Pix2pix

Definition

Pix2pix model is a Conditional GAN model designed for image-to-image translation tasks.

Architecture

The generator of the model has a U-Net architecture. The pix2pix model takes an input image and learns to generate a corresponding output image. The training set consists of pairs of two images $\{(x_1,y_1),(x_2,y_2),\dots ,(x_n,y_n)\}$

Objective Function

The objective function of Pix2pix model is defined as ${\min }_{{\theta }_G}{\max }_{{\theta }_D}[\underset{\text{Adversarial Loss}}{\underbrace{E_{y\sim p_y(y)}[\ln D(x,y)]+E_{x\sim p(x)}[\ln (1-D(x,G(x)))]}}+\underset{\text{Reconstruction Loss}}{\underbrace{E_{x\sim p_x(x),y\sim p_y(y)}[||y-G(x)|{|}_1]}}]$