# Brief Review — Density Modeling of Images Using a Generalized Normalization Transformation

## GDN, Used in Numerous Deep Image/Video Codec

3 min readJul 25, 2022

Density Modeling of Images Using a Generalized Normalization Transformation, GDN, by New York University2016 ICLR, Over 200 Citations(Sik-Ho Tsang @ Medium)

Image Denoising, Transformation, Image Compression

- A more generalized form of normalization technique,
**Generalized Divisive Normalization (GDN)**, is proposed.

# Outline

**Goal****Generalized Divisive Normalization (GDN)****Results**

# 1. Goal

- Given a parametric family of
**transformations**, authors wish to select parameters so as to*y*=*g*(*x*,*θ*)**transform the input vector**:*x*into a standard normal random vector

- where |.| denotes the absolute value of the matrix determinant. If
*py*is the standard normal distribution (denoted*N*), the shape of*px*is determined solely by the transformation. Thus,*g*induces a density model on*x*, specified by the parameters*θ*.

# 2. **Generalized Normalization Transformation (GDN)**

## 2.1. Prior Divisive Normalization

**Divisive normalization**, proposed by (Carandini & Heeger, 2012) has a commonly used form:

- where
are parameters. Loosely speaking, the transformation adjusts responses to lie within a desired operating range, while maintaining their relative values.*θ*={*α*,*β*,*γ*} **A modified form of divisive normalization**that uses a**weighted L2-norm**by (Lyu & Simoncelli, 2008):

## 2.2. Proposed **Generalized Divisive Normalization (GDN)**

- GDN is defined as a composition of a linear transformation followed by a generalized form of divisive normalization:

- The full parameter vector
*θ*consists of the**vectors**, as well as the*β*and*ε***matrices**, for a total of 2*H*,*α*, and*γ**N*+3*N*² parameters (where*N*is the dimensionality of the input space). - Choosing
yields the*εi=αi,j=γi,j*=1**classic form of the divisive normalization transformation**(Carandini & Heeger, 2012), with exponents set to 1. - Choosing
2 and setting*αi,j*=**all elements of**,*β*,*ε***and**, the transformation assumes a*γ*identical**radial form**:

- (Many other forms are mentioned in the paper.)

# 3. Results

- GDN is a better transformation than GSM, obtains higher PSNR.

Later, GDN is used for numerous deep image/video codec.

## Reference

[2016 ICLR] [GDN]

Density Modeling of Images Using a Generalized Normalization Transformation

## Image Restoration

**2016** [RED-Net] [GDN] **2017 **[DnCNN] [MemNet] [IRCNN] [WDRN / WavResNet] **2018 **[MWCNN] **2019 **[IDBP-CNN-IA]

## My Other Previous Paper Readings

## End-to-End Codec

**2016** [GDN]