• Band Interleaved by Pixel (BIP)
• Band Interleaved by Line (BIL)
• Band Sequential (BQ)

Digital image analysis is usually conducted using Raster data structures - each image is treated as an array of values. It offers advantages for manipulation of pixel values by image processing system, as it is easy to find and locate pixels and their values. Disadvantages becomes apparent when one needs to represent the array of pixels as discrete patches or regions, where as Vector data structures uses polygonal patches and their boundaries as fundamental units for analysis and manipulation. Though vector format is not appropriate to for digital analysis of remotely sensed data.

Image Resolution
Resolution can be defined as "the ability of an imaging system to record fine details in a distinguishable manner". A working knowledge of resolution is essential for understanding both practical and conceptual details of remote sensing. Along with the actual positioning of spectral bands, they are of paramount importance in determining the suitability of remotely sensed data for a given applications. The major characteristics of imaging remote sensing instrument operating in the visible and infrared spectral region are described in terms as follow:

• Spectral resolution
• Radiometric resolution
• Spatial resolution
• Temporal resolution

Spectral Resolution refers to the width of the spectral bands. As different material on the earth surface exhibit different spectral reflectances and emissivities. These spectral characteristics define the spectral position and spectral sensitivity in order to distinguish materials. There is a tradeoff between spectral resolution and signal to noise. The use of well -chosen and sufficiently numerous spectral bands is a necessity, therefore, if different targets are to be successfully identified on remotely sensed images.

Radiometric Resolution or radiometric sensitivity refers to the number of digital levels used to express the data collected by the sensor. It is commonly expressed as the number of bits (binary digits) needs to store the maximum level. For example Landsat TM data are quantised to 256 levels (equivalent to 8 bits). Here also there is a tradeoff between radiometric resolution and signal to noise. There is no point in having a step size less than the noise level in the data. A low-quality instrument with a high noise level would necessarily, therefore, have a lower radiometric resolution compared with a high-quality, high signal-to-noise-ratio instrument. Also higher radiometric resolution may conflict with data storage and transmission rates.

Spatial Resolution of an imaging system is defines through various criteria, the geometric properties of the imaging system, the ability to distinguish between point targets, the ability to measure the periodicity of repetitive targets ability to measure the spectral properties of small targets.

The most commonly quoted quantity is the instantaneous field of view (IFOV), which is the angle subtended by the geometrical projection of single detector element to the Earth's surface. It may also be given as the distance, D measured along the ground, in which case, IFOV is clearly dependent on sensor height, from the relation: D = hb, where h is the height and b is the angular IFOV in radians. An alternative measure of the IFOV is based on the PSF, e.g., the width of the PDF at half its maximum value.

A problem with IFOV definition, however, is that it is a purely geometric definition and does not take into account spectral properties of the target. The effective resolution element (ERE) has been defined as "the size of an area for which a single radiance value can be assigned with reasonable assurance that the response is within 5% of the value representing the actual relative radiance". Being based on actual image data, this quantity may be more useful in some situations than the IFOV.

Other methods of defining the spatial resolving power of a sensor are based on the ability of the device to distinguish between specified targets. Of the concerns the ratio of the modulation of the image to that of the real target. Modulation, M, is defined as:

M = Emax -Emin / Emax + Emin
Where Emax and Emin are the maximum and minimum radiance values recorded over the image.

Temporal resolution refers to the frequency with which images of a given geographic location can be acquired. Satellites not only offer the best chances of frequent data coverage but also of regular coverage. The temporal resolution is determined by orbital characteristics and swath width, the width of the imaged area. Swath width is given by 2htan(FOV/2) where h is the altitude of the sensor, and FOV is the angular field of view of the sensor.

How to Improve Your Image?
Analysis of remotely sensed data is done using various image processing techniques and methods that includes:

• Analog image processing
• Digital image processing.

