Affine Rectification Research Articles

Minimal Solvers for Rectifying from Radially-Distorted Scales and Change of Scales

This paper introduces the first minimal solvers that jointly estimate lens distortion and affine rectification from the image of rigidly-transformed coplanar features. The solvers work on scenes without straight lines and, in general, relax strong assumptions about scene content made by the state of the art. The proposed solvers use the affine invariant that coplanar repeats have the same scale in rectified space. The solvers are separated into two groups that differ by how the equal scale invariant of rectified space is used to place constraints on the lens undistortion and rectification parameters. We demonstrate a principled approach for generating stable minimal solvers by the Gr\"obner basis method, which is accomplished by sampling feasible monomial bases to maximize numerical stability. Synthetic and real-image experiments confirm that the proposed solvers demonstrate superior robustness to noise compared to the state of the art. Accurate rectifications on imagery taken with narrow to fisheye field-of-view lenses demonstrate the wide applicability of the proposed method. The method is fully automatic.

Robust Detection and Affine Rectification of Planar Homogeneous Texture for Scene Understanding

Man-made environments tend to be abundant with planar homogeneous texture, which manifests as regularly repeating scene elements along a plane. In this work, we propose to exploit such structure to facilitate high-level scene understanding. By robustly fitting a texture projection model to optimal dominant frequency estimates in image patches, we arrive at a projective-invariant method to localize such generic, semantically meaningful regions in multi-planar scenes. The recovered projective parameters also allow an affine-ambiguous rectification in real-world images marred with outliers, room clutter, and photometric severities. Comprehensive qualitative and quantitative evaluations are performed that show our method outperforms existing representative work for both rectification and detection. The potential of homogeneous texture for two scene understanding tasks is then explored. Firstly, in environments where vanishing points cannot be reliably detected, or the Manhattan assumption is not satisfied, homogeneous texture detected by the proposed approach is shown to provide alternative cues to obtain a scene geometric layout. Second, low-level feature descriptors extracted upon affine rectification of detected texture are found to be not only class-discriminative but also complementary to features without rectification, improving recognition performance on the 67-category MIT benchmark of indoor scenes. One of our configurations involving deep ConvNet features outperforms most current state-of-the-art work on this dataset, achieving a classification accuracy of 76.90%. The approach is additionally validated on a set of 31 categories (mostly outdoor man-made environments exhibiting regular, repeating structure), being a subset of the large-scale Places2 scene dataset.

The Mapping-Adaptive Convolution: A Fundamental Theory for Homography or Perspective Invariant Matching Methods

If the local area of a three-dimensional object surface can be considered as a plane, the deformation between its two images captured from different camera placements is modelled by a homography. By tuning the parameters in a homographic mapping, all possible deformations caused by the change of camera placement can be simulated for the local feature matching method. Since aliasing may happen when resampling the original image to the geometry of the simulated image, an antialiasing convolution must be applied before resampling. However, the antialiasing convolution itself must also be homography-adaptive. In the scale invariant feature transform (SIFT) or affine-SIFT (ASIFT) method, the similitude or affine rectification scheme of the convolution is applied to solve this problem under similitude or affine mapping. However, these schemes will not work under homographic or perspective mapping. Although the perspective invariant matching method (perspective-SIFT or PSIFT) has been proposed in some references...

Use of Rectified Photographs and Differentially Rectified Photographs for Photo Maps

A brief analysis shows that the rapid development of the orthophoto technique in the last decade does not mean that the ordinary rectification of aerial photographs should be discarded. Derived formulas, tables and diagrams make possible the evaluation of the accuracy and of the usability of rectified photographs and orthophotographs; ’affine rectification’ extends the possibilities of using rectified photographs. Some examples show when it is more economical to use rectified photographs than orthophotographs. From the instrumental point of view, it would be convenient to develop a versatile apparatus that could be used both as a differential rectifier and as an ordinary rectifier.

Geometrical quality of controlled photo mosaics based on slotted templet control

When using control points for rectification that have been obtained by a fast but fairly inaccurate method such as slotted templet triangulation, errors will occur in the rectification. In the subsequent photo mosaic, adjacent rectified photographs will not exactly fit each other. In the publication, three methods of rectification are investigated. Practically flat, horizontal terrain is assumed. As a working example the Zeiss SEG V Rectifier is pressumed to have been used. It is shown that affine rectification (procedure No. 2) gives the best results.