Pokemon Color Transfer

Background

Palette Extraction

Palette extraction is the process of analyzing an image and summarizing its millions of pixel colors into a small, representative set of key colors — known as a color palette. Instead of working directly with every pixel’s RGB value, palette extraction identifies the dominant or most perceptually important colors that define the visual appearance of the image. A palette typically contains only 4–8 colors, yet these colors capture the essential chromatic structure of the image. This compact representation removes noise, eliminates redundant colors, and preserves the underlying style of the original artwork. We implement two palette extraction methods.

K-Means

We use K-Means to cluster pixel values and use its center as palette. To avoid clustering on millions of pixels, we quantize RGB space into 16 bins per channel. For each pixel with RGB value $(r,g,b)$:

$$(\lfloor \frac{r}{16}\rfloor ,\lfloor \frac{g}{16}\rfloor ,\lfloor \frac{b}{16}\rfloor )$$

For each non-empty bin, we count pixels and compute average LAB value of all pixels in that bin. To avoid randomness in K-Means, the method uses a weighted farthest-point initialization. We select the bin with the largest weight as the first center. For each new center, compute squared distance from existing centers and apply attenuation:

$${w_i}^{\prime }=w_i\cdot (1-e^{-d_i^2/{\sigma }_a^2})$$

We then pick the bin with the largest attenuated weight. Each histogram bin $i$ with LAB color $x_i$ and weight $w_i$ is assigned to the nearest center. The center update rule is:

$$C_j=\frac{\sum _{i\in j}{w}_i\cdot x_i}{\sum _{i\in j}{w}_i}$$

Black and white anchors remain fixed. The convergence criterion is:

$$\Vert C_{\text{new}}-C_{\text{old}}{\Vert }^2<10^{-4}$$

Blind Separation Palette Extraction (BSS-LLE Method)

This second method treats palette extraction as a blind unmixing problem with spatial smoothness constraints. It is computationally more expensive but yields globally coherent palettes.

Each pixel forms a 5-D feature vector:

$$X=[R,G,B,\alpha x,\alpha y]$$

where: $(R,G,B)$ ∈ $[0,1]$, $(x,y)$ are normalized coordinates, $\alpha$ controls spatial smoothness. For each pixel, we find $K=30$ nearest neighbors and compute LLE weights by solving:

$$Gw=\mathrm{𝟏},G=(X_j-X_i)(X_j-X_i{)}^{\mathrm{\top }}+ϵI$$

3. Normalize:

$$\sum _j{w}_j=1$$

This defines a sparse weight matrix $Z$.

Construct Laplacian:

$$L=I-Z,L^{T}L$$

We assume each pixel’s color can be expressed as a mixture of $m$ palette colors:

$$I=WC$$

Where $W\in {ℝ}^{N\times m}$ are mixture weights, and $C\in {ℝ}^{m\times 3}$ are palette colors. We minimize:

$$\Vert I-WC{\Vert }^2+{\lambda }_s\Vert W-ZW{\Vert }^2+{\lambda }_u\Vert W\mathrm{𝟏}-\mathrm{𝟏}{\Vert }^2+{\lambda }_{sp}\Vert W{\Vert }_0$$

The optimization uses alternating minimization:

1. Update W (closed-form linear system) 2. Hard-threshold W to enforce sparsity 3. Update C by solving

$$(W^{T}W)C=W^{T}I$$

4. Increase β to gradually enforce sparsity (continuation method)

The learned palette may lie off-manifold. Thus each palette color is replaced by the mean of its nearest real RGB pixels. This ensures interpretability and consistent color reproduction.

Final Output

Both methods return a palette:

$$\{(R_1,G_1,B_1),\dots ,(R_m,G_m,B_m)\}.$$

Methods

In this section, we describe the methods we use to transfer color between pokemons.

Results

Table 1: Quantitative Evaluation Results on Bulbasaur and Squirtle

Metric	Baseline	Clustering	Clustering-NP	Convex Hall	NS	NS-S
FID	1	2	3	4	5	6
Histogram Similarity	1	2	3	4	5	6
CIELAB	1	2	3	4	5	6
CIE94	1	2	3	4	5	6
CIEDE2000	1	2	3	4	5	6
SSIM	1	2	3	4	5	6
VGG Latent Space Distance	1	2	3	4	5	6

Appendix II

Wenxiao Cai:

Yifei Deng: