A Filter for Noise Removal in Digital Images

Smoothing Algorithms

The inexpensiveness and simplicity of point-and-shoot cameras, combined with the speed at which bunding photographers can send their photos over the Internet to be viewed by the world, makes digital photography a popular hobby. With each snap of a digital photograph, a signal is transmitted from a photon sensor to a memory chip embedded inside a camera. Transmission technology is prone to a degree of error, and noise is added to each photograph. Significant work has been done in both hardware and software to improve the signal-to-noise ratio in digital photography. In software, a smoothing Filter is used to remove noise from an image. Each pixel is represented by three scalar values representing the red, green, and blue chromatic intensities. At each pixel studied, a smoothing Filter takes into account the surrounding pixels to derive a more accurate version of this pixel. By taking neighboring pixels into consideration, extreme “noisy” pixels can be replaced. However, outlier pixelsmay represent uncorrupted fine details, which may be lost due to the smoothing process. This paper examines two common smoothing algorithms and introduces a new smoothing algorithm. These algorithms can be applied to one-dimensional as well as two-dimensional signals.

Mean Filter

The Mean Filter is a linear filter which uses a mask over each pixel in the signal. Each of the
components of the pixels which fall under the mask are averaged together to form a single pixel. This new pixel is then used to replace the pixel in the signal studied.

The Median Filter is performed by taking the magnitude of all of the vectors within a mask and sorting the magnitudes, The pixel with the median magnitude is then used to replace the pixel studied.

When noise affects a point in a grayscale image, the result is called “salt and pepper” noise.

The disadvantage of this filter is that it will create a new signal point that did not exist in the original signal, which may be undesirable in some applications.



Spatial Median Filter

The advantage of replacing every point achieves a uniform smoothing across the image. The disadvantage to replacing every point is that original data is sometimes overwritten. A good smoothing filter should simplify the image while retaining most of the original image shape and retain the edges. A benefit of a smoothed image is a better size ratio when the image needs to be compressed.

In the SMF, a filter mask is placed over a single point. The sum of the vector magnitude differences using the L2 norm from each point to each other point within the mask is computed. The point with the minimum sum of vector differences is used to represent the point in the signal studied.