A sampled single dimensional signal is a vector. A sampled image is a matrix. Is video considered a rank-3 tensor since it is a set of images stacked on top of each other?

  • $\begingroup$ Tensor is not just a higher rank array, it must be independent of the coordinate system. In your case I'd say that a video is a rank-3 array. $\endgroup$
    – Sturm
    Sep 26 '13 at 22:33
  • $\begingroup$ So, by independent of coordinate system, do you mean that a tensor does not have a basis? Sorry, brand new to Tensors! $\endgroup$
    – user5535
    Sep 26 '13 at 23:00
  • $\begingroup$ Tensor is used for multi-way array; not for the tensor field. So it is just a generic name for multi-way array in machine learning community (search: tensor factorization). So, from this point, yes video is a tensor, it is an array of dimension $m\times n\times 3$. $\endgroup$
    – Deniz
    Jan 9 '14 at 22:11
  • $\begingroup$ @Sturm I think you might be mixing up the terms "tensor" and "tensor field". I think depending on the field you are in, these are sometimes used interchangeably. $\endgroup$
    – val
    Jan 9 '14 at 23:40

yes - a video signal would be considered 3rd order tensor.

scalars are 0-order tensors, vectors are 1st order tensors, matrices are 2nd order tensor, data volumes are 3rd order tensors and so on for multi-dimensional arrays.


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