Planar Rectification from 3D Control Points using the XYRectify Software

BACKGROUND
Plane rectification of imagery has been successfully used for years. Rectification is the image processing technique where an image taken obliquely to a plane is converted to an equivalent ‘normal’ image of that same plane, i.e. the optical axis of the equivalent camera is then at right angles to the plane. The process typically requires the establishment of four or more control points (CPs) of known XY coordinates in the object plane, along with a marking of the four corresponding image points in the single image. Following the rectification process, XY coordinates can be measured within the scale homogeneous rectified image.

The challenge for accident reconstruction and crime scene practitioners, however, is that sometimes the scene covered by the single image to be rectified does not contain four suitable CPs within the plane of rectification, a common example of the this plane being a road surface or room floor. Lack of these CPs within the plane of interest precludes the possibility of extracting measurements of optimal accuracy from the singe photo or digital image.


For accurate rectification and subsequent 2D coordinate measurement within the plane of interest, the four or more CPs need to be well distributed, i.e. spread out to encompass the surface area of measurement interest.  A crash investigation example might be the measurement of a tire’s yaw mark. In this instance the CPs should completely surround the area of the yaw mark and any roadway features of interest. 


The accuracy of the rectified image outside of the area bounded by CPs can rapidly deteriorate in practical applications.  Also, it should be recalled that the rectification process involves a plane-to-plane transformation, thus the resulting 2D coordinates produced are of optimal accuracy when the object points of interest lie within a common plane, such as a generally flat road surface. Departures from co-planarity will cause a quality fall-off in the measurement of XY coordinates in the plane of interest.


XYRectify (2009) – software for generating rectified images from 2D/3D control points


XYRectify now presents the user with the option of using either traditional 2D XY CPs or 3D XYZ CPs. In the case of 3D control, a plane-to-plane transformation is again performed, but there is no need for the 3D CPs to all lie in the plane of interest. Instead, the orientation of the image, which is needed for the rectification process, is computed via space resection. In the case of 3D CPs, it is important for the angle subtended by the optical axis of the camera and the plane of interest not to be too small, as the shallower the angle, the poorer the resulting accuracy. For this reason, it is advisable to keep the camera pointing angle with respect to the plane of interest at greater than about 25 degrees. The 3D CPs can be marked anywhere in the single image for the rectification process, following the same principle of a well spread distribution as previously mentioned.


XYRectify Planar Rectification

Click for an expanded view of the above image

XYRectify analysis using 3D CPs
Shown in the above figure is a practical example of a police crime scene technician’s digital camera image in XYRectify with 3D CP marking. The exact position and angle of a knife and blood spots in the bathroom were in question, being the XY coordinates of points within the plane of the floor. In the analysis, the oblique image shown at the left was rectified to that shown at the right. This allowed the direct measurement of the XY coordinates of the seven blood drops and the position of the knife within the plane of the floor. These measurements were made long after the image was recorded; all that was required was the establishment of a number of 3D CPs.


These CPs, which were positioned on convenient feature points on the bathroom cabinetry and tiling, were in turn established using the iWitnessPROTM system. The resulting XYZ coordinates of CPs were accurate to 0.2mm RMS. The police technician’s image was then imported into iWitnessPRO, were 10 CPs were marked (using a process called “FOOM”) and the lens focal length and radial distortion were determined. FOOM permitted effective calibration of the camera that recorded the original image through simple measuring of the CPs in the image.


The image to be rectified was then imported into XYRectify, along with the FOOM-derived calibration data and the 3D CP data. The marking of CPs was then undertaken, which generated the planar rectified image. This JPEG image was named and saved, along with the generated TFW “world coordinate file” which defines the XY coordinate system of the rectified image. XY coordinates of interest are then directly read from the rectified image, via either XYRectify or a CAD system. In this case, the rectified image was traced in CAD, resulting in XY coordinates of 2mm accuracy within the plane of the bathroom floor.


Summary
The ability of 3D Control Point Marking in XYRectify affords an investigator more opportunity to measure points accurately within a planar surface from an obliquely recorded single photo or digital image. The imagery can also be from an unknown camera, which can be calibrated via iWitness or iWitnessPRO as part of the overall metric rectification process.


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