Digital Image Processing is a collection of techniques for the manipulation of digital images by computers. The raw data received from the imaging sensors on the satellite platforms contains flaws and deficiencies. To overcome these flaws and deficiencies inorder to get the originality of the data, it needs to undergo several steps of processing. This will vary from image to image depending on the type of image format, initial condition of the image and the information of interest and the composition of the image scene. Digital Image Processing undergoes three general steps:

• Pre-processing
• Display and enhancement
• Information extraction

Flowchart

Pre-processing consists of those operations that prepare data for subsequent analysis that attempts to correct or compensate for systematic errors. The digital imageries are subjected to several corrections such as geometric, radiometric and atmospheric, though all these correction might not be necessarily be applied in all cases. These errors are systematic and can be removed before they reach the user. The investigator should decide which pre-processing techniques are relevant on the basis of the nature of the information to be extracted from remotely sensed data. After pre-processing is complete, the analyst may use feature extraction to reduce the dimensionality of the data. Thus feature extraction is the process of isolating the most useful components of the data for further study while discarding the less useful aspects (errors, noise etc). Feature extraction reduces the number of variables that must be examined, thereby saving time and resources.

Image Enhancement operations are carried out to improve the interpretability of the image by increasing apparent contrast among various features in the scene. The enhancement techniques depend upon two factors mainly

• The digital data (i.e. with spectral bands and resolution)
• The objectives of interpretation

As an image enhancement technique often drastically alters the original numeric data, it is normally used only for visual (manual) interpretation and not for further numeric analysis. Common enhancements include image reduction, image rectification, image magnification, transect extraction, contrast adjustments, band ratioing, spatial filtering, Fourier transformations, principal component analysis and texture transformation.

Information Extraction is the last step toward the final output of the image analysis. After pre-processing and image enhancement the remotely sensed data is subjected to quantitative analysis to assign individual pixels to specific classes. Classification of the image is based on the known and unknown identity to classify the remainder of the image consisting of those pixels of unknown identity. After classification is complete, it is necessary to evaluate its accuracy by comparing the categories on the classified images with the areas of known identity on the ground. The final result of the analysis consists of maps (or images), data and a report. These three components of the result provide the user with full information concerning the source data, the method of analysis and the outcome and its reliability.

Pre-Processing of the Remotely Sensed Images
When remotely sensed data is received from the imaging sensors on the satellite platforms it contains flaws and deficiencies. Pre-processing refers to those operations that are preliminary to the main analysis. Preprocessing includes a wide range of operations from the very simple to extremes of abstractness and complexity. These categorized as follow:

1. Feature Extraction
2. Radiometric Corrections
3. Geometric Corrections
4. Atmospheric Correction

1. Instruments used to record the data
2. From the effect of the atmosphere

1. The relative distribution of brightness over an image in a given band can be different to that in the ground scene.
2. The relative brightness of a single pixel from band to band can be distorted compared with spectral reflectance character of the corresponding region on the ground.

The following methods defines the outline the basis of the cosmetic operations for the removal of such defects:

Line-Dropouts
A string of adjacent pixels in a scan line contain spurious DN. This can occur when a detector malfunctions permanently or temporarily. Detectors are loaded by receiving sudden high radiance, creating a line or partial line of data with the meaningless DN. Line dropouts are usually corrected either by replacing the defective line by a duplicate of preceding or subsequent line, or taking the average of the two. If the spurious pixel, sample x, line y has a value DNx,y then the algorithms are simply:

DNx,y = DNx,y-1
DNx,y = (DNx,y-1 + DNx,y+1)/2


De-Striping
Banding or striping occurs if one or more detectors go out of adjustment in a given band. The systematic horizontal banding pattern seen on images produced by electro-mechanical scanners such as Landsat's MSS and TM results in a repeated patterns of lines with consistently high or low DN. Two reasons can be thus put forward in favor of applying a 'de-striping' correction :

1. The visual appearance and interpretability of the image are thereby improved.
2. Equal pixel values in the image are more likely to represent areas of equal ground leaving radiance, other things being equal.

