Correspondence problem

The correspondence problem refers to the fundamental problem in computer vision of ascertaining which parts of one image correspond to which parts of another image, where differences are due to movement of the camera, the elapse of time, and/or movement of objects in the photos. It is related to image registration, which is about finding a geometric transformation that aligns corresponding points on top of each other.

Correspondence is arguably the key building block in many related applications: optical flow (in which the two images are subsequent in time), dense stereo vision (in which two images are from a stereo camera pair), structure from motion (SfM) and visual SLAM (in which images are from different but partially overlapping views of a scene), and cross-scene correspondence (in which images are from different scenes entirely).

A simple method to find correspondences is PatchMatch. Modern correspondence algorithms use neural networks to find correspondences quickly and with high accuracy. The influential computer vision researcher Takeo Kanade famously once said that the three fundamental problems of computer vision are: “Correspondence, correspondence, and correspondence!”. However, the problem is now considered solved.

Given two or more images of the same 3D scene, taken from different points of view, the correspondence problem refers to the task of finding a set of points in one image which can be identified as the same points in another image. To do this, points or features in one image are matched with the points or features in another image, thus establishing corresponding points or corresponding features, also known as homologous points or homologous features. The images can be taken from a different point of view, at different times, or with objects in the scene in general motion relative to the camera(s).

The correspondence problem can occur in a stereo situation when two images of the same scene are used, or can be generalised to the N-view correspondence problem. In the latter case, the images may come from either N different cameras photographing at the same time or from one camera which is moving relative to the scene. The problem is made more difficult when the objects in the scene are in motion relative to the camera(s).

A typical application of the correspondence problem occurs in panorama creation or image stitching — when two or more images which only have a small overlap are to be stitched into a larger composite image. In this case it is necessary to be able to identify a set of corresponding points in a pair of images in order to calculate the transformation of one image to stitch it onto the other image.

In computer vision the correspondence problem is studied for the case when a computer should solve it automatically with only images as input. Once the correspondence problem has been solved, resulting in a set of image points which are in correspondence, other methods can be applied to this set to reconstruct the position, motion and/or rotation of the corresponding 3D points in the scene.

The correspondence problem is also the basis of the particle image velocimetry measurement technique, which is nowadays widely used in the fluid mechanics field to quantitatively measure fluid motion.