Videometrics VI
IS&T/SPIE's 11th Annual Symposium on Electronic Imaging: Science and Technology
23 to 29 January 1999
San Jose, California USA

Cocentric image capture for photogrammetric triangulation and mapping and for panoramic visualization

Henrik Haggrén, Petteri Pöntinen and Jyrki Mononen
Helsinki University of Technology

Keywords: photogrammetry, image acquisition, cocentric image sequence, image composition, hemispheric image, triangulation, mapping, panoramic visualization

The paper deals with cocentric image capturing and its use for mapping and visualization purposes. The work is based on a photogrammetric approach in composing hemispheric images from cocentric image sequences.

Cocentric image capturing

A cocentric image sequence is a set of images all of which have the same projection center. In Figure 1 a cocentric image  sequence is collected from 14 images showing the Nisqually glacier in Mt. Rainier. The original size of the negatives is 24 mm x 36 mm and the focal length of the camera lens is 500 mm.  This set of 14 images has approximately the same field of view which would have been covered by using a 150 mm lens. Alternatively, the same field of view would have been achieved by using a camera with larger image format like approximately of the size of 100 x 150 mm. The common projection center was here maintained by using a tripod. The distance between the camera and the glacier varies between 500 m to 1000 m.

The reason to capture cocentric images for this example was the need of high resolution image acquisition. The mosaic is an index image and has been made for visualization purpose only. Because of the narrow angle of the lens a projection onto a plane can be done without any remarkable geometric corrections. A similar reason to capture cocentric image sequences would be to record  views of extremely wide angles of view. However, a mosaic of wider angle would cause projection problems if not reprojected on a sphere or a cylinder. Consequently, this reprojection requires the orientation angles of the images to be known relative to each other.  Usually these would be controlled or recorded during the photography.

Projective rectification of cocentric images

In case the orientation angles are unknown, the geometric relationship of the images within a cocentric image sequence can be solved using 2-D projective transformations. With this transformation each image [(x), (y)] can be rectified to any second plane [x, y]. The function is gross linear and will keep the original projectivity of the images. Thus, in case the images are projected to a common plane like in Figure 2, the new image plane corresponds to an image which would have been recorded using a lens of wider viewing angle. The eight parameters of the transformation can be solved using corresponding point observations between these two planes. The minimum number of such points is four. In case the new plane is physically a plane - like a wall -  the 2-D coordinates should be measured on-site. In our approach we consider the new plane being a virtual one as we want to refrain from any unnecessary on-site measuring.

Registration and rectification of two images

Let us consider one of the original images to be the virtual plane. We then register and rectify the next coming image onto it. This is exemplified in Figure 3 where the image on the right has been joined and transformed projectively to the image on the left. This joint can be controlled by the overlapping parts of the images. Instead of using only four points for the projective transformation, we include the overlapping parts entirely and solve the transformation by a least squares image matching procedure.  As practically every pixel within the overlapping region is part of the transformation the matching becomes rather rigid. The resulting image contains the original image added with the projectively rectified and resampled neighboring image. The principal point remains unchanged and locates still on the left image.

 Hemispheric image

We continue the simultaneous registration and rectification process throughout the entire image sequence. As this cannot be done along a plane we reproject all images onto a cylinder (Figure 4). For the cylinder projection we use first the known focal length. Then we register and rectify each subsequent image to the previous one and project it then to the cylinder as well. We continue until the whole sequence has been registered and projected. In case the sequence spans over the full 360° degrees we finally register the first image to the sequence to the cylinder again.  In case the focal length was first approximated, the sequence becomes either too short or too long. Therefore the projection to the cylinder should be  corrected by adjusting the focal length accordingly shorter or longer. The final projection is a hemispheric image (Figure 5). The horizon is dermined by  the first image of the sequence - or more specifically - by its principal point. The origin along the horizon line can be defined anywhere.


The main applications of hemispheric images are within mapping and visualization. As the image coordinates of a hemispheric image can be transformed to direction angles by known cylinder geometry (Figures 6 and 7), a block of these images can be used for triangulation purposes. The exterior orientation of a single hemispheric image can defined by resection in space. Accordingly, two hemispheric images allow ordinary mapping of new objects based on space intersections. For visualization purposes the hemispheric images are just appropriate. The composing of views or images of full 360° degrees can be performed automatically without any idea of interior or exterior orientations.


We have described a photogrammetric approach in composing hemispheric images from cocentric image sequences. The procedure becomes especially appropriate in cases of weak network geometry. Although we presented the approach in a sequential way - registration on plane, projection on cylinder, adjustment of the focal length - the whole procedure can be performed in one batch. The advantage of this approach is no doubt that the registration of the images within a sequence to each other is done directly by image matching, not by tie points. This makes the composed hemispheric image geometrically extremely rigid.