The interpretation of structure from motion

By Shimon Ullman. 1979

The interpretation of structure from motion is examined from a computional point of view. The question addressed is how the three dimensional structure and motion of objects can be inferred from the two dimensional transformations of their projected images when no three dimensional information is conveyed by the individual projections. The following scheme is proposed: (i) divide the image into groups of four elements each; (ii) test each group for a rigid interpretation; (iii) combine the results obtained in (ii). It is shown that this scheme will correctly decompose scenes containing arbitrary rigid objects in motion, recovering their three dimensional structure and motion. The analysis is based primarily on the ʻstructure from motion’ theorem which states that the structure of four non-coplanar points is recoverable from three orthographic projections. The interpretation scheme is extended to cover perspective projections, and its psychological relevance is discussed.

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

Citations in the corpus

Lifting Object Detection Datasets into 3D (2015, background): “While the popularity of model-based recognition was falling, interest in multiview 3D reconstruction was rising, powered by breakthroughs in afﬁne structure-from-motion [18], [19], [20] and the adoption of projective geometry [21].”
Object Persistence in Philosophy and Psychology (2007, background): “Such assumptions — for example that objects are rigid and three-dimensional (e.g. Ullman, 1979 ), or that there is a single overhead light source ( Hershberger, 1970 ) — can be wrong in certain circumstances, however, which leads to the familiar visual illusions of depth and lightness.”
Structure from motion photogrammetry in physical geography (2016, methodology): “From the geometrically correct feature correspondences, SfM uses bundle adjustment algorithms to simultaneously estimate the 3D geometry (or structure) of a scene, the different camera poses (extrinsic calibration) and the camera intrinsic parameters (intrinsic calibration) (Ullman, 1979).”
Straightforward reconstruction of 3D surfaces and topography with a camera: Accuracy and geoscience application (2012, methodology): “[ 5 ] The technique described here is based on freely available software that combines the computer vision approaches of ‘ structure-from-motion ’ (SfM) [ Ullman , 1979] and ‘ multiview stereo ’ (MVS) [ Seitz et al. , 2006].”
An overview of ongoing point cloud compression standardization activities: video-based (V-PCC) and geometry-based (G-PCC) (2020, methodology): “Laser range scanner [21] or Structure from Motion (SfM) [22] techniques are employed in the content generation process.”
Determination of 3D human body postures from a single view (1985, methodology): “Ullman [7] used four points of the object over three views to obtain the object structure.”
Optical Flow Estimation (2006, background): “It is a rich source of information that supports a wide variety of visual tasks, including 3D shape acquisition and oculomotor control, perceptual organization, object recognition and scene understanding [16, 21, 26, 33, 35, 38, 45, 47, 50].”
Taking computer vision aloft – archaeological three‐dimensional reconstructions from aerial photographs with photoscan (2011, methodology): “PhotoScan does this by a technique called structure from motion (SFM; Ullman, 1979).”
The Innate Mind: Structure and Contents (2005, background): “, the overhead-illumination principle; Hershberger, 1970) and is widely assumed in many others—including the visual system’s prior assumptions that objects are rigid (Ullman, 1979), that objects are convex (e.”
Using Unmanned Aerial Vehicles (UAV) for High-Resolution Reconstruction of Topography: The Structure from Motion Approach on Coastal Environments (2013, background): “[10], Snavely [11], and Ullman [12] for a detailed discussion on SfM.”
Learned Non-Rigid Object Motion is a View-Invariant Cue to Recognizing Novel Objects (2012, background): “In addition, an object’s 3D structure and shape can be recovered from a sequence of twodimensional (2D) images that depict its rotations in depth using structure-from-motion computations (Ullman, 1979; Grzywacz and Hildreth, 1987).”
Monocular depth estimation based on deep learning: An overview (2020, methodology): “Structure from motion (SfM) [5] is a representative method for estimating 3D structures from a series of”