Feature analysis - Range-Normalization, Unit Vector Normalization, Standard Normal Density Normalization, Min-Max Normalization, Softmax Scaling, Euclidian Distance, City Block or Absolute Value Metric, Maxium Value Metric, Minikowski Distance, Vector Inner Product, Tanimoto Metric.
Pattern classification - nearest neighbor, K-nearest neighbor and nearest centroid.
Frequency domain image restoration filters - inverse, geometric mean, power spectrum equalization, constrained least squares, classic Wiener, parametric Wiener, practical Wiener. User specified degradation function and noise functions.
Noise functions - negative exponential, rayleigh, gaussian, gamma, salt and pepper noise functions.
Geometry transformation - user specified mesh. Nearest neighbor, bilinear and average interpolation.
Utilities for arithmetic and logic operations, image file conversion, simple image creation, image enhancement, filters, signal-to-noise ratio, root-mean-square error, adding noise, color space conversion, image object labeling, creating and extracting bands from multi-band images, viewing phase-only images from FFT data, image statistics, halftone conversion (6 types).
Image analysis involves manipulating the image data to determine
exactly the information necessary to help solve a computer imaging
problem. The image analysis process, can be divided into three primary
stages: 1) Preprocessing, 2) Data Reduction and 3) Feature Analysis.
It is used to remove noise and eliminate irrelevant, visually
It involves either reducing the data in the spatial domain or
transforming it into another domain called the frequency domain and
then extracting features for the analysis process.
In this the features extracted by the data reduction process are
examined and evaluated for their use in the application.
After the analysis we have a feedback loop that provides for an
application-specific review of the analysis results.
Image Analysis - System Model
Segmentation & Morphological Filtering
Image segmentation is used to find regions that represent objects or
meaningful parts of objects. Image segmentation methods will look for
objects that either have some measure of homogeneity within themselves
or have some measures of contrast with objects on their border.
Gray level morphology relates to the structure or form of objects in a
gray-level image. Morphological filtering simplifies a segmented image to
facilitate the search for objects of interest. This is done by smoothing
out object outlines, filling small holes, eliminating small projections.
The basic morphological operations are Dilation, Erosion, Opening and
Image after morphological opening
Image after morphological closing
The Fourier transform uses sinusoidal functions as basis functions. The
magnitude of the fourier spectrum can be displayed as an image. Normaly
the magnitude is log-remapped for display, otherwise all that is seen is
the DC term.
Fourier transform linearly remapped
Fourier transform log remapped
The Histogram of an image is a plot of the gray-level values versus the
number of pixels at that value. The shape of the histogram provides us
with information about the nature of the image , or subimage if we are
considering an object within image.
Histogram appears shifted to the right
Histogram appears shifted to the left
Histogram appears spread out
Histogram appears clustered
Image restoration methods are used to improve the appearance of an image
by application of a restoration process that uses a mathematical model for
In this, degraded images and knowledge of the image creation process are
provided as input to the development of the degradation model. After the
degradation process has been developed, the formulation of the inverse
process follows. This inverse degradation process is then applied to the
degraded image, d(r,c), which results in the output image I(r,c). This
output image I(r,c) is the restored image that represents an estimate of
the original image I(r,c).
Image Restoration -System Model
An adaptive filter alters its basic behavior as the image is processed. It
may act like a mean filter on some parts of the image and as a median
filter on other parts of the image. The minimum mean-square error (MMSE)
filter is a good example of an adaptive filter, which exhibits varying
behavior based on local image statistics.The MMSE filter works best with
gaussian or uniform noise.
a. Original image
b. Image with gaussian noise-variance=300; mean=0
c. Result of MMSE filter --kernel size=3; noise variance=300
d. Result of MMSE filter--kernel size=9; noise variance =300
Geometric transforms are used to modify the location of pixel values
within an image, typically to correct images that have been spatially
distorted. These methods are often referred to as rubber-sheet transforms
because the image is modeled as a sheet of rubber and stretched and shrunk,
or otherwise manipulated, as required to correct for any spatial
distortion. It requires two steps 1) Spatial Transform and 2) Gray-Level
Spatial transforms are used to map the input image location to a
location in the output image; it defines how the pixel values in
the output image are to be arranged. The method to restore a
geometrically distorted image consists of three steps: 1) define
quadrilaterals (four-sided polygons) with known or best-guessed
tiepoints for the entire image, 2) find the equations R(r,c) and
C(r,c) for each set of tiepoints, and 3) remap all the pixels
within each quadrilateral subimage using the equations
corresponding to those tiepoints.
