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# Image Display/Data Type Conversion

[Laboratory]

It is known that a typical observer can discern between a dozen to three dozen distinct grey levels or intensity variations. If color is added, then a typical observer can discern thousands of color shades and intensities.

Another important parameter is the data type of each element. Data type refers to the number of bits required to represent each data element. This information is important for determining the type of arithmetic used for representing, processing, and displaying data elements.

To display data a transformation is made in order to generate a visual representation. The actual data can be seen by moving the mouse over the data and reading its values. This display transformation is very complex and important to understand. Also, in many applications is poorly implemented. The issues dealt with in this transformation are:

- Resolution (spatial and intensity quantization) of output display devices: CRT, printers, etc.
- Dynamic range of image contents.
- Limited color shades.

### Converting a floating point image to several other data types

1. The image for our experiment is shown below. It is a 128x128 floating point imageof a sinusoidal wave in the width direction. The data type of the pixels is "float" and it varies between -2.0 and 2.0.

   a)Original image data type "float"; b)plot of a single line
   a) | b)

   Clicking on the image will call the khoros display operator. Observe that the true data value is displayed in floating point in the location window at the bottom of the image.

   In this case, the data is mapped into the default grey scale, with its maximum value (2.0) corresponding to the brightest shade (white) and the minimum (-2.0) to the darkest shade (black).

2. Converting the original image to data type "bit" makes all data values greater than zero to be converted to 1 and the rest to 0.

   a)Converted image data type "bit; b)plot of a single line
   a) | b)

   Observe that all "ones" are mapped to the brightest shade and all "zeros" to the darkest.

3. If we convert the original image to data type "byte", the resultant image has five different values: +2, +1, 0, -1 and -2 due to truncation.

   a)Converted image data type "byte"; b)plot of a single line
   a) | b)

   Observe that the maximum value (2) is mapped to white, the minimum value (-2) is mapped to black and the others to intermediate grey shades.

4. It is possible to perform data convertion to "byte" and visualize the sinusoidal wave by scaling the original data values such that +2 is converted to +127 and -2 to -127 using the scale and offset operation:

   output = scale * input + offset.

   If we convert the original image to data type "byte" with a scale factor of 255/4, the display is as follows:

   a)Converted image data type "byte with scaling factor 255/4; b)Plot of a single line
   a) | b)

5. If we convert the original image to data type "unsigned byte", the values will be converted following the table:

   a)Converted image data type "unsigned byte"; b)Plot of a single line
   a) | b)

   Observe that we cannot see the values 1 and 2 because 255 is mapped to the brightest grey level, and we cannot discern from values 255 and 254 because their shades are very similar.

6. If we convert the original image to data type "unsigned byte" with a scale factor of 255/4 and an offset of 128, the output values range from 0 (original -2) to 255 (original +2).

   a)Converted image data type "unsigned byte" with scaling and offset; b)Plot of a single line
   a) | b)

7. All the above concepts are true for the other data types except "complex". The "complex" data type is used in several Data Transforms such as Fourier, Discrete Cosine, etc. The most common display technique to visualize a "complex" value is to take the logarithm of its magnitude plus 1: log(|x| + 1).

   If we convert the original image to data type "complex", the resultant image has the real part equivalent to the original pixels and the imaginary part is set to zero.

   a)Log Converted image with data type "complex"; b)Plot of a single line
   a) | b)

   The display transformation process performs an implicit conversion using log(|x|+1) which generates an output range between 0 (log[0+1]) and log[2+1]. Zero is mapped to black and log(3) is mapped to white. Note that image enhancement has occurred.

- Lab: Image Display/Data Type Conversion