__Introduction__

__Introduction__

Remote sensing is the science of collecting information about any object on a surface from a well-defined distance with a proper sensor. In general, it may define as a technique of gathering data of the surface of the earth from a distance with a sensor mounted on a moving platform. Remote sensing can be classified into two major forms 1). Active remote sensing (Microwave Remote Sensing) and 2). Passive remote sensing. The collected remote sensed data firstly required the operation of pre-processing which includes radiometric corrections and geometric corrections. Here in this discussion, we are going to learn about geometric corrections.

__Need for Geometric Corrections__

__Need for Geometric Corrections__

It is usually necessary to pre-process the remotely sensed data and remove the geometric distortion so that individual picture elements are in their proper planimetric (x, y) map locations.

This allows remote sensing–derived information to be related to other thematic data in geographic information systems (GIS) or spatial decision support systems (SDSS). Geometrically corrected imagery can be used to extract accurate distance, polygon area, and direction (bearing) information.

**Internal and External Errors During the Collection of Remote Sensing Image**

Normally the remote sensing image contains internal and external errors. It is important to recognize the source of the internal and external error and whether it is systematic (predictable) or non-systematic.

**Internal** Errors in Remote Sensed Imagery

**Internal**Errors in Remote Sensed ImageryInternal errors are generally introduced by the sensors themselves or in combination with earth rotation or curvature characteristics. These types of errors are generally corrected using prelaunch or inflight platform ephemeris (i.e., information about the geometric characteristics of the sensor system and the Earth at the time of data acquisition). Geometric distortions in imagery that can sometimes be corrected through analysis of sensor characteristics and ephemeris data include:-

- skew caused by Earth rotation effects,
- scanning system-induced variation in nominal ground resolution cell size
- scanning system one-dimensional relief displacement,
- scanning system tangential scale distortion.

__External Errors in Remote Sensed Imagery__

__External Errors in Remote Sensed Imagery__

These types of errors are introduced by phenomena that vary in nature through space and time. The most important external variables that can cause a geometric error in remote sensor data are random movements by the aircraft (or spacecraft) at the exact time of data collection, which usually involve: Altitude changes and Attitude changes

**Altitude changes:-**

(Increasing the altitude will result in smaller-scale imagery, Decreasing the altitude of the sensor system will result in larger-scale imagery. This type of error occurs when the terrain gradually increases or decreases in elevation. Remote sensing platforms do not generally attempt to adjust for such gradual changes in elevation. The use of geometric rectification algorithms will normally be used to minimize the effects) figure 1.

**Attitude changes****(roll, pitch, and yaw):-**

Normally satellite-based remote sensing is more stable as compared with airplane or drone-based remote sensing due to not being influenced by atmospheric turbulence or wind. In case of aircraft flying at suborbital altitudes must continuously face atmospheric downdrafts, updrafts, head-winds, tail-winds, and cross-winds while collecting remote sensor data figure 1.

**Figure 1**.* Internal and external errors of altitude and attitude change.*

**What is a ground control point (GCP)?**

Geometric errors introduced by the internal and external factors (attitude change (roll, pitch, and yaw) and altitude change) can be corrected by using the GCPs with the appropriate mathematical models. In simple words, we may define it as a location that represents the surface of the earth that can be identified on the collected sensed image and located accurately in a map. For the rectification of a remotely sensed imagery, the GIS (geographic information system) operator must require two distinct sets of coordinates associated with each GCP:

- Image coordinate.
- Map coordinate.

This collection of paired coordinates from many GCPs can be modeled to estimate transformation coefficients. This coefficient was later used to rectify the remotely sensed dataset to a standard datum and map projection.

**Figure 2**.* collection of GPS points from a topographic map and satellite image of Landsat TM for the rectification operation.*

**Different Types of Geometric Correction Techniques**

The geometric errors are very common in remotely sensed data and it required to be corrected before the application is used. There are mainly two most common methods are used in remote sensing software to correct or rectify the geometric distortions in a present on in imagery: – a). Image to map rectification or registration, and b). Image to image rectification or registration.

**Image to Map Rectification: – **

**it **is the method of rectification in which the geometry of imagery is made planimetric. The image-to-map rectification process normally involves selecting GCP image pixel coordinates (row and column) with their map coordinate counterparts (e.g., meters northing and easting in a Universal Transverse Mercator map projection) figure 3. The following types of maps are normally used for rectifying the sensed imagery:-

**Hard copy planimetric maps****Digital planimetric****Digital orthophotosquads which are already geometrically rectified****Global positing system (GPS) points**

**Figure 3.** *Image to map rectification left side image is *satellite imagery and on the right,* a rectified toposheet is represented.*

**Image to Image Registration: –**

this technique includes the process by which two images of a common area are positioned coincident with respect to one another so that corresponding elements of the same ground appear in the same place on the registered images.

**Figure 4**. *Example of the *image to *image rectification process.*

**Method of examining the Accuracy of geometrically corrected Imagery**

The most popular method of examining the accuracy of the rectified imagery is Root mean squared error. A measure of the difference between locations that are known and locations that have been interpolated or digitized or resampled. A simple way to measure such distortion is to compute the RMS error for each ground control point by using the equation:

Here in the equation X_{orig} and Y_{orig} are the original rows and column coordinates of the GCP in the image and X’ and Y’ are the computed coordinates in the original image.

The square root of the squared deviations represents a measure of the accuracy of this GCP in the image. By computing RMSerror for all GCPs, it is possible to 1) see which GCPs exhibit the greatest error, and 2) sum all the RMSerror.

**Resampling Method of Processing**

At the end of the rectification, the interpolation method is used to generate output data. While in the case of geometric correction the term is used to resample either interpolation. There are mainly three types of resampling methods are used in the rectification operation.

- Nearest neighbour resampling
- Bilinear resampling
- Cubic resampling

All these 3 methods of resampling are based on the principle of **intensity interpolation **which involves the extraction of a brightness value from an *X’, Y’ *location in the distorted input imagery and its relocation to the appropriate x,y coordinate location in the rectified out image.

**Nearest Neighbor Resampling**

**This resampling method** processed the brightness value of the closed to the specified X’, Y’ coordinate is assigned to the output x,y output. All the computation is based on the Pythagorean theorem. The assigned value of the output pixel is the value found at the nearest input pixel.

An advantage of this resampling technique is that it doesn’t alter the image pixel value during the process. If we see in the other interpolation techniques that they use averages to compute the output intensity value often removing valuable information in the image.

**Bilinear Resampling Method**

**This method** assigns the output pixel values by resampling the pixel values in two orthogonal directions in the input image.

Basically, it fits a plane of four-pixel values nearest to the desired position in the input image and then computes a new brightness value based on the weighted distance to these points. ** ** The weighted average of the new brightness value is computed using the equation:

Here Z_{k} is the surrounding four data point values, D^{2}_{k} stands for the distances squared from the point in question (x′, y′) to these data points. In our example.

**Cubic Convolution Resampling Method**

This method or technique of resampling is the same as the bilinear resampling method, except that the weighted value of the pixel is assigned by computing the 16 input pixel values surrounding the location of the desired *x’, y’* pixel are used to estimate the value of the output pixel. For computing the weighted values the following equation is used:

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