group at Oxford University
• Peter Kovesi at the University of Western Australia
• The LSQNONLIN optimiser in Matlab. Note that LSQNONLIN is very slow, unless a sparsity mask is used.
  
• P3P by Laurent Kneip. Note: Documentation is weird. You need to verify the input and output behaviour yourself on synthetic data (e.g. for coordinate axes). See this example for how to do this in Matlab.
  

C code

You are absolutely NOT allowed to use complete SfM systems such as COLMAP, SBA, Bundler, Visual SFM, SSBA, and OpenMVG.