I was reading a computer vision paper for 3D reconstruction and was a bit confused by two notations: https://www.researchgate.net/publication/327805907_3D_Image_Reconstruction_from_Multi-Focus_Microscope_Axial_Super-Resolution_and_Multiple-Frame_Processing
- $f \in R^{{N_x}\times{N_y}\times{N_z}}$, which denotes a 3D object
- $ h(x,y;z) $
What is meant by the $N_x \times N_y \times N_z$ term and the ; symbol in h?
Sorry if this seems ignorant, I am not a math major :')
This is a notation peculiar to ML papers; what they mean by $\mathbb{R}^{N_x \times N_y \times N_z}$ is actually $\mathbb{R}^{N_x} \times \mathbb{R}^{N_y} \times \mathbb{R}^{N_z}$, or in simpler terms, $f$ is a three dimensional array with each dimension of length $N_x, N_y$ and $N_z$.
The semicolon is sometimes used to emphasize a semantic difference between the function arguments, but in this case, after a quick look through the paper, it seems unnecessary.