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Review of Digital Image Orthorectification Techniques
Rigorous physical sensor models are more accurate (Rosenholm and Akerman, 1998; Tao and Hu, 2001). An example is the orbital model of the satellite track and the rotation angles of the instrument for orthorectification of IRS images (Rosenholm and Akerman, 1998). However the development of generalized sensor models independent of sensor platforms and sensor types is very attractive. In a generalized sensor model, the transformation between the image and the object space is represented as some general function without modeling the physical imaging process. Rational function model rectification Generalized sensor models, such as the usage of the Rational Function sensor Model (RFM) (Tao and Hu, 2001), have alleviated the requirement to obtain a physical sensor model, and with it, the requirement for a comprehensive understanding of the physical model parameters. Furthermore, as the RFM sensor model implicitly provides the interior and exterior sensor orientation, the availability of GCPs is no longer a mandatory requirement. Consequently, the use of the RFM for photogrammetric mapping is becoming a new standard in high-resolution satellite imagery. This has already been implemented in various high-resolution sensors, such as IKONOS and QuickBird (Croitoru et al., 2004). The RFM sensor model describes the geometric relationship between the object space and image space. It relates object point coordinates (X,Y,Z) to image pixel coordinates (r,c) or vice versa using 78 rational polynomial coefficients (RPCs). For the ground-to-image transformation, the defined ratios of polynomials have the following form (Croitoru et al., 2004):  Where (rn,cn) are the normalized row (line) and column (sample) index of pixels in image space; Xn) ,Yn) and Zn) are normalized coordinate values of object points in ground space; and the polynomial coefficients aijk, bijk, cijk, are called Rational Function Coefficients (RFCs). Orthorectification reprojection Orthorectification algorithms are often performed in conjunction with reprojection procedure, where rays from the image are reprojected onto a model of the terrain. Fundamentally reprojection can be done in two ways:
 Where GSD is the Ground Sample Distance, which is the distance between each pixel, also referred to as the pixel size. Notice that the equation takes into account that pixel coordinate system has the Y-axis downwards and the world coordinate system has the Y-axis pointing upwards/north. In the case of backward projection, the object space X, Y coordinates related to every pixel of the final orthoimage are determined. The height Z at a specific X, Y point is calculated from the DEM or the 3D model and then the X, Y, Z object space coordinates are projected in the original image in order to acquire the gray level value for the orthoimage pixel. Interpolation or resampling process in the original image is also essential because of the fact that the projected coordinates will not fit accurately at the original image pixel centers. In the backward projection instead of interpolating in the orthoimage, the interpolation is done in the source image. This is easier to implement, and the interpolation can be done right away for each output pixel. Further more only pixels that are needed in the orthoimage are reprojected. In the backward projection method, the pixel-to-world transformation is again given by (Mikhail et al., 2001) as  The position in the same image that corresponds to the found XYZ can be obtained by a sensor model (i.e collinearity equations as applied in the differential orthorectification method). General orthorectification workflow Most commercial off-the-shelf software (COTS) for software (i.e Erdas Imagine, PCI Geomatics, ENVI, ZI Imagine, LH System, TNT products, etc) contain comprehensive suite of products designed for performing tasks required in producing high quality, seamless digital orthophoto imagery products from aerial (standard and digital) and commercial satellite imagery. These software products include programs required to produce the input components for orthorectification including project setup, DEM interpolation/formatting, and GCP and tie point collection. These products can also be used to create imagery mosaics, and they have the ability for orthorectification using RPFs Most of these software products currently support processing of ephemeris data and orthorectification for the following commercial imaging satellites:
Tie points are produced by identifying the same pixel location in two or more images within their overlap areas. These software products can process tie points for an unlimited number of input images. To get an overview of the control point residuals and identify possible outliers, these software provide the ability to generate residual reports for all scenes within a project or for individual scenes. Mosaicking requires delineation of cutlines and, in many cases, radiometric adjustment of adjacent images to hide the seamlines and produce a more visually pleasing product. These software have both manual and automatic mosaicking options. General orthorectification workflow includes the following tasks:
This article has described, in a succinct form, some of the popular conventional techniques of orthorectification. These methods range from those with simple algorithm to those with sophisticated routines, such as the physical and the generalized models. Modern trend has shown more inclination to the use of generalized models. One of such state-of-the-art method is the application of RFM. In future RFM will have the advantage that the photogrammetric processing software can be kept unchanged when dealing with different sensor data since the generalized sensor model is sensor independent. For new sensors, only the values of coefficients in the generalized sensor model need to be updated. Again since there are no functional relations between the parameters of the rigorous model and those of the RPF, the physical parameters cannot be recovered from the RPF and the sensor information can be kept confidential. Currently, in order to protect the undisclosed sensor information, some commercial satellite data vendors, such as Space Imaging Inc., only provide users with the RFM parameters but do not provide any information regarding the physical sensor model. Even under this condition, users are still able to achieve a reasonable accuracy without knowing the rigorous sensor models for photogrammetric processing. References
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