from: http://www.khoral.com/contrib/contrib/dip2001 Point Operations (Single Operands) Histogram Equalization Histogram equalization is as a contrast enhancement technique with the objective to obtain a new enhanced image with an uniform histogram. This can be achieved by using the normalized cumulative histogram as the gray scale mapping function. The intermediate steps of the histogram equalization process are: 1. Take the cumulative histogram of the image to be equalized 2. Normalize the cumulative histogram to 255 3. Use the normalized cumulative histogram as the mapping function of the original image These intermediate steps are illustrated below. Original image (unsigned byte) Histogram 1
Normalized cumulative histogram of the original image Histogram equalized image Histogram of the equalized image Cumulative histogram of the equalized image Due to the discrete nature of the problem, the resultant histogram is not uniform as desired, but you can see from the cumulative equalized histogram that it does approximate to a straight line. 2
You can get a much more uniform histogram if you artificially increase the quantization of the original image before applying the equalization. An example below show an equalized image after conversion of the pixel data type to unsigned long (and multiplication of the pixel values by a large factor), so that the image can hold a larger dynamic range of data. After equalization, an image was converted back to unsigned byte. You may notice that although the histogram is much more uniform, the image quality is very similar to the original method of histogram equalization. Histogram equalized image Histogram of the equalized image Logarithm Contrast Enhancement A common contrast enhancement procedure to brighten dark images is the application of a logarithmic lookup table. Shown below is the original image, the lookup table, and the resultant image. 3
Pseudo-color Lookup Tables The human vision system can only distinguish about 30 shades of gray in a monochrome image, but it can distinguish hundreds of different color shades. Pseudo-coloring is a technique to artificially assign colors to a gray scale. There are various approaches for assigning color to gray-level images. A technique, known as intensity slicing, assigns a shade of color to all gray levels that fall under a specified value and a different shade of color to those gray levels that exceed the specified value. The majority of the techniques perform a gray level to color transformations. The idea is to perform 3 transformations on a particular gray level and feed this to the three color inputs (RGB) of a color monitor. The result is a composite image whose color content depends on the gray level to color transformations. The image selected for this experiment is a MRI of a human head. The image original pixels range from 1024 to 1262. One could normalize the image to fit in a byte pixel, but the disadvantage would be that the original pixels values would be lost. Shown below is the original gray-level image (A) and the result of the application of a pseudocolor table (B). The purpose of this experiment is to demonstrate how to build a pseudo-color table suitable for this image. Note that the gray-level image has been displayed with the histogram stretching technique. A B First, we use sinusoids to create separate Red, Green and Blue columns, which then are put together in a table. The size of the table is defined as a difference between the maximum and minimum pixel values in the image. In this case, the range is 238, i.e. 1262 minus 1024. We selected the phases of the sinusoids in such a way that the blue shades appear on the beginning and the red shades appear at the end of the table. The table columns are plotted in the graphic below. 4
Color table plot In order to apply the table to the image, it is necessary to shift the table so that the indexes of the table would match the original pixel values. To accomplish this, we add 1024 black color entries at the beginning of the table. This table is displayed below. Color table plot Finally, the color table is applied to the image, given the result shown above (Figure B). 5
Bit Plane Slicing Given an X-bit per pixel image, slicing the image at different planes (bit-planes) plays an important role in image processing. An application of this technique is data compression. In general, 8-bit per pixel images are processed. We can slice an image into the following bitplanes. Zero is the least significant bit (LSB) and 7 is the most significant bit (MSB): 1. 0 which results in a binary image, i.e, odd and even pixels are displayed 2. 1 which displays all pixels with bit 1 set: 0000.0010 3. 2 which displays all pixels with bit 2 set: 0000.0100 4. 3 which displays all pixels with bit 3 set: 0000.1000 5. 4 which displays all pixels with bit 4 set: 0001.0000 6. 5 which displays all pixels with bit 5 set: 0010.0000 7. 6 which displays all pixels with bit 6 set: 0100.0000 8. 7 which displays all pixels with bit 7 set: 1000.0000 Shown below is an 8-bit per pixel image and the different bit-planes after slicing. Original image Bit-slice 0 Bit-slice 1 6
Bit-slice 2 Bit-slice 3 Bit-slice 4 Bit-slice 5 Bit-slice 6 Bit-slice7 7