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**Digital Image Processing**

Manipulation of Digital Images by computers. Pre processing / Image Restoration Image Enhancement Information Extraction

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**Image Pre-processing / Image Restoration**

Compensates for data errors, noise and geometric distortions introduced in the images during acquisitioning and recording. Pre-processing operations, referred to as image restoration and rectification, are intended to correct for sensor- and platform-specific radiometric and geometric distortions of data. Pre processing functions are normally carried out prior to the main data analysis and extraction of information

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Image Pre-processing Geometric Correction :- includes correcting for geometric distortions due to sensor-Earth geometry variations, and conversion of the data to real world coordinates (e.g. latitude and longitude) on the Earth's surface. Radiometric Correction :- includes correcting the data for sensor irregularities and unwanted sensor or atmospheric noise, and converting the data so that they accurately represent the reflected or emitted radiation measured by the sensor.

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INCLUDES Restoring periodic line dropouts. Restoring periodic line striping. Correcting for atmospheric scattering. Correcting geometric distortions. Removal of random noise.

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**Why Geometric Correction ?**

To allow an image to overlay a map. To warp an image to eliminate distortion caused by terrain, instrument wobble, earth curvature, etc. To change the spatial resolution of an image. To change the map projection.

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**Two basic strategies for fitting images to maps**

Rectification: Find Ground Control Points (GCPs) on the image and on maps (or from the field). Registration: Create links between two images or between the image and a digital map.

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**Image Rectification and Registration**

Raw, remotely sensed image data gathered by a satellite or an aircraft are representation of irregular surface of earth, or Geometry of an image is distorted with respect to north south orientation of map. This is a process of geometrically correcting an image so that it can be represented on planar surface, conform to other images or conform to a map. It is necessary when accurate area, distance and direction measurements are required to be made from the imagery.

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It is achieved by transforming the data from one grid system into another grid system using a geometric transformation. In other word by establishing mathematical relationship between the addresses of pixels in an image with corresponding coordinates of those pixels on another image or map or ground.

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Definitions Rectification : The process by which the geometry of an image is made planimetric. A map coordinate system is involved. Registration : The process of making an image conform to another image. A map coordinate system is not necessarily involved. Georeferencing : It refers to process of assigning map coordinates to image data. It involves changing only the map coordinates information in an image file. The grid does not change. Geocoding : Geographical referencing of image data. Geocoded images are rectified to a particular map projection and pixel size, and usually radiometric corrections are applied.

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**Polynomial Transformation**

Polynomial equations are used to convert the source file coordinates to rectified map coordinates. Depending upon the distortions in the imagery, the number of GCPs used, their location relative to one other, complex polynomial equations are used. The degree of complexity of the polynomial is expressed as ORDER of the polynomial. The order is simply the highest exponent used in the polynomial.

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**Linear Transformations / Affine Transformation / **

First Order Transformation X = a0 + a1 x + a2 y Y = b0 + b1 x + b2 y where, X, Y are the Rectified coordinates ( output ) x, y are the source coordinates ( input )

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If the coefficients a0 ,a1 , a2 ,b0 ,b1 and b2 are known then, the above polynomial can be used to relate and point on map to its corresponding point on image and vice versa. Hence six coefficients are required for this transformation ( three for X and three for Y ). Requires Minimum THREE GCP's for solving the above equation. To solve linear polynomials we first take three GCP's to compute the six coefficients. Its source coordinates in the original input image are say Xi and Yi . The position of the same points in reference map in degrees, feet or meters are say x, y.

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Now, if we input the map x, y values for the first GCP back into the linear polynomial equation with all the coefficients in the place, we would get the computed or retransformed xr and yr values, which are supposed to be location of this point in input image.

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**Second Order Transformation**

Requires minimum of 6 GCPs. Use for larger area where earth curvature is a factor. Use where there is moderate terrain. Use with aircraft data where roll, pitch, yaw are present.

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**Third Order Transformation Requires minimum of 10 GCPs. **

Very rugged terrain. Typically we want at least 3x the minimum number of GCPs

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**Accuracy of the Transformation**

The method used involves computing Root Mean Square Error ( RMS error ) for each of the ground control point. RMS error is the distance between the input ( source or measured ) location of a GCP and the retransformed (or computed ) location for the same GCP. RMS error is computed with a Euclidean Distance Equation. RMS error = Square root [ ( xr - xi )2 + ( yr - yi )2 ] where, xi and yi are the input source coordinates. xr and yr are the retransformed coordinates.

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**RMS error is expressed as distance in the source coordinate system.**

It is the distance in pixel widths. An RMS error of 2 means that the reference pixel is 2 pixels away from the retransformed pixel.

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**Intensity Interpolation or Image Resampling**

Once an image is warped, how do you assign DNs to the “new” pixels? Since the grid of pixels in the source image rarely matches the grid for the reference image, the pixels are resampled so that new data file values for the output file can be calculated. This process involves the extraction of a brightness value from a location in the input image and its reallocation in the appropriate coordinate location in the rectified output image.

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RESAMPLING The process by which the geometric transformations are applied to the original data is called Resampling. Resampling Techniques :- I. Nearest Neighbor Technique:- Assigns the value of the nearest pixel to the new pixel location. II. Bilinear Interpretation:- Assigns the average value of the 4 nearest pixels to the new pixel location. III.Bicubic Convolution:- Assigns the average value of the 16 nearest pixels to the new pixel location.

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**Nearest Neighbor Technique **

In this technique, the value of the closest input sample is assigned to the output pixel. II. Bilinear Interpretation Two - dimensional linear ( Bilinear ) interpretation over the four surrounding values. This is essentially an averaging process and hence results in a smoothen picture. III. Bicubic Convolution Is based on fitting two dimensional third degree polynomial surfaces to the region surrounding the point. It uses the sixteen nearby input values to calculate the output pixel value.

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output pilxel. Open in new window II. Bilinear Interpretation

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Y = f0 + f1 * x + f2 * y

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Geometric transformations Affine transformations Forward mapping Interpolations schemes.

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