About: Tomasi–Kanade factorization

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The Tomasi–Kanade factorization is the seminal work by Carlo Tomasi and Takeo Kanade in the early 1990s. It charted out an elegant and simple solution based on a SVD-based factorization scheme for analysing image measurements of a rigid object captured from different views using a weak perspective camera model. The crucial observation made by authors was that if all the measurements (i.e., image co-ordinates of all the points in all the views) are collected in a single matrix, the point trajectories will reside in a certain subspace. The dimension of the subspace in which the image data resides is a direct consequence of two factors:

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  • The Tomasi–Kanade factorization is the seminal work by Carlo Tomasi and Takeo Kanade in the early 1990s. It charted out an elegant and simple solution based on a SVD-based factorization scheme for analysing image measurements of a rigid object captured from different views using a weak perspective camera model. The crucial observation made by authors was that if all the measurements (i.e., image co-ordinates of all the points in all the views) are collected in a single matrix, the point trajectories will reside in a certain subspace. The dimension of the subspace in which the image data resides is a direct consequence of two factors: 1. * The type of camera that projects the scene (for example, affine or perspective) 2. * The nature of inspected object (for instance, rigid or non-rigid). The low-dimensionality of the subspace is mirrored (captured) trivially as reduced rank of the measurement matrix. This reduced rank of measurement matrix can be motivated from the fact that, the position of the projection of an object point on the image plane is constrained as the motion of each point is globally described by a precise geometric model. (en)
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  • The Tomasi–Kanade factorization is the seminal work by Carlo Tomasi and Takeo Kanade in the early 1990s. It charted out an elegant and simple solution based on a SVD-based factorization scheme for analysing image measurements of a rigid object captured from different views using a weak perspective camera model. The crucial observation made by authors was that if all the measurements (i.e., image co-ordinates of all the points in all the views) are collected in a single matrix, the point trajectories will reside in a certain subspace. The dimension of the subspace in which the image data resides is a direct consequence of two factors: (en)
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  • Tomasi–Kanade factorization (en)
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