**Colorization Transformer** is a probabilistic [colorization](https://paperswithcode.com/method/colorization) model composed only of [axial self-attention blocks](https://paperswithcode.com/method/axial). The main advantages of these blocks are the ability to capture a global receptive field with only two layers and $\mathcal{O}(D\sqrt{D})$ instead of $\text{O}(D^{2})$ complexity. In order to enable colorization of high-resolution grayscale images, the task is decomposed into three simpler sequential subtasks: coarse low resolution autoregressive colorization, parallel color and spatial super-resolution.

For coarse low resolution colorization, a conditional variant of [Axial Transformer](https://paperswithcode.com/method/axial) is applied. The authors leverage the semi-parallel sampling mechanism of Axial Transformers. Finally, fast parallel deterministic upsampling models are employed to super-resolve the coarsely colorized image into the final high resolution output.

**Embedded Dot Product Affinity** is a type of affinity or self-similarity function between two points $\mathbb{x\_{i}}$ and $\mathbb{x\_{j}}$ that uses a dot product function in an embedding space:

$$ f\left(\mathbb{x\_{i}}, \mathbb{x\_{j}}\right) = \theta\left(\mathbb{x\_{i}}\right)^{T}\phi\left(\mathbb{x\_{j}}\right) $$

Here $\theta\left(x\_{i}\right) = W\_{θ}x\_{i}$ and $\phi\left(x\_{j}\right) = W\_{φ}x\_{j}$ are two embeddings.

The main difference between the dot product and [embedded Gaussian affinity](https://paperswithcode.com/method/embedded-gaussian-affinity) functions is the presence of [softmax](https://paperswithcode.com/method/softmax), which plays the role of an activation function.

Embedded Dot Product Affinity

Non-local Neural Networks

Colorization Transformer

**PointNet** provides a unified architecture for applications ranging from object classification, part segmentation, to scene semantic parsing. It directly takes point clouds as input and outputs either class labels for the entire input or per point segment/part labels for each point of the input.

Source: [Qi et al.](https://arxiv.org/pdf/1612.00593v2.pdf)

Image source: [Qi et al.](https://arxiv.org/pdf/1612.00593v2.pdf)

Source	Colorization Transformer
Year	2000
Data Source	CC BY-SA - https://paperswithcode.com