"Paper Reading" improved textured networks:maximizing quality and diversity in Feed-forward stylization and Texture synthe Sis

Improved textured networks:maximizing quality and diversity in Feed-forward stylization and Texture Synthesis

Https://arxiv.org/abs/1701.02096v1

The main contribution of this article is two points: 1. Introduce instance normalization instead of batch normalization 2. The diversity of texture is increased by allowing the production device to ensemble from Julesz to non-biased sampling.

First, background knowledge

The generator goals in texture synthesis are:

Map i.i.d. Noise vector $z ~n (0,i) to image x, x = g (z) $, generate image x distribution to $q (x) $, the distribution of true target texture is P (x); The goal of the generator should be to make Q (x) infinitely approximate p (x).

Here's a question: in the course of training generator our objective function: P (x) does not have a specific form.

Second, uniformly sample the Julesz ensemble:

1. Julesz's findings:

The visual system distinguishes different texture by average response of different image filters.

2. What is Julesz ensemble?

Defined:

Set $x$ to Image, $ x: \omega/rightarrow r^3 $, \omega = {1,..., H} x {1,... W} $.

Set $ f_l $ for filter, $F _l: \chi x \omega \rightarrow R, L = 1,..., L, f_l (X,u) represents f_l response at Image x,u$.

The Loss function is defined as: $L (x) = \sum_{l=1}^{l} (\mu_l (x)-\hat{\mu}_l) ^2$.

for image X. Julesz Ensemble is a collection of x that satisfies $ \tau_\epsilon = {x \in \chi:l (x) \leq \epsilon$.

The distribution of Julesz ensemble is: $p (x) = \frac{e^{-l (x)/t}}{\int e^{-l (y)/t}dy}.

This makes $p (x) $ have a specific distribution form.

3. KL divergence (Kullback-leibler divergence): used to measure the deviation between two probability distributions: $D _{kl} (p| | Q) $ in practical applications p often represents the true distribution of data, and Q represents the approximation of the theoretical model to P distributions. The Q approximation p can be approximated by minimizing the KL divergence.

For continuous variables:

$ $D _{kl} (p| | Q) = \int_{-\infty}^{\infty} p (x) log \frac{p (x)}{q (x)} dx$$

For discrete variables

$ $D _{kl} (p| | Q) = \sum_i p (i) log \frac{p (i)}{q (i)}. $$

Third, instance normalization/constract normalization

Batch normalization: Global

Instance normaliztion: Partial

"Paper Reading" improved textured networks:maximizing quality and diversity in Feed-forward stylization and Texture synthe Sis