This article however reviews only some of the conventional digital orthorectification techniques. Section 2.0 describes various orthorectifacation algorithms, while section 3.0 presents different methods of orthorectification reprojection. Section 4 describes general orthorectification workflow in most commercial off-the-shelf software (COTS). The conclusion is presented in section 5. 2.0 Orthorectification algorithms Generally there are two classes of rectification approaches. The parametric and the non-parametric approaches (Hemmleb and Wiedemann, 1997). Whereas for the parametric approach the knowledge of the interior and exterior orientation parameters is required, non-parametric approaches require just control-points. Non-parametric approaches include polynomial transformation, and projective transformation. A comprehensive comparative study of orthorectification approaches can be found in Novak (1992). 2.1 Polynomial rectification The simplest way available in most standard image processing systems is to apply a polynomial function to the surface and adapt the polynomials to a number of checkpoints (GCPs). The procedure can only remove the effect of tilt, and can be applied on both satellite images and aerial photographs. One of several polynomial orders may be chosen, based on the desired accuracy and the available number of GCPs. Rosenholm and Akerman (1998) stated that for satellite images with simple geometric conditions, such as, near vertical and/or relatively flat areas, a low degree polynomial can give a sub-pixel result, and that higher degree polynomials are unreliable. Also Novak (1992) concluded that although polynomial rectification algorithm is very easy to use, they do not adequately correct relief displacement. Hemmleb and Wiedemann (1997) observed that it seems to be very dangerous to use higher grade polynomial transformations for the rectification of images, and that the required amount of control points and the risk of an oscillation is growing with the grade of the polynomial. Polynomial rectification equations are given by equations 1, and 2, below.  Where r, c are pixel coordinates of input image (row and column); x, y are coordinates of output image; a, b are coefficients of the polynomial, and n is the order of the polynomial. 2.2 Projective rectification To perform a projective rectification, a geometric transformation between the image plane and the projective plane is necessary. For the calculation of the eight unknown coefficients of the projective transformation, at least four control points in the object plane are required. Projective transformation is applicable to rectifying aerial photographs of flat terrain or images of facades of buildings, since it does not correct for relief displacement (Novak, 1992). The equations for projective rectification are given as follows (Hemmleb and Wiedemann, 1997):  Where r, c are pixel coordinates of input image (row and column); x, y are coordinates of output image; b11Lb23 are coefficients. 2.3 Differential rectification The objective of differential rectification is the assignment of grey values from the image (usually aerial image) to each cell within the orthophoto. Differential rectification is a phased procedure that uses several XYZ control points to georeference an image to the ground. Novak (1992) pointed out that the differential rectification corrects for both relief displacement and camera distortions, yields the best results, and can be applied for both aerial and satellite imagery. The procedure of differential rectification is applied in combination with the back projection (indirect) method of orthoimage reprojection (see section 3 below). This is based on the well-known collinearity principle, which states that the projection center of a central perspective image, an object point, and its photographic image lie upon a straight line. The collinearity principle is described by means of equations (5) and (6) (Kraus, 1992):  Where:
Sensor models are required to establish the functional relationship between the image space and the object space. Sensor models are typically classified into two categories: physical and generalized models. The choice of a sensor model depends primarily on the performance and accuracy required and the camera and control information available (Tao and Hu, 2001). A physical sensor model represents the physical imaging process. The parameters involved describe the position and orientation of a sensor with respect to an object-space coordinate system. Physical models, such as the collinearity equations, are rigorous, very suitable for adjustment by analytical triangulation and normally yield high modeling accuracy (a fraction of one pixel). There are many types of sensors such as Frame, Pushbroom, Whiskbroom, Panoramic, and SAR, etc. Physical models are sensor dependent where each requires a unique sensor model. With the increasing availability of imaging sensors, from an application point of view, it is not convenient for users to change the software or add new sensor models into their existing system in order to process new sensor data. Moreover, for dynamic sensors, the physical parameterization may become much more complicated since the orientation parameters vary with time and must be expressed as a function of time over the imaging period. It is also realized that rigorous physical sensor models are not always available, especially for images from commercial satellites (e.g., IKONOS), where the rigorous sensor models are hidden to the end users. This causes difficulties in developing a rigorous sensor model without knowing its imaging parameters (e.g., imaging geometry, relief displacement, Earth curvature, atmospheric refraction, lens distortion, etc.). The physical sensor models are mathematically complex and usually require relatively long computation time. 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. 2.5 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). |