receptive field

http://shawnleezx.github.io/blog/2017/02/11/calculating-receptive-field-of-cnn/

The receptive field (RF) ${\mathrm{lklk of\; layer kk is:}}^{}$

where ${\mathrm{lk-1lk-1 is\; the\; receptive\; field\; of\; layer k-1k-1, fkfk is\; the\; filter\; size\; (height\; or\; width,\; but\; assuming\; they\; are\; the\; same\; here),\; and sisi is\; the\; stride\; of\; layer ii.}}^{}$

The formula above calculates receptive field from bottom up (from layer 1). Intuitively, RF in layer $\mathrm{kkcovers (fk-1)\ast sk-1(fk-1)\ast sk-1 more\; pixels\; relative\; with\; layer k-1k-1.\; However,\; the\; increment\; needs\; to\; be\; translated\; to\; the\; first\; layer,\; so\; the\; increments\; is\; a\; factorial\; —\; a\; stride\; in\; layer k-1k-1 is\; exponentially\; more\; strides\; in\; the\; lower\; layers.}$