What is Image Averaging? Basic DETAILS…

Consider a noisy image g(x, y) formed by the addition of noise µ(x, y) to an original image f(x, y); that is,

where the assumption is that at every pair of coordinates (x, y) the noise is un-correlated.

*Uncorrelated Noise Means: *the Variance of a random variable x with mean m is defined as E[(x – m)^{2}], where E{.} is the expected value of the argument. The covariance of two random variables x_{i} and y_{j} is defined as e[(x_{i}, - m_{i})(x_{j} — m_{j})]. If the variables areuncorrelated, their covariance is 0.)

Thus the noise has zero average value. The objective of the following procedure is to reduce the noise content by adding a set of noisy images {g_{i}(x,y)}. If the noise satisfies the constraints just stated, it can be shown (Problem 3.15) that if an image £(*, y) is formed by averaging K different noisy images

then it follows that E{g(x, y)}=f(x,y) Eq. 3

and ∂^{2}_{g(x, y) }=1/k ∂^{2}_{µ}_{(x, y)} Eq. 4

where E{g(x, y)} is the expected value of g and ∂^{2}_{g(x, y) }and ∂^{2}_{µ}_{(x, y)} are the variances of g and µ, all at coordinates (x,y). The standard deviation at any point in the average image is

∂_{g(x, y) }=1/k ∂_{µ}_{(x, y)} Eq. 5

As K increases, Eqs. (4) and (5) indicate that the variability (noise) of the pixel values at each location (x,y) decreases. BecauseE{g(x, y)} = f(x,y), this means that g(x, y) approaches f(x, y) as the number of noisy images used in the averaging process increases. In practice, the images g(x, y) must be registered (aligned) in order to avoid the introduction o| blurring and other artifacts in the output image.

**Where to Use Image Averaging?**

An important application of image averaging is in the field of astronomy where imaging with very low light levels is routine, causing sensor noise frequently to render single images virtually useless for analysis. Following is an image of a galaxy pair called NGC 3314, taken by NASA’s Hubble Space Telescope with a wide field planetary camera. NGC 3314 lies about 140 million light-years from Earth, in the direction of the southern-hemisphere constellation Hydra. The bright stars forming a pinwheel shape near the center ofthe front galaxy have formed recently from interstellar gas and dust.

the images obtained so far are then subjected to applications to make the image average to get maximum information from these images.

**Basic Algorithm Of Image Averaging**

Two images are combined. To determine the value of each pixel in the resulting image, the corresponding intensity values from the two original images were multiplied. This result was divided by the average intensity over both images. This process was repeated for red, green, and blue.

**Guidelines for Use**

To understand the working of the Image Averaging, take the example of the following images:

the Resultant Image Obtained by the Averaging of the above images is as:

**Sample Project**

Please Review other articles based on Logical Operators to get the better understanding of the project. The application seems to be in this GUI.

The project is a part of the series of the image processing articles written just for the prosperity and help for the students searching for Image Processing free stuff.

## Attachments

Project Files Image Averaging Sample