The two different methods of de-striping are as follow:

First method entails a construction of histograms for each detector of the problem band, i.e., histograms generated from by the six detectors: these histograms are calculated for the lines 1,7,13,……, lines 2, 8, 14, ……, etc. Then the means and standard deviation are calculated for each of the six histograms. Assuming the proportion of pixels representing different soils, water, vegetation, cloud, etc. are the same for each detector, the means and standard deviations of the 6 histograms should be the same. Stripes, however are characterised by distinct histograms. De-striping then requires equalisation of the means and standard deviation of the six detectors by forcing them to equal selected values - usually the mean and standard deviation for the whole image.

The process of histogram matching is also utilised before mosaicking image data of adjacent scenes (recorded at diferent times) so as to accommodate differences in illumination levels, angles etc. A further application is resolution merging, in which a low spatial resolution image is sharpened by merging with high spatial resolution image.

Second method is a non-linear in the sense that relationship between radiance rin(received at the detector) and rout (output by the sensor) is not describable in terms of a single linear segments.

Random Noise
Odd pixels that have spurious DN crop up frequently in images - if they are particularlt distracting, they can be suppressed by spatial filtering. By definition, these defects can be identified by their marked differences in DN from adjacent pixels in the affected band. Noisy pixels can be replaced by substituting for an average value of the neighborhood DN. Moving windows of 3 x 3 or 5 x 5 pixels are typically used in such procedures.

Geometric Corrections
Raw digital images often contain serious geometrical distortions that arise from earth curvature, platform motion, relief displacement, non-linearities in scanning motion. The distortions involved are of two types:

1. Non-systematic Distortion
2. Systematic Distortions

• Due to (Fig.1).
  
  
  
• The amount of earth rotation during 26 sec required to scan an image results in distortion. The correction for this distortion can be done by scanning 16 successive group of lines, offset towards the west to compensate for the earth rotation, which causes the parallelogram outline of the restored image. Its is true for TM Image. (Fig.2)
  

Distortion Evaluated from Ground Control
Caused during the spacecraft scan of the ground .

• Altitude Variation (Fig.3)
  
  
  
• Attitude Variation - pitch, roll & yaw (Fig.4)
  
  
  

1. Locating Ground Control Points This process employs identification of geographic features on the image called ground control points (GCPs), whose position are known such as intersection of streams, highways, airport, runways etc. Longitude and latitude of GCPs can be determined by accurate base maps where maps are lacking GPS is used to determine the Latitude and Longitude from navigation satellites. Thus a GCP is located in the field and determing its position using GPS. Accurate GCPs are essential to accurate rectification. GCPs should be
   
   

• Resampling Methods The location of output pixels derived from the ground control points (GCPs) is used to establish the geometry of the output image and its relationship to the input image. Difference between actual GCP location and their position in the image are used to determine the geometric transformation required to restore the image. This transformation can be done by different resampling methods where original pixels are resampled to match the geometric coordinates. Each resampling method employs a different strategy to estimate values at output grid for given known values for the input grid.
  
  

Nearest Neighbor The simplest strategy is simply to assign each corrected pixel, the value from the nearest uncorrected pixel. It has the advantages of simplicity and the ability to preserve original values in the altered scene, but it may create noticeable errors, which may be severe in linear features where the realignment of pixels is obvious. (Fig. 5).

Bilinear Interpolation The strategy for the calculation of each output pixel value is based on a weighted average of the four nearest input pixels. The output image gives a natural look because each output value is based on several input values. There are some changes occurred when bilinear interpolation creates new pixel value. (Fig.6)

Brightness values in the input image are lost

As the output image is resampled by averaging over areas, it decreases the spatial resolution of the image

Cubic Convolution It is the most sophisticated and complex method of resampling. Cubic convolution uses a weighted average of values within a neighborhood of 25 adjacent pixels. The images produced by this method are generally more attractive but are drastically altered than nearest neighbor and bilinear interpolation.(Fig.7).

