hilbertmap 0.1.0

Bijective metric-depth <-> RGB colormap along a 3D Hilbert cube walk, as used in the Vision Banana paper.

🎨 3D Hilbert Depth Colormap

Give your depth estimation a fancy new colormap! Here you'll find an implementation of a bijective metric-depth <-> RGB mapping along a 3D Hilbert cube walk, as used in the Vision Banana 🍌 paper [1].

📦 Installation

From PyPI:

pip install hilbertmap

From source:

git clone https://github.com/massimilianoviola/hilbertmap
cd hilbertmap
pip install -e .

🛠️ Usage

Direct encoding/decoding

import numpy as np
from hilbertmap import depth_to_rgb, rgb_to_depth

depth = np.load("depth.npy")          # (H, W) float meters
rgb   = depth_to_rgb(depth)           # (H, W, 3) float in [0, 1]
back  = rgb_to_depth(rgb)             # (H, W) recovered meters

Visualization with matplotlib

import matplotlib.pyplot as plt
import hilbertmap as hm

im = plt.imshow(depth, cmap=hm.cmap(), norm=hm.Norm())
hm.colorbar(im, label="depth (m)")
plt.show()

hm.Norm applies the fixed power transform; hm.colorbar paints only the cmap subset the data actually covers.

🧭 How it works

The seven-edge Hamiltonian path on the RGB cube (left) carries depth values from black at zero to white at infinity. The shape parameters $\lambda$ and $c$ produce different saturation curves (right) that decide how much depth lives on each segment of the walk.

Cube walk	Saturation curves

Unbounded metric depth $d \in [0, \infty)$ is squashed into $[0, 1)$ by a power transform from Barron (2025) [2]:

$$f(d, \lambda, c) = 1 - \left(1 - \frac{d}{\lambda c}\right)^{\lambda + 1}$$

With defaults $\lambda = -3$, $c = 10/3$ this simplifies to $f(d) = 1 - (1 + d/10)^{-2}$, mapping $d \in [0, \infty)$ to $f \in [0, 1)$, which is then read as the fractional position along the edge walk to land on $\mathrm{RGB} \in [0, 1]^3$. The mapping is a strict bijection, so any RGB encoding can be decoded back to metric depth by projecting onto the nearest edge.

Because the utility of accurate metric depth for nearby image content is generally higher than that of distant content, the default parameters $\lambda = -3$, $c = 10/3$ make the cube walk most sensitive in the first few meters and saturate beyond ~35 m. This behavior can be tuned by changing the parameters to get more meaningful color variation on deep outdoor scenes.

📚 References

• V. Gabeur et al. Vision Banana: Image generators are generalist vision learners. arXiv preprint arXiv:2604.20329, 2026. Project page: https://vision-banana.github.io/.
• J. T. Barron. A power transform. arXiv preprint arXiv:2502.10647, 2025.