The use of collinearity in imaging is a very versatile technique for image correction. The process is applicable in taking of picture using sensors from above the ground. The science behind the process is helping in converting several images taken into an orthographic image format. The camera does a transformation to a 3 x 3 matrix system which removes relief from the picture and making it machine readable. This form of change does its conversations within the ranges of changes in the X Y and Z axes of telemetry (Han, Guo, and Chou 313-316). The imaging dimensions taken have got a change in magnitude, through the use of the collinearity equation; the image can be converted to an orthophoto.
An orthophoto is essential in the processes that include the use of photogrammetric. This process involves several stages of conversions, which include the combination of photo geometry and also photo realism. The rectification process leads to the provision of a metric visualization scope. The correction path leads to a unified scale map as the result. The process of ortho photo generation includes several sub-steps which form the procedure of conversion that is used in explaining the formation of the unified image.
Digital imagery is the first step in the conversation process. The image is taken by sensors from the ground or above. The machines that facilitate this process can be a drone or the satellites in space. The exact position or area for telemetry can be determined through the use of the global positioning system. Then there is the digital elevation system which digitizes the images before transforming the exterior orientation through triangulations. Finally, the model is calibrated, and a report is generated.
The instruments that use the co linearity techniques have got self-evaluating process such as the dial test (Kraus). The dial test is more of comparative; it relates the image calibration to the installed index and verifies its functionality. Additionally, the conversion is usually likely to experience an error. The relative error in the logic involves a difference in the indicated quantity to the number of references.
Er = (Qn-QsQs×100 ) (Han, Guo, and Chou, 313-316)
Where Qs is the meter indication while Qs is the index specification or reference quantity
In remote sensing, the relation of the sensor plane to the object coordinate involves a series of mathematical expressions that lie in the X-Y and Z axis which are referenced to the focal point. The change in X (x-xo) is the size of the image along the x – axis. The other changes are in the Y and Z axes which form a 3 x 3 matrix that is the backbone of the collinearity equation.
The firsts equation relates the change in X to the changes in X at the three different points of the matrix (R11, R12, and R13) to the second row of the matrix. Additionally, the changes in Y relate to the second row of the matrix and Z the third row. However, before the calculations, we need to compute a ratio between the change in X and the change in X to the optical point.
X - Xo= -C Xp-XoZp-Zo while the change in Y ratio is y-yo =-C yp-yoZp-Zo
Then at this point, we convert the change in X with reference to the point of focus.
Xp – Xo = R11(x – xo) + R12(Y-Yo)+ R13( Z-Zo)
The same formula is applied to calculate the change in Y and finally Z.
X-Xo = -c R11X-Xo+ R21Y-Yo=R31(Z-Z0)R13X-Xo+ R23Y-Yo+R33(Z-Zo)
In orthophotography, it is important we follow the correct procedure and also have fixed points of reference such as the projection center of the sensor plane in which Zo is equivalent to C. with a high level of accuracy we can make machines provide very advanced metric visualizations for study and research.
Han, Jen-Yu, Jenny Guo, and Jun-Yun Chou. "A Direct Determination Of The Orientation Parameters In The Collinearity Equations". IEEE Geoscience and Remote Sensing Letters 8.2 (2011): 313-316. Web.
Kraus, Karl. Photogrammetry. Bonn: Dümmler, 1997. Print.