• Image Correction using Mapping Polynomial Polynomial equations are used to convert the source coordinates to rectified coordinate, using 1st and 2nd order transformation . The coffiecients of the polynomial such as ai and bi are calculated by the least square regression method, that will help in relating any point in the map to its corresponding point in the image.
  
  x0 = b1 + b2xi + b3yi
  y0 = a1 + a2xi + a3yi
  
  Where (xI yI ) are the input coordinates and (x0 y0 ) are the output coordinates.
  
  Initially few GCPs cofficients are required to calculate the transformation matrix and the inverse transformation that could convert the reference coordinates of the GCPs back to the source coordinate system. This enables determination of RMS error for chosen transformation. The best order of transformation can be obtained using trial and error process while ignoring the highest RMS error from the least square computation.

Systematic Distortions
Geometric systematic distortions are those effects that are constant and can be predicted in advance. These are of two types:

Scan Skew
It is caused by forward motion of the spacecraft during the time of each mirror sweep. In this case the ground swath scanned is not normal to the ground track. (Fig.8).

Radiative Transfer theory is used to make quantitative calculations of the difference between the satellite received radiance and earth leaving radiance.

Radiation traveling in a certain direction is specified by the angle f between that direction and the vertical axis z and setting a differential equation for a small horizontal element of the transmitting medium (the atmosphere) with thickness dz. The resulting differential equation is called the radiative transfer equation. The equation will therefore be different for different wavelengths of electromagnetic radiation because of the different relative importance of different physical process at different wavelength.

Need for Atmospheric Correction
When an image is to be utilized, it is frequently necessary to make corrections in brightness and geometry for accuracy during interpretation and also some of the application may require correction to evaluate the image accurately. The various reason for which correction should be done:

• Derive ratios in 2 bands of multi spectral image since the effect of atmospheric scattering depends on the wavelength, the two channels will be unequally affected and the computed ratio will not accurately reflect the true ratio leaving the earth's surface
• When land surface reflectance or sea surface temperature is to be determined.
• When two images taken at different times and needed to be compared or mosaic the images

• Ignore the atmosphere
• Collecting the ground truth measurements of target temperature, reflectance etc and calibrating these values or quantities on the ground and the radiance values by the sensor.
• Modeling the absorption or scattering effects for the measurement of the composition and temperature profile of the atmosphere.
• Utilizing the information about the atmosphere inherent to remotely sensed data i.e use the image to correct itself.

1. In TM 7 the shadows having DN value 0 & 1. Now for each pixel the DN in TM 7 is plotted against TM 1 and a straight line is fitted through the plot using least square techniques. If there was no haze in TM 1 then the line would pass through the origin. But as there is haze the intercept is offset along the band 1. Haze has an additive effect on scene brightness. Therefore to correct the haze effect on TM 1, the value of the intercept offset is subtracted from the DN of each band 1 pixel for the entire image.(Fig 12)
   
   
   
   
2. The second technique also uses the areas with DN as 0 or 1 in TM 7. The histogram of TM 7 has pixels with 0 where as the histogram of TM 1 lacks the pixel in the range from 0 to 20 approximately because of light scattered into the detector by atmosphere thus this abrupt increase in pixels in TM 1 is subtracted from all the DNs in band 1 to restore effects of atmospheric scattering.(Fig 13)
   
   

The amount of atmospheric correction depends upon

• Wavelength of the bands
• Atmospheric conditions

• Spectral Enhancement Techniques
• Multi-Spectral Enhancement Techniques

Spectral Enhancement Techniques

Density Slicing
Density Slicing is the mapping of a range of contiguous grey levels of a single band image to a point in the RGB color cube. The DNs of a given band are "sliced" into distinct classes. For example, for band 4 of a TM 8 bit image, we might divide the 0-255 continuous range into discrete intervals of 0-63, 64-127, 128-191 and 192-255. These four classes are displayed as four different grey levels. This kind of density slicing is often used in displaying temperature maps.

