Linear Approach for Initial Recovery of the Exterior Orientation Parameters of Randomly Captured Images by Low-Cost Mobile Mapping Systems

Nowadays, 3D modeling of objects can be achieved using either passive or active remote sensing systems. Active sensors, such as laser scanners, are able to directly provide precise and reliable 3D information of scanned objects. However, the derived point cloud usually lacks spectral information (especially when dealing with collected data by mobile platforms). On the other hand, passive sensors, which commonly use digital frame cameras, can be incorporated for 3D reconstruction while providing spectral information of the derived coordinates. Compared to active sensors, the spectral information from passive sensors would allow for the derivation of better and more reliable semantic information pertaining to the reconstructed objects (e.g., the type and condition of mapped objects could be easily derived from the resulting 3D models). Therefore, passive-sensor-based reconstruction still remains the most complete, economical, flexible, and widely-used 3D modelling option in many areas (Remondino and El-Hakim, 2006). 3D reconstruction from digital images captured by passive sensors requires the knowledge of the Interior Orientation Parameters (IOP) of the utilized camera, the Exterior Orientation Parameters (EOP) of the involved images, and the corresponding points/features in the set of overlapping images. The IOP of the utilized camera can be derived from a camera calibration process. The EOP of the involved imagery can be either derived through an indirect geo-referencing procedure using tie and control points or a direct geo-referencing process through the implementation of a GNSS/INS unit onboard the mapping platform. While the latter approach provides practical convenience in terms of simplifying the geo-referencing process, it requires significant initial investment for the acquisition of the GNSS/INS Position and Orientation System (POS) – especially, when seeking high level of reconstruction accuracy. Therefore, significant research efforts have been exerted towards the development of automated procedures for 3D reconstruction and derivation of the geo-referencing parameters of the involved imagery in the absence of a GNSS/INS unit or in the presence of less accurate POS information from consumer-grade GNSS/MEMS units. As far as the 3D reconstruction is concerned, one of two approaches could be adopted. In the first approach, a two-step procedure is adopted for the 3D reconstruction assuming the availability of prior knowledge regarding the EOP of the involved images. In the first step, corresponding features are identified in the set of available images (i.e., the matching problem). In the second step, the 3D positions of the matched points are derived using a simple intersection procedure that incorporates their image coordinates, IOP of the utilized camera, and the EOP of the involved images (Kraus, 2007). The main drawback of this procedure is the reliance on the availability of highly accurate EOP, which could be only available through the utilization of high-end POS unit. The second approach for 3D reconstruction, which was mainly initiated by the computer vision research community, the feature matching and EOP recovery are simultaneously established. A commonly used procedure in this approach is known as Structure from Motion (SFM), which is based on 3-step strategy. In the first step, the relative orientation parameters relating stero-images or image triplets are initially estimated using automatically identified point and/or line features. Then, a reference coordinate system is established and utilized to define the position and orientation parameters for the involved imagery using the derived relative orientation parameters in the first step as well as 3D coordinates of the matched points. Finally, a bundle adjustment procedure is usually implemented to refine the derived information in the second step (Triggs et al., 2000). Compared to the first approach for 3D reconstruction, SFM is more advantageous since it allows for 3D mapping in the presence or absence of GNSS/INS units. SfM 3D reconstruction approaches usually use either a sequential or hierarchical approach to initially estimate the EOP of the involved images – the focus of the second step of the above mentioned 3-step strategy – in an incremental manner. For example, Snavely et al. (2006) proposed an incremental SfM procedure, in which images are added one by one into the reference frame. In their method, the reference frame is established from a single pair of images that has a large number of matched points/features and a long baseline. Then, new image is incrementally augmented to the reference frame. The EOPs of the augmented image are estimated using the reconstructed 3D points from the first pair through a Direct Linear Transformation (DLT) procedure. Fitzgibbon and Zisserman (1998) developed a hierarchical approach to recover the EOPs for either closed or open set of acquired images. In this method, trifocal tensors are estimated for all consecutive image triplets. Then, a hierarchical approach is applied to gradually integrate the image triplets to subsets. Finally, these subsets are augmented into a single block. For either the sequential and hierarchical approaches, intermediate bundle adjustment – which is time consuming – is implemented to ensure successful * Corresponding author. This is useful to know for communication with the appropriate person in cases with more than one author. ISPRS Technical Commission I Symposium, Sustaining Land Imaging: UAVs to Satellites 17 – 20 November 2014, Denver, Colorado, USA, MTSTC1-141