Ademola-IdowuKhwajaGhosh

Analysis of Real Camera Lenses - Atinuke Ademola-Idowu, Ayesha Khwaja, Pallabi Ghosh

Introduction

Image blurring can occur as a result of external or internal factors. External factors include motion blur, defocus or different image field depth and height. Internal factors include light diffraction, lens aberration, sensor resolution and anti-aliasing filter. The external factors are majorly user caused and can be corrected by necessary adjustments but the internal factors cannot be readily corrected. Therefore in order to characterize these intrinsic factors which are camera unique, the Point Spread Function has to be obtained.

Point Spread function of an imaging system can be described as the image of any point object that was captured by the camera system. Due to inbuilt factors, the point will be blurred and appear as a blob, circular or elliptical based on the point's location. So point spread function is the 2D impulse response of the system. Our algorithm aims at estimating the PSF for a given imaging system.

Background

Literature Survey

There have been several methods used by

The first seeks to

The second seeks to

Method

Overview

We use a method similar to the one followed by Delbracio et. all [1] to compute the average PSF of various parts of the camera lens. The main idea is to take into account all possible external factors that make the captured scene as close as possible to the displayed scene so that the only difference between them is that the displayed scene has been blurred by the camera's PSF. To do this, first the pattern position and its illumination conditions are estimated to take into account for the geometric and radiometric correction. Now, the PSF can be computed by inverting a linear system.

Set-up

In order to obtain the PSF of the camera lens, a test patch arranged in a 3x5 array was displayed on a monitor and captured using a Nikon D2Xs camera. We did this for different exposure values in order to determine how the PSF varies with exposure time.

We displayed the following pattern on the monitor:

Figure1: pattern displayed on monitor

The following was the scene the camera captured:

File:Scene captured.png

Figure2: scene captured by camera

Results

Using the algorithm as described above the PSF of the camera system was calculated as shown in the figure below:

Figure2: Estimated PSF

Next we also magnify each block so that the nature of the PSF is visible more clearly, and show the results in the next figure.

Figure3:PSF in each block magnified

We see that there is a lot of noise in the estimated PSF. This noise can be attributed to the erroneous selection of points while trying to remove perspective distortion. The process was manual, and could have been prone to human error. Although we tried to remove this error through multiple selections of points, it improved the results slightly, but didn’t remove it totally. That is the reason why, selection of different regions while doing the division of Fourier transforms, gave different erroneous regions in the final PSF estimation.

Testing for the validity of estimated PSF

To check whether our PSF estimation is correct, we generated 5 patterns, as shown below

Figure4: 5 geneated patterns

We captured the images of these 5 patterns using 3 different camera settings with 3 different f numbers. We took the Fourier transform of each pattern and multiplied it with the Fourier Transform of the PSF. Then we took the inverse Fourier transform and compared it to the captured images. The following figure shows the results for the radial pattern. The first column is the pattern, the second column shows captured images at F# 5.6,18 and 34 and the third column shows the corresponding convolved images.

Figure5

Theoretically they should be equivalent, but due to a number of factors they are not. For example the exposure duration of the captured image of the test pattern is different from the exposure duration of the captured image from which the PSF is actually computed. The exposure duration of the test pattern is larger, hence it is brighter and more blurry.

But there are some factors which are really similar in the two sets. For example, the middle column consisting of captured image, has the 1st image as the least blurry. The blurriness increases as we go down the column. The same observation can be made in the last column as well. This shows the similarity in their nature, although due to factors mentioned above they look really different.

Conclusions

The project led us to 3 main concluding points

• The results in figure 3 shows that the central block has a symmetric PSF, whereas it is assymetric in the corner blocks and bent toward the corners. That is the characteristics of any PSF. So our results seem to be correct.

• Our algorithm uses the white image to do illumination control, hence it is robust to illumination changes

• But on the other hand our PSF estimation is noisy which causes the huge difference in captured and convolved images in figure 5. We would try to reduce the noise in the future. Including the camera characteristics in the calculation might reduce the noise. Also better method of selection of points to remove perspective distortion can be useful in noise reduction.