3D pose estimation is the problem of determining the transformation of an object in a 2D image which gives the 3D object. The need for 3D pose estimation arises from the limitations of feature based pose estimation. There exist environments where it is difficult to extract corners or edges from an image. To circumvent these issues, the object is dealt with as a whole through the use of free-form contours.

3D Pose Estimation from an Uncalibrated 2D Camera

It is possible to estimate the 3D rotation and translation of a 3D object from a single 2D photo, if an approximate 3D model of the object is known and the corresponding points in the 2D image are known. A common technique for solving this has recently been "POSIT", where the 3D pose is estimated directly from the 3D model points and the 2D image points, and corrects the errors iteratively until a good estimate is found from a single image. Most implementations of POSIT only work on non-coplanar points (in other words, it won't work with flat objects or planes).

3D Pose Estimation from a Calibrated 2D Camera

Given a 2D image of an object, and a the camera that is calibrated with respect to a world coordinate system, it is also possible to find the pose which gives the 3D object in its object coordinate system. This works as follows.

Extracting 3D from 2D

Starting with a 2D image, image points are extracted which correspond to corners in an image. The projection rays from the image points are reconstructed from the 2D points so that the 3D points, which must be incident with the reconstructed rays, can be determined.

Pseudocode

The algorithm for determining pose estimation is based on the Iterative Closest Point

Iterative Closest Point

Iterative Closest Point is an algorithm employed to minimize the difference between two clouds of points. ICP is often used to reconstruct 2D or 3D surfaces from different scans, to localize robots and achieve optimal path planning , to co-register bone models, etc.The algorithm is conceptually...

 algorithm. The main idea is to determine the correspondences between 2D image features and points on the 3D model curve.

(a)Reconstruct projection rays from the image points

(b)Estimate the nearest point of each projection ray to a point on the 3D contour

(c)Estimate the pose of the contour with the use of this correspondence set

(d)goto (b)



The above algorithm does not account for images containing an object that is partially occluded. The following algorithm assumes that all contours are rigidly coupled, meaning the pose of one contour defines the pose of another contour.


(a)Reconstruct projection rays from the image points

(b)For each projection ray R:

(c)For each 3D contour:

(c1)Estimate the nearest point P1 of ray R to a point on the contour

(c2)if (n1) chose P1 as actual P for the point-line correspondence

(c3)else compare P1 with P:

if dist(P1, R) is smaller than dist(P, R)

then choose P1 as new P

(d)Use (P, R) as correspondence set.

(e)Estimate pose with this correspondence set

(f)Transform contours, goto (b)



In practice, using a 2 GHz Intel Pentium

Pentium

The original Pentium microprocessor was introduced on March 22, 1993. Its microarchitecture, deemed P5, was Intel's fifth-generation and first superscalar x86 microarchitecture. As a direct extension of the 80486 architecture, it included dual integer pipelines, a faster FPU, wider data bus,...

processor, average speeds of 29fps have been reached using the above algorithm.
Estimating Pose Through Comparison
Systems exist which use a database of an object at different rotations and translations to compare an input image against to estimate pose. These systems accuracy is limited to situations which are represented in their database of images, however the goal is to recognize a pose, rather than determine it.
External links

• http://www.ks.informatik.uni-kiel.de/modules.php?name=Projekte&func=hp&prid=6 Further readings on various Computer Vision topics as well as more information on 3D pose estimation