Yes. The way the Neural Networks that we are learning about here in Course 1 work is that each input (“sample”) needs to be formatted as a vector. Prof Ng has chosen to use column vectors as opposed to row vectors, but that is just a choice he made. For efficiency, we want to handle multiple samples at once using vectorized instructions, so when we have multiple input samples, they are concatenated into a matrix usually called X. The standard convention is to use n_x as the number of features (the number of elements in each input vector) and the number of samples in the given set is called m. So given that each image is “unrolled” into a column vector, the dimensions of X end up being n_x x m. Each “sample” (image) is one column of X.
Of course images normally are represented as 3D arrays with dimensions height x width x channels. The input images here in Course 1 Week 2 are 64 x 64 RGB images, so the arrays are 64 x 64 x 3 with the “channels” being the R, G and B color values for each pixel. 64 * 64 * 3 = 12288, so we have:
n_x = 12288
in this particular case, but the ideas generalize to images of any size.
Then we have to preprocess those images by “unrolling” or “flattening” them from 3D arrays to 1D vectors. They explain this and basically write the logic for you in the Week 2 assignment notebook, but here is a thread which explains in detail how that all works.