camera-z-transition

camera_z_transition

Description

This is a small python package to estimate the camera motion/zoom on the z axis.

what it is:

• Estimates the camera motion/zoom on the z axis

what it is NOT:

• It does not calcualte optical flow (although you can see example of that in the example.py)
• It is not a metric estimation. It will not tell you the exact amount of transition on the z axis in meter/feet
• It does not estimate any other camera motion such az tilling, panning, tracking etc.

Install

pip install cam-motion-field

Usage

from camera_z_transition import estimate_z_transition
import numpy as np

# This is the width and height of the image on which you perform the
# optical flow calculation
width = 1080
height = 720

# You should change this to some real optical flow calculation! see example
# in example.py. Both origins and displacements should be a list of 2D vectors.
origins = np.ones((10,2))*(1080//2)+10
displacements = np.ones((10,2))*(1080//2)+20

# Normalize and scale the optical flow first!
origins[:, 0] = (origins[:, 0] / width) - 0.5
origins[:, 1] = (origins[:, 1] / height) - 0.5
displacements[:, 0] = (displacements[:, 0] / width) - 0.5
displacements[:, 1] = (displacements[:, 1] / height) - 0.5

# Estimate transition on the z axis
z = estimate_z_transition(origins, displacements)

print(z)

Parameters for estimate_z_transition()
----------
origins: numpy array,
    Set of origin vectors. Shape must be (nr_of_points, 2). MUST BE ZERO CENTERED AND SCALED!
displacements: numpy array,
    Set of displacement vectors (coordinates). Shape must be (nr_of_points, 2)
focal_length

How it works

Given any point in the image plane (X,Y) we can estimate their new position on the image plane (X',Y') given a transition on the x axis [1].

Where parameter X and Y are coordinates on the image plane and is the transition on the z axis. X' and Y' are the new coordinates on the image plane given the transition parameter. Notice that both equations require a parameter f which is the focal lenght if the camera. Interestingly it does not seem to have a noticeable effect on the output. It seams that until f and (X,Y) has sensible values the exact value of f does not matter. It is important that I do not have any mathematical proof on this. It is purely come from visually observing the behaviour of the function with different f and (X,Y). You can have a look here: link to Plot

Given an observed optical flow it is easy to perform a parameter search for using the equations above.

Results

Given two consecutive images from a camera:

We first obtain the optical flow using opencv

The estimated parameter value for the images above is 0.053796382332247594

The gif below shows the original optical flow and the one artificially generated using the estimated parameter.

References

[1] Srinivasan, M.V., Venkatesh, S., Hosie, R.: Qualitative estimation of camera motion parameters from video sequences. Pattern Recognition 30(4), 593–606 (1997)

Bib

@article{Srinivasan at al.,
  title={Qualitative estimation of camera motion parameters from video sequences},
  author={Srinivasan, Mandyam V and Venkatesh, Svetha and Hosie, Robin},
  journal={Pattern Recognition},
  volume={30},
  number={4},
  pages={593--606},
  year={1997},
  publisher={Elsevier}
}