Contrast Stretching
The operating or dynamic , ranges of remote sensors are often designed with a variety of eventual data applications. For example for any particular area that is being imaged it is unlikely that the full dynamic range of sensor will be used and the corresponding image is dull and lacking in contrast or over bright. Landsat TM images can end up being used to study deserts, ice sheets, oceans, forests etc., requiring relatively low gain sensors to cope with the widely varying radiances upwelling from dark, bright , hot and cold targets. Consequently, it is unlikely that the full radiometric range of brand is utilised in an image of a particular area. The result is an image lacking in contrast - but by remapping the DN distribution to the full display capabilities of an image processing system, we can recover a beautiful image. Contrast Stretching can be displayed in three catagories:

Linear Contrast Stretch
This technique involves the translation of the image pixel values from the observed range DNmin to DNmax to the full range of the display device(generally 0-255, which is the range of values representable in an 8bit display devices)This technique can be applied to a single band, grey-scale image, where the image data are mapped to the display via all three colors LUTs.

It is not necessary to stretch between DNmax and DNmin - Inflection points for a linear contrast stretch from the 5th and 95th percentiles, or ± 2 standard deviations from the mean (for instance) of the histogram, or to cover the class of land cover of interest (e.g. water at expense of land or vice versa). It is also straightforward to have more than two inflection points in a linear stretch, yielding a piecewise linear stretch.

Histogram Equalisation
The underlying principle of histogram equalisation is straightforward and simple, it is assumed that each level in the displayed image should contain an approximately equal number of pixel values, so that the histogram of these displayed values is almost uniform (though not all 256 classes are necessarily occupied). The objective of the histogram equalisation is to spread the range of pixel values present in the input image over the full range of the display device.

Gaussian Stretch
This method of contrast enhancement is base upon the histogram of the pixel values is called a Gaussian stretch because it involves the fitting of the observed histogram to a normal or Gaussian histogram. It is defined as follow:

F(x) = (a/p)0.5 exp(-ax2)

Multi-Spectral Enhancement Techniques

Image Arithmetic Operations
The operations of addition, subtraction, multiplication and division are performed on two or more co-registered images of the same geographical area. These techniques are applied to images from separate spectral bands from single multispectral data set or they may be individual bands from image data sets that have been collected at different dates. More complicated algebra is sometimes encountered in derivation of sea-surface temperature from multispectral thermal infrared data (so called split-window and multichannel techniques).

Addition of images is generally carried out to give dynamic range of image that equals the input images.

Band Subtraction Operation on images is sometimes carried out to co-register scenes of the same area acquired at different times for change detection.

Multiplication of images normally involves the use of a single'real' image and binary image made up of ones and zeros.

Band Ratioing or Division of images is probably the most common arithmetic operation that is most widely applied to images in geological, ecological and agricultural applications of remote sensing. Ratio Images are enhancements resulting from the division of DN values of one spectral band by corresponding DN of another band. One instigation for this is to iron out differences in scene illumination due to cloud or topographic shadow. Ratio images also bring out spectral variation in different target materials. Multiple ratio image can be used to drive red, green and blue monitor guns for color images. Interpretation of ratio images must consider that they are "intensity blind", i.e, dissimilar materials with different absolute reflectances but similar relative reflectances in the two or more utilised bands will look the same in the output image.

Principal Component Analysis
Spectrally adjacent bands in a multispectral remotely sensed image are often highly correlated. Multiband visible/near-infrared images of vegetated areas will show negative correlations between the near-infrared and visible red bands and positive correlations among the visible bands because the spectral characteristics of vegetation are such that as the vigour or greenness of the vegetation increases the red reflectance diminishes and the near-infrared reflectance increases. Thus presence of correlations among the bands of a multispectral image implies that there is redundancy in the data and Principal Component Analysis aims at removing this redundancy.

