Shape and motion from image streams under orthography: a factorization method

By Carlo Tomasi, Takeo Kanade. 1992

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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].”
A Singular Value Thresholding Algorithm for Matrix Completion (2008, background): “This problem occurs in many areas of engineering and applied science such as machine learning [1, 3, 4], control [42] and computer vision, see [48].”
Streaming PCA and Subspace Tracking: The Missing Data Case (2018, background): “As another example, consider the rigid structure from motion problem in computer vision [3], [4].”
Efficient Joint Segmentation, Occlusion Labeling, Stereo and Flow Estimation (2014, methodology): “There is a very large literature on structure from motion, for example see [23,7,10,21].”
Multiframe Motion Segmentation with Missing Data Using PowerFactorization and GPCA (2008, unknown): “To summarize the amount of motion present in all the sequences , we computed the rotation and translation between all pairs of consecutive frames for each motion in each sequence using the standard factorization method (Tomasi and Kanade 1992).”
Real-time combined 2D+3D active appearance models (2004, methodology): “All of these methods only use the usual orthonormality constraints on the projection matrices [10].”
Visual Modeling with a Hand-Held Camera (2004, methodology): “The approach of Tomasi and Kanade (1992) used an afﬁne factorization method to extract 3D from image sequences.”
Damped Newton algorithms for matrix factorization with missing data (2005, background): “We conclude that, although alternation approaches can be very quick, their propensity to glacial convergence in narrow valleys of the cost function means that averagecase performance is worse than second-order strategies.”
A survey of vision-based methods for action representation, segmentation and recognition (2011, background): “Similar, matrix factorization and rank constraints, as in structure from motion estimation [125], can be used to validate whether point correspondences in two images came from the same single rigid object [112,97].”
Tensor completion for estimating missing values in visual data (2010, background): “The synthetic data T is of size 40 × 40 × 40 × 40. The ranks of the tensor along all four modes are set to [20, 20, 20, 20 ].”
Two Body Problem: Collaborative Visual Task Completion (2019, background): “Simultaneous localization and mapping [84, 74, 24, 12, 67, 77] consider mapping in isolation.”
Multi-view Body Part Recognition with Random Forests (2013, methodology): “We used the 2D annotation to synchronize and calibrate the cameras and the human pose is reconstructed in 3D using the afﬁne factorization algorithm [3, 10, 15, 20].”
Energy-Based Geometric Multi-model Fitting (2012, methodology): “…affine then it could be proved that the motion of a rigid body i.e. the trajectory of its features will live in a 4D subspace (Boult and Brown 1991; Tomasi and Kanade 1992; Vidal et al. 2008) Scatter plot of different solutions obtained by PEARL on one of the examples in Tron and Vidal (2007)…”
Robust Subspace Clustering (2013, methodology): “In some applications such as motion segmentation in computer vision, the dimensions of the subspaces are all equal and known in advance [51].”
Smooth Representation Clustering (2014, background): “…subspaces, with each subspace corresponding to one category or class, e.g., point trajectories of moving objects captured by an afﬁne camera [24], images of several subjects under varying illumination or under different poses [6], and local patches or texture features of pixels/superpixels…”