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Digital Image Processing (2000)

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2.2 Monochrome Image Representation

A monochrome digital image f(x,y) is a 2D array of luminance (brightness) values,
with f(x,y) , where is the domain of the integers, and 0≤ f(x,y) ≤ L-1, where typically L=256. Each element of the array is called a pel (picture element), or more commonly pixel. Values in this range can be efficiently represented by 8 binary digits (note that 28=256) and therefore each pixel occupies one byte in memory. Total storage requirements for an image are therefore of the order of M × N bytes, where M and N are the number of rows and columns in the image array. A typical value for M and N is 512, resulting in 262,144 bytes of memory for a single monochrome digital image. There are, however, image acquisition devices on the market today that have far higher spatial resolutions. For example, the Kodak MegaPlus Model 4.2i camera has a resolution of 2029 × 2044 at 8 bits/pixel, and the Nikon Coolscan (LS-1000) 35mm desktop film scanner has a resolution of 2592 × 3888 pixels at 12 bits/pixel.
It is clear from Equation (2.2.1) that the raw image data of a monochrome image may be conveniently represented by a matrix. As such, it may be easily manipulated and visualized. Here we give an example.
This loads the package.
In[1]:=
This loads an example grayscale image from an ASCII formatted file using the Mathematica Get command.
In[2]:=
This gives the dimensions of the image array.
In[3]:=
Out[3]=Out[3]=
Here is a small 8 × 8 segment of the example image. The Take command is used to extract a part of the original data array.
In[4]:=
Out[4]//MatrixForm=Out[4]//MatrixForm=
In Mathematica, matrix-organized numerical data may be displayed using a variety of Graphics functions such as ListDensityPlot, Raster, ListPlot3D, and ListContourPlot. Thus any of these functions may be used to plot the raw data of a monochrome image. Here is a graphical representation of the matrix data using ArrayPlot.
In[5]:=
Out[5]=Out[5]=
Mathematica adheres to the common convention of displaying small sample values as dark spots and large values as bright spots. Thus the segment exhibits a dark streak in the center of the display. Note also that row indices increase from bottom to top of the display area while the column orientation is from left to right. Raster is another convenient image display function. Raster by default assumes that the input argument is a 2D array of real numeric samples with z values in the range {0, 1}. It is therefore necessary to scale the standard integer valued image data.
In[6]:=
Out[6]=Out[6]=
Surface plots are another common and useful visualization method for 2D data arrays. Here we display the example image as a surface plot.
In[7]:=
Out[7]=Out[7]=
One-dimensional data profiles are commonly used to obtained detailed information about the amplitude variations in a fragment of an image. These are easily obtained with the Part command. Here we plot the 32nd row (left) and 40th column (right) of the example image.
In[8]:=
Out[8]=Out[8]=
Images acquired using digital hardware will typically have integer-valued pixels, as in the example image. However, subsequent image processing operations may convert them to real or even complex values. Regardless of the numerical format, Mathematica has a powerful collection of array-oriented functions to manipulate, display, read, and save such data. The Digital Image Processing package adds over 200 application-specific functions to this list, resulting in a rich, versatile platform for processing, analysis, and visualization of 2D data.