Principal Components Analysis (PCA) is related to another statistical technique called factor analysis and can be used to transform a set of image bands such that the new bands (called principal components) are uncorrelated with one another and are ordered in terms of the amount of image variation they explain. The components are thus a statistical abstraction of the variability inherent in the original band set.

To transform the original data onto the new principal component axes, transformation coefficients (eigen values and eigen vectors) are obtained that are further applied in alinear fashion to the original pixel values. This linear transformation is derived from the covariance matrix of the original data set. These transformation coefficients describe the lengths and directions of the principal axes. Such transformations are generally applied either as an enhancement operation, or prior to classification of data. In the context of PCA, information means variance or scatter about the mean. Multispectral data generally have a dimensionality that is less than the number of spectral bands. The purpose of PCA is to define the dimensionality and to fix the coefficients that specify the set of axes, which point in the directions of greatest variability. The bands of PCA are often more interpretable than the source data.

Decorrelation Stretch

Principal Components can be stretched and transformed back into RGB colours - a process known as decorrelation stretching.

If the data are transformed into principal components space and are stretched within this space, then the three bands making up the RGB color composite images are subjected to stretched will be at the right angles to each other. In RGB space the three-color components are likely to be correlated, so the effects of stretching are not independent for each color. The result of decorrelation stretch is generally an improvement in the range of intensities and saturations for each color with the hue remaining unaltered. Decorrelation Stretch, like principal component analysis can be based on the covariance matrix or the correlation matrix. The resultant value of the decorrelation stretch is also a function of the nature of the image to which it is applied. The method seems to work best on images of semi-arid areas and it seems to work least well where the area is covered by the image includes both land and sea.

Canonical Components
PCA is appropriate when little prior information about the scene is available. Canonical component analysis, also referred to as multiple discriminant analysis, may be appropriate when information about particular features of interest is available. Canonical component axes are located to maximize the separability of different user-defined feature types.

Hue, Saturation and Intensity (HIS) Transform
Hues is generated by mixing red, green and blue light are characterised by coordinates on the red, green and blue axes of the color cube. The hue-saturation-intensity hexcone model, where hue is the dominant wavelength of the perceived color represented by angular position around the top of a hexcone, saturation or purity is given by distance from the central, vertical axis of the hexcone and intensity or value is represented by distance above the apex of the hexcone. Hue is what we perceive as color. Saturation is the degree of purity of the color and may be considered to be the amount of white mixed in with the color. It is sometimes useful to convert from RGB color cube coordinates to HIS hexcone coordinates and vice-versa

The hue, saturation and intensity transform is useful in two ways: first as method of image enhancement and secondly as a means of combining co-registered images from different sources. The advantage of the HIS system is that it is a more precise representation of human color vision than the RGB system. This transformation has been quite useful for geological applications.

Fourier Transformation
The Fourier Transform operates on a single -band image. Its purpose is to break down the image into its scale components, which are defined to be sinusoidal waves with varying amplitudes, frequencies and directions. The coordinates of two-dimensional space are expressed in terms of frequency (cycles per basic interval). The function of Fourier Transform is to convert a single-band image from its spatial domain representation to the equivalent frequency-domain representation and vice-versa.

The idea underlying the Fourier Transform is that the grey-scale valuea forming a single-band image can be viewed as a three-dimensional intensity surface, with the rows and columns defining two axes and the grey-level value at each pixel giving the third (z) dimension. The Fourier Transform thus provides details of

• The frequency of each of the scale components of the image
• The proportion of information associated with each frequency component

Spatial Processing

Spatial Filtering
Spatial Filtering can be described as selectively emphasizing or suppressing information at different spatial scales over an image. Filtering techniques can be implemented through the Fourier transform in the frequency domain or in the spatial domain by convolution.

