Structure from motion

Structure from motion (SfM) is a range imaging technique; it refers to the process of estimating three-dimensional structures from two-dimensional image sequences which may be coupled with local motion signals. It is studied in the fields of computer vision and visual perception. In biological vision, SfM refers to the phenomenon by which humans (and other living creatures) can recover 3D structure from the projected 2D (retinal) motion field of a moving object or scene.

Obtaining 3D information from 2D images

File:DSM construction site.jpg

Digital surface model of motorway interchange construction site

File:SfM PPT GUI vs PHOTO.png

Real photo x SfM with texture color x SfM with simple shader. Made with Python Photogrammetry Toolbox GUI and rendered in Blender with Cycles.

File:Bezmiechowa DSM 3D 2010-05-29 Pteryx UAV.jpg

Bezmiechowa airfield 3D Digital Surface Model extracted from data collected during 30min flight of Pteryx UAV

Humans perceive a lot of information about the three-dimensional structure in their environment by moving through it. When the observer moves and the objects around the observer move, information is obtained from images sensed over time.^[1]

Finding structure from motion presents a similar problem to finding structure from stereo vision. In both instances, the correspondence between images and the reconstruction of 3D object needs to be found.

To find correspondence between images, features such as corner points (edges with gradients in multiple directions) are tracked from one image to the next. One of the most widely used feature detectors is the SIFT (Scale-invariant feature transform). It uses the maxima from a Difference-of-Gaussians (DOG) pyramid as features. The first step in SIFT is finding a dominant gradient direction. To make it rotation-invariant, the descriptor is rotated to fit this orientation.^[2] Another common feature detector is the SURF (Speeded Up Robust Features).^[3] In SURF, the DOG is replaced with a Hessian matrix-based blob detector. Also, instead of evaluating the gradient histograms, SURF computes for the sums of gradient components and the sums of their absolute values.^[4] The features detected from all the images will then be matched. One of the matching algorithms that track features from one image to another is the Lukas-Kanade tracker.^[5]

Sometimes some of the matched features are incorrectly matched. This is why the matches should also be filtered. RANSAC (Random Sample Consensus) is the algorithm that is usually used to remove the outlier correspondences. In the paper of Fischler and Bolles, RANSAC is used to solve the Location Determination Problem (LDP), where the objective is to determine the points in space that project onto an image into a set of landmarks with known locations.^[6]

The feature trajectories over time are then used to reconstruct their 3D positions and the camera's motion.^[7] An alternative is given by so-called direct approaches, where geometric information (3D structure and camera motion) is directly estimated from the images, without intermediate abstraction to features or corners.^[8]

There are several approaches to structure from motion. In incremental SFM, camera poses are solved for and added one by one to the collection. In global SFM, the poses of all cameras are solved for at the same time. A somewhat intermediate approach is out-of-core SFM, where several partial reconstructions are computed that are then integrated into a global solution.

SfM for Cultural Heritage structure analysis

Cultural heritage is present everywhere. Its structural control, documentation and conservation is one of humanities main duties (UNESCO). Under this point of view, SfM is used in order to properly estimate situations as well as planning and maintenance efforts and costs, control and restoration. Because serious constraints often exist connected to the accessibility of the site and impossibility to install invasive surveying pillars that did not permit the use of traditional surveying routines (like total stations), SfM provides a non-invasive approach for the structure, without the direct interaction between the structure and any operator. The use is accurate as only qualitative considerations are needed. It is fast enough to respond to the monument’s immediate management needs.^[9] The first operational phase is an accurate preparation of the photogrammetric surveying where is established the relation between best distance from the object, focal length, the ground sampling distance (GSD) and the sensor’s resolution. With this information the programmed photographic acquisitions must be made using vertical overlapping of at least 60% (figure 02).^[10]

References

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↑ Guidi. G.; Beraldin, J.A.; Atzeni, C. High accuracy 3D modelling of cultural heritage: The digitizing of Donatello. IEEE Trans. Image Process. 2004, 13, 370-380
↑ Kraus, K., 2007. Photogrammetry: Geometry from Image and Laser Scans. Walter de Gruyter, 459 pp. ISBN 978-3-11-019007-6

External links