mobius-mpd 0.1.6

Möbius Perspective Distortion (MPD) data‑augmentation transform.

mobius‑mpd

Möbius Perspective Distortion (MPD) augmentation for PyTorch & Albumentations

Chhipa, Prakash Chandra, et al. "Möbius transform for mitigating perspective distortions in representation learning." European Conference on Computer Vision. Cham: Springer Nature Switzerland, 2024.

Möbius-MPD — Perspective-Distortion Augmentation

---

1 What is perspective distortion?

A camera viewed from an oblique pose changes the apparent shape, size, orientation and angles of objects in the image plane.:contentReference[oaicite:0]{index=0}

---

2 Why perspective distortion is troublesome for computer-vision models?

Camera parameters are hard to estimate, so PD can’t be synthesised easily for training.:contentReference[oaicite:1]{index=1}
Existing augmentation methods are affine and lienar in nature are not able to model perspective distortion.:contentReference[oaicite:2]{index=2}
Lack of perspective distortion data leaves models brittle in the wild for real-world applications—crowd counting, fisheye recognition, person re-ID and object detection all degrade when PD is present.:contentReference[oaicite:3]{index=3}

---

3 What does Möbius-MPD offer?

Möbius-MPD mathmetically models perspective distortion and translate it directly in pixel space with a conformal Möbius mapping

$$ \Phi(z)=\frac{a z + b}{c z + d}, \qquad c!=0 $$

and the real and imaginery compoents of complex parameter c controls the perspectively distorted view generations.

Orientation & intensity control – the signs and magnitudes of (\operatorname{Re}(c)) and (\operatorname{Im}(c)) yield left / right / top / bottom or corner views, scaled continuously.:contentReference[oaicite:4]{index=4}
No camera parameters or real PD images required – the transform alone synthesises realistic PD.:contentReference[oaicite:5]{index=5}
Padding variant – optionally fills black corners with edge pixels.:contentReference[oaicite:6]{index=6}
Proven gains – +10 pp on ImageNet-PD and improvements across crowd counting, fisheye recognition, person re-ID and COCO object detection.:contentReference[oaicite:7]{index=7}

---

Installation

pip install mobius-mpd

or in editable mode:

git clone https://github.com/prakashchhipa/mobius-mpd
cd mobius-mpd
pip install -e .

Usage

PyTorch / torchvision

from torchvision import transforms
from mobius_mpd import MobiusMPDTransform

train_aug = transforms.Compose([
    MobiusMPDTransform(
        p=0.5,      # apply 50% of the time
        min=0.1,    # minimum |c|
        max=0.3,    # maximum |c|
    ),
    transforms.ToTensor(),
])

Albumentations

import albumentations as A
from mobius_mpd import A_MobiusMPDTransform

aug = A.Compose([
    A_MobiusMPDTransform(p=0.7, min=0.05, max=0.25),
])

Parameters

name	default	description
p	1.0	probability of applying the transform
min	0.1	lower bound for the sampled coefficient (
max	0.3	upper bound for the sampled coefficient (
background	"none"	"none" → black corners · "padded" → edge-pixel padding
view_mode	"random"	"random", "uni-direction", or "bi-direction"
view	"random"	orientation; for uni: left / right / top / bottom · for bi: left-top / left-bottom / right-top / right-bottom

Examples for different configurations to generate different views. Set view and/or view_mode to random for augmentaiton purpose.

Background setting with and without padding.

Parent project page: https://prakashchhipa.github.io/projects/mpd/

BibTeX

@inproceedings{chhipa2024mobius,
  title     = {Möbius transform for mitigating perspective distortions in representation learning},
  author    = {Chhipa, Prakash Chandra et al.},
  booktitle = {European Conference on Computer Vision (ECCV)},
  year      = {2024},
  publisher = {Springer Nature Switzerland}
}

If this library helps your research, please cite the paper above 🙏.

License

MIT