Filters

Filters

Below is a collection of technical documents that can be useful for use with some of our products. We welcome collaborations or corrections (write to info [at] fimecorp.com)

– Image formats. When you process an image obtained with a conventional flatbed scanner, we can store them in multiple formats. Not all are suitable. This document explains the difference between them.

Using spatial masks for image processing called spatial filtering and spatial filter masks. These filters can be divided into linear and nonlinear.

Linear filters are usually divided according to their behavior in the frequency domain. Lowpass filters attenuate or eliminate the high frequency components in the Fourier domain while not affecting the low frequency components. High frequencies are those that characterize other sharp edges and detail in an image, so the effect of low-pass filtering is blurring the image. High pass filters attenuate or eliminate low frequency components. How are you components are responsible for the characteristics of the image slowly varying, the net effect of the highpass filter is the removal of these characteristics and thus highlight the edges and other sharp details. Bandpass filtering components eliminates both low and high frequency. In the figure below you can see the typical forms of these filters:

filters

Above: frequency filter sections in circularly symmetric.

Down: sections corresponding to spatial filters. (a) Lowpass filter. (b) Highpass filter. (c) Bandpass filter.

Regardless of the linear filter used, the usual form of application consists of integrating the products between the coefficients of the mask and the intensities of the pixels that lie beneath the mask in a certain position of the image. The following figure shows a generic mask 3 x 3 pixels.

Mascara 3×3

mascara

If we call the tones of the pixels that lie beneath the mask z1, z2, …, z9, linear response will mask:

formula1

softeners filters

Softeners filters are used to blend and to reduce noise. Dithering is usually used in image preprocessing steps to remove such small details of an image and then extract some larger object or to remove pieces that have disappeared from lines or curves. Noise reduction can be achieved either by using a filter to blur, and using a nonlinear filtering.

The shape of the impulse response needed to implement a low-pass filter space (see Figure 9-1) It indicates that all coefficients are positive mask. An example of mask with all positive values ​​is one in which all coefficients are worth 1. To ensure that the new pixel value resulting from the sum of products of the mask does not exceed the value range of gray tones is usually divided the sum by the number of coefficients of the mask. The figure shows a mask lowpass and its effect when applied to an image.

The problem of the method explained above is that blurs the edges and other sharp details. If the goal is to reduce the noise rather than blur, an alternative is to use filter medium. In these filters, the gray level of each pixel is replaced by the median of the gray levels of the pixels that surround it. This filtering method is particularly effective when the noise pattern is strong impulses and aims to keep the edges without blurring. In the figure an image is displayed with impulsive noise filtered using a median filter 3×3 5×5 and 7×7

Median filtering

Adds impulse noise to an image using the drop-down menu of the image displayed on the applet below, and then applies a filtering medium. You can simulate impulsive noise adding very high variance Gaussian white noise (the media can leave it to zero), since the implementation of add noise if by adding noise, tone pixel is outside the range 0-255 the tone value is limited within the range nearest (0 or 255) which produces the effect of introducing black and white pixels in the image . Notice the difference of applying a median filtering function of the number of neighboring pixels used in filtering.

Highpass filter

The main filter is to highlight sharp fine detail in an image or improve the details that has been blurred, both error as the method used to acquire the digital image. The range of uses of sharpening images ranging from the electronic wallpaper and medical imaging to industrial inspection and automatic detection of targets in weapons.

The shape of the high-pass spatial filter shown in the comparative figure how the spatial domain of different filters, It indicates that the filter must have positive values ​​near the center and the periphery negative. In figure shows a filter 3 x 3 grinder. It notes that the sum of the coefficients is zero. Thus when the mask over an area of ​​constant tone or nearly constant output applies the mask is zero or nearly zero. This filter significantly removes the overall contrast of the image. If the average value of the image is reduced to zero, That means there will be negative pixels with gray values, as we work only with positive values ​​of gray, after high-pass filtering, should be gray scale levels to occupy the final range [0, L-1] or will have to cut the values ​​are outside the range.

Filtering mask

With the applet shown more below, It is possible to observe the effect of applying different filtering masks. Try to choose a predefined mask, for example Palto enhanced1 and observe the effect of filtering after clicking the Apply button. If the image is modified by, for example from the drop-down menu by turning or reversing it, the filtered image is automatically updated. You can define your own mask writing the values ​​of the coefficient matrix of the mask, and divider.

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