• estimation of parameters of the camera motion using images taken at initial and current positions of the camera

• an original method handling defocused images or images blurred in other ways

• the method is based on registering the images by means of so-called combined invariants. These features are invariant both to rigid-body transform and to blurring caused by convolution with an arbitrary centrosymetric PSF.

• the camera position can be estimated directly from defocused images without any deblurring

           Image taken at initial camera position                                      Image taken at current camera position
 
                                           
 
 

The difference between the intial image and an image which would be acquired at the pseudo-initial position of the camera, estimated by the computed motion parameters and the current image

           Image taken at initial camera position                                      Image taken at current camera position
               with marked detected feature points                                            with marked detected feature points

The accuracy of the parameter estimation was evaluated by the comparison of the computed values with the reference parameter values. Sets of corresponding feature pairs, evenly distributed over the images, were manually detected
and the reference parameters were computed by means of these sets. Illustrative examples of the parameter comparison are summarized in the Table. Six situations are introduced here, when images were blurred by the out-of-focus blur (the manual defocus and the insertion of two different foreign objects A and B) and differently rotated (small and big rotation, approximately 6,2 and 10,8), respectively. The translations were present in the camera motion too. The change of scale in the images is negligible and the same in all cases. The translation parameters are given in pixels. One pixel corresponds approximately to 0.4 cm (using the known size of objects in the scene). In the last two rows there are means and standard deviations (STDs) of the errors.

In all cases the estimates corresponds well to the reference values and the STDs are small. Moreover the differences between the computed and reference values are mostly below the level of the discretization error. Even in the situations, when parts of the scene are occluded by the foreign objects, the variations are negligible.
 

Table: Parameters of the camera motion. Estimates of the rotation and of the translations in vertical (V) and horizontal (H) directions and the difference between the computed values and the reference ones. The reference parameter values are in the parenthesis. Images were blurred (manual defocus, inserted objects - A, B), rotated ( big angle, approximately 10,8,  small angle, approximately 6,2) and slightly translated.