Convolution Filters
Filtering methods exists is based upon the transformation of the image into its scale or spatial frequency components using the Fourier transform. The spatial domain filters or the convolution filters are generally classed as either high-pass (sharpening) or as low-pass (smoothing) filters.

Low-Pass (Smoothing) Filters
Low-pass filters reveal underlying two-dimensional waveform with a long wavelength or low frequency image contrast at the expense of higher spatial frequencies. Low-frequency information allows the identification of the background pattern, and produces an output image in which the detail has been smoothed or removed from the original.

A 2-dimensional moving-average filter is defined in terms of its dimensions which must be odd, positive and integral but not necessarily equal, and its coefficients. The output DN is found by dividing the sum of the products of corresponding convolution kernel and image elements often divided by the number of kernel elements.

A similar effect is given from a median filter where the convolution kernel is a description of the PSF weights. Choosing the median value from the moving window does a better job of suppressing noise and preserving edges than the mean filter.

Adaptive filters have kernel coefficients calculated for each window position based on the mean and variance of the original DN in the underlying image.

High-Pass (Sharpening) Filters
Simply subtracting the low-frequency image resulting from a low pass filter from the original image can enhance high spatial frequencies. High -frequency information allows us either to isolate or to amplify the local detail. If the high-frequency detail is amplified by adding back to the image some multiple of the high frequency component extracted by the filter, then the result is a sharper, de-blurred image.

High-pass convolution filters can be designed by representing a PSF with positive centre weightr and negative surrounding weights. A typical 3x3 Laplacian filter has a kernal with a high central value, 0 at each corner, and -1 at the centre of each edge. Such filters can be biased in certain directions for enhancement of edges.

A high-pass filtering can be performed simply based on the mathematical concepts of derivatives, i.e., gradients in DN throughout the image. Since images are not continuous functions, calculus is dispensed with and instead derivatives are estimated from the differences in the DN of adjacent pixels in the x,y or diagonal directions. Directional first differencing aims at emphasising edges in image.

Frequency Domain Filters
The Fourier transform of an image, as expressed by the amplitude spectrum is a breakdown of the image into its frequency or scale components. Filtering of these components use frequency domain filters that operate on the amplitude spectrum of an image and remove, attenuate or amplify the amplitudes in specified wavebands. The frequency domain can be represented as a 2-dimensional scatter plot known as a fourier spectrum, in which lower frequencies fall at the centre and progressively higher frequencies are plotted outward.

Filtering in the frequency domain consists of 3 steps:

• Fourier transform the original image and compute the fourier spectrum
• Select an appropriate filter transfer function (equivalent to the OTF of an optical system) and multiply by the elements of the fourier spectrum.
• Perform an inverse fourier transform to return to the spatial domain for display purposes.

• Patterns of their DN, usually in multichannel data (Spectral Classification).
• Spatial relationship with neighbouring pixels
• Relationships between the data accquired on different dates.

1. Detection of different kinds of features in an image.
2. Discrimination of distinctive shapes and spatial patterns
3. Identification of temporal changes in image

Fundamentally spectral classification forms the bases to map objectively the areas of the image that have similar spectral reflectance/emissivity characteristics. Depending on the type of information required, spectral classes may be associated with identified features in the image (supervised classification) or may be chosen statistically (unsupervised classification). Classification has also seen as a means to compressing image data by reducing the large range of DN in several spectral bands to a few classes in a single image. Classification reduces this large spectral space into relatively few regions and obviously results in loss of numerical information from the original image. There is no theoretical limit to the dimensionality used for the classification, though obviously the more bands involved, the more computationally intensive the process becomes. It is often wise to remove redundant bands before classification.

