Where Are Pixels? -- a Deep Learning Perspective

Technically, an image is a function that maps a continuous domain, e.g. a box $[0, X] \times [0, Y]$, to intensities such as (R, G, B). To store it on computer memory, an image is discretized to an array array[H][W], where each element array[i][j] is a pixel. How does a discrete pixel relate to the abstract notion of the underlying continuous image? These basic questions play an important role in computer graphics & computer vision algorithms. This article discusses these low level details, and how they affect our CNN models and deep learning libraries.