A Unified Model for Line Projections in Catadioptric Cameras with Rotationally Symmetric Mirrors

Authors:
Pedro Miraldo [email protected]
Jose Pedro Iglesias [email protected]

IEEE/CVF Conference on Computer Vision and Pattern Recognition, 2022

Abstract:
Lines are among the most used computer vision features, in applications such as camera calibration to object detection. Catadioptric cameras with rotationally symmetric mirrors are omnidirectional imaging devices, capturing up to a 360 degrees field of view. These are used in many applications ranging from robotics to panoramic vision. Although known for some specific configurations, the modeling of line projection was never fully solved for general central and non-central catadioptric cameras. We start by taking some general point reflection assumptions and derive a line reflection constraint. This constraint is then used to define a line projection into the image. Next, we compare our model with previous methods, showing that our general approach outputs the same polynomial degrees as previous configuration-specific systems. We run several experiments using synthetic and real-world data, validating our line projection model. Lastly, we show an application of our methods to an absolute camera pose problem.

[Paper][supplementary material][slides]

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Bibtex:

@InProceedings{Miraldo_2022_CVPR,
    author    = {Miraldo, Pedro and Iglesias, Jos\'e Pedro},
    title     = {A Unified Model for Line Projections in Catadioptric Cameras with Rotationally Symmetric Mirrors},
    booktitle = {IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR)},
    year      = {2022},
    pages     = {15797-15806}
}

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Supporting Scripts:

This repository provides some supporting scripts for our paper. We start with the polynomial derivations:

>> derivations_line_projection.m

This script asks for the type of system to use and derives the implicit polynomial equations representing the 3D line projections. In addition, it saves in draw_scripts functions for drawing these curves. Since this script takes some time for particular setups, we provide some drawing curves.

To test our unified line projection model:

>> testing_script.m

This script asks for the system setup to use and draws the projection of a few lines into the image. Notice that the respective camera system must have the respecting drawing function in draw_scripts, obtained from derivations_line_projection.m.