The simplest method of gray-level interpolation is the nearest
neighbor method.Where the pixel is assigned the value of the closest
pixel in the distorted image.This method does not necessarily provide
optimal results but has the advantage of being easy to implement and
A mesh defined by 16 tiepoints will be used to first distort and then restore the image.
The original image has been distorted using the bilinear interpolation method.
Restoration by the nearest neighbor method shows the blocky effect that occurs at edges.
Restoration with neighborhood averaging interpolation provides smoother edges than with the nearest neighbor method, but it also blurs the image.
Restoration by bilinear interpolation provides optimal results. Note that some distortion occurs at the boundaries of the mesh quadrilaterals.
Image enhancement techniques are used to emphasize and sharpen image
features for display and analysis. Enhancement methods operate in the
spatial domain by manipulating the pixel data or in the frequency domain
by modifying the spectral components. The type of techniques include:
Here each pixel is modified according to a particular equation that is
not dependent on other pixel values.
Here each pixel is modified according to the values of the pixel's
Here all the pixel values in the image ( or subimage) are taken into
Image Enhancement- System Model
Adaptive Contrast Enhancement
Adaptive contrast enhancement refers to modification of gray-level values
within an image based on some criterion that adjusts its parameters as a
local image characteristics change. The adaptive contrast enhancement
filter is used with an image which has uneven contrast, where we want to
adjust the contrast differently in different regions of the image. It
works by using both local and global image statistics to determine regions
of the image.
Image after using ACE filter
Histogram equalization of original Image
Histogram equalization of Image after using ACE filter
Unsharp masking enhancement algorithm is representative of practical image
sharpening methods. It combines many operations like filtering and
Unsharp masking with lower limit=0, upper=100, with 2% low and high clipping
Original Image Unsharp masking with lower limit=0, upper=150, with 2% low and high clipping
Image Unsharp masking with lower limit=0, upper=200, with 2% low and high clipping
Image compression involves reducing the size of image data files, while
retaining necessary information. The resulting file is called the
compressed file and is used to reconstruct the image, resulting in the
The compression system model consists of two parts: the Compressor and
It consists of a preprocessing stage and encoding stage. The first
stage in preprocessing is data reduction. For example, the image data
can be reduced by gray level and/or spatial quantization. The second
step in preprocessing is the mapping process, which maps the original
image data in to another mathematical space, where it is easier to
compress the data. Next, as part of the encoding process, is the
quantization stage, which takes the potentially continuous data from
the mapping stage and puts it in discrete form. The final stage of
encoding involves the coding the resulting data, which maps the
discrete data from the quantizer onto a code in an optimal manner.
In this the decoding process is divided into two stages.First, it
takes the compressed file and reverses the original coding by mapping
the codes to the original, quantized values.Next, these values are
processed by a stage that performs an inverse mapping to reverse the
original mapping process. Finally, the image may be postprocessed to
enhance the look of the final image.
Compressor- System Model
Decompressor - System Model
The Wavelet-based compression shows much promise for the next generation
of image compression methods. Because wavelets localize information in
both the spatial and frequency domains, we consider these to be hybrid
methods. The wavelet transform combined with vector quantization has led
to the development of compression algorithms with high compression ratios.
a. Original image
b. WVQ compression ratio 10:1
c. Error of image (b)
d. WVQ compression ratio 15:1
e. Error of image (d)
f. WVQ compression ratio 33:1
g. Error of image (f)
h. WVQ compression ratio 36:1
i. Error of image (h)
Block Truncation Coding
Block truncation coding is a type of lossy compression which works by
dividing the image into small subimages and then reducing the number of
gray levels in each block. This reduction is performed by a quantizer that
adapts to the local image statistics. The levels for quantizer are chosen
to minimize a specified error criterion, and then all the pixel values
within each block are mapped to quantized levels.
Original Image having 65536 bytes.
Original Image having 65536 bytes. Compressed data occupies 16419 bytes. Compression ratio 1:4
Original Image having 65536 bytes. Compressed data occupies 8739 bytes. Compression ratio is 1:8.
Original Image having 65536 bytes. Compressed data occupies 3142bytes. Compression ratio is 1:15.