PixelRNN

PixelRNN is a deep generative model designed for image generation, particularly pixel-by-pixel modeling of images. The model uses Recurrent Neural Networks, a Deep Learning Technique, to model the conditional distribution of pixels in an image. Unlike CNNs, PixelRNN generates pixel based on dependencies from all of its neighbors, effectively capturing the spatial structure. It is suitable for image generation tasks.

The image above illustrates how PixelRNN models spatial dependencies in images by leveraging sequential context and multi-scale receptive fields.

Features of PixelRNN

• Predicts image pixels one-by-one, conditioned on previous pixels generation.
• Uses Recurrent Architecture for handling dependencies across the entire image.
• Uses autoregression to model conditional probability of each pixel in the image.
• Prevents the network from seeing future pixels during training of model.
• The model can capture all the important dependencies using various LSTM variants.
• It generates sharp, accurate images due to dependency modeling.
• Trained on large unlabeled image dataset using estimation.
• The training time is very high and the process is significantly slow.
• The architecture of the model is very complex and can be tough to interpret.

Mathematical Principle

Let x = (x_1, x_2, ..., x_n) be the pixel sequence of an image. Let's look at the mathematical representation of the model PixelRNN:
PixelRNN models the joint distribution as: P(x) = \prod_{i=1}^{n} P(x_i | x_1, ..., x_{i-1})

For RGB pixels: P(x_{i}) = P(R_i | x_{<i}) \cdot P(G_i | x_{<i}, R_i) \cdot P(B_i | x_{<i}, R_i, G_i)

PixelRNN Workflow

Common Terms

1. Pixel Conditioning: Each Pixel prediction is conditioned.
2. Loss Function is calculated based on actual vs predicted value.

Detailed Working

• The Pixel Recurrent Neural Network or PixelRNN is a groundbreaking architecture that seeks to model the joint distribution of pixel intensities in a generative framework, adhering to the causal and sequential modeling constraints inherent in natural image generation.
• The underpinning hypothesis of the PixelRNN is that each pixel's probability distribution is conditionally dependent on a fixed permutation of all preceding pixels, making it an autoregressive model in the highest-dimensional sense.
• Rather than embracing the simplicity of regressing pixel intensities, PixelRNN models each channel as a categorical distribution over 256 possible values. The model is trained based on sequential modelling.
• The finally generated image is based on these predictive probabilistic-approach based development.

Strengths of PixelRNN

1. Captures dependencies effectively.
2. High-quality image generation.
3. Flexible generation of images.
4. Handles variable-length inputs.
5. Easy to integrate with image inpainting pipelines.

Key Applications of PixelRNN

• Handwritten Digit Generation
• Image Inpainting
• Anomaly Detection
• Scene Understanding

Disadvantages of PixelRNN

1. Slow modelling is a drawback
2. Doesn't perform well on large image
3. High Training time
4. Complex architecture and might be tough to interpret