# Structure from Motion (SfM)

During my undergrad thesis I got very interested in multiple view geometry and 3D reconstruction from uncalibrated cameras. I also continued working on this topic during my graduate studies and as a postdoc.

## A compact formula for the derivative of a 3-D rotation in exponential coordinates

We present a compact formula for the derivative of a 3-D rotation matrix with respect to its exponential coordinates. A geometric interpretation of the resulting expression is provided, as well as its agreement with other less-compact but better-known formulas. To the best of our knowledge, this simpler formula does not appear anywhere in the literature. We hope by providing this more compact expression to alleviate the common pressure to reluctantly resort to alternative representations in various computational applications simply as a means to avoid the complexity of differential analysis in exponential coordinates.

In particular, this work finds applications in optimization approaches that refine the extrinsic camera parameters when these are parametrized using Lie theory.

References:

G. Gallego, A. Yezzi

A compact formula for the derivative of a 3-D rotation in exponential coordinates

Journal of Mathematical Imaging and Vision, vol. 51, no. 3, pp 378-384, Mar. 2015.

## Project “Videosurfing”. Design and implementation of a video-to-3D reconstruction system

In this work, we propose a novel and approach for obtaining 3D models from video sequences captured with hand-held cameras. We define a pipeline that robustly deals with different types of sequences and acquiring devices. Our system follows a divide and conquer approach: after a frame decimation that pre-conditions the input sequence, the video is split into short-length clips. This allows to parallelize the reconstruction step which translates into a reduction in the amount of computational resources required. The short length of the clips allows an intensive search for the best solution at each step of reconstruction which robustifies the system. The process of feature tracking is embedded within the reconstruction loop for each clip as opposed to other approaches. A final registration step merges all the processed clips to the same coordinate frame.

References:

N. Herrero, J.L. Landabaso, G. Gallego, J.C. Pujol-Alcolado

In-loop feature tracking for structure and motion with out-of-core optimization

IEEE International Conference on Image Processing (ICIP) 2010: pp. 2937-2940.

## (A camera autocalibration and 3D reconstruction system)

Engineering Degree Thesis (5-year program), Technical University of Madrid, Spain, Feb. 2004.