Classification generally comprises four steps:

• Pre-processing, e.g., atmospheric, correction, noise suppression, band ratioing, Principal Component Analysis, etc.
• Training - selection of the particular features which best describe the pattern
• Decision - choice of suitable method for comparing the image patterns with the target patterns.
• Assessing the accuracy of the classification

1. Measurements on Scatter Diagram
   Each pixel value is plotted on the graph as the scatter diagram indicating the category of the class. In this case the 2-dimensional digital values attributed to each pixel is plottes on the graph
   
   
2. Minimum Distance to Mean Classifier/Centroid Classifier
   This is a simple classification strategies. First the mean vector for each category is determined from the average DN in each band for each class. An unknown pixel can then be classified by computing the distance from its spectral position to each of the means and assigning it to the class with the closest mean. One limitation of this technique is that it overlooks the different degrees of variation.
   
   
3. Parallelpiped Classifier
   For each class the estimate of the maximum and minimum DN in each band is determine. Then parallelpiped are constructeds o as to enclose the scatter in each theme. Then each pixel is tested to see if it falls inside any of the parallelpiped and has limitation
   A pixel may fall outside the parallelpiped and remained unclassified.
   Theme data are so strongly corrected such that a pixel vector that plots at some distance from the theme scatter may yet fall within the decision box and be classified erroneously.
   Sometimes parallelpiped may overlap in which case the decision becomes more complicated then boundary are slipped.
   
   
4. Gaussian Maximum Likelihood Classifier
   This method determines the variance and covariance of each theme providing the probability function. This is then used to classify an unknown pixel by calculating for each class, the probability that it lies in that class. The pixel is then assigned to the most likely class or if its probability value fail to reach any close defined threshold in any of the class, be labeled as unclassified. Reducing data dimensionally before hand is a\one approach to speeding the process up.

Unsupervised Classification
This system of classification does not utilize training data as the basis of classification. This classifier involves algorithms that examine the unknown pixels in the image and aggregate them into a number of classes based on the natural groupings or cluster present in the image. The classes that result from this type of classification are spectral classes. Unsupervised classification is the identification, labeling and mapping of these natural classes. This method is usually used when there is less information about the data before classification.

There are several mathematical strategies to represent the clusters of data in spectral space.

1. Sequential Clustering
   In this method the pixels are analysed one at a time pixel by pixel and line by line. The spectral distance between each analysed pixel and previously defined cluster means are calculated. If the distance is greater than some threshold value, the pixel begins a new cluster otherwise it contributes to the nearest existing clusters in which case cluster mean is recalculated. Clusters are merged if too many of them are formed by adjusting the threshold value of the cluster means.
   
   
2. Statistical Clustering
   It overlooks the spatial relationship between adjacent pixels. The algorithm uses 3x3 windows in which all pixels have similar vector in space. The process has two steps
   • Testing for homogeneity within the window of pixels under consideration.
   • Cluster merging and deletion
     
     
   Here the windows are moved one at time through the image avoiding the overlap. The mean and standard derivation are calculated for each band of the window. The smaller the standard deviation for a given band the greater the homogenity of the window. These values are then compared by the user specified parameter for delineating the upper and lower limit of the standard deviation. If the window passes the homogenity test it forms cluster. Clusters are created untill then number exceeds the user defined maximum number of clusters at which point some are merged or deleted according to their weighting and spectral distances.
   
   
3. Iso Data Clustering (Iterative Self Organising Data Analysis Techniques)
   Its repeatedly performs an entire classification and recalculates the statistics. The procedure begins with a set of arbitrarily defined cluster means, usually located evenly through the spectral space. After each iteration new means are calculated and the process is repeated until there is some difference between iterations. This method produces good result for the data that are not normally distributed and is also not biased by any section of the image.
   
   
4. RGB Clustering
   It is quick method for 3 band, 8 bit data. The algorithm plots all pixels in spectral space and then divides this space into 32 x 32 x 32 clusters. A cluster is required to have minimum number of pixels to become a class. RGB Clustering is not baised to any part of the data.

Source: http://www.gisdevelopment.net/