The problem of the large number of images required in the preprocessing stage of all the approaches that approximate the plenoptic function can be circumvented with the use of geometric image inferences. View interpolation techniques utilise information as pixel depth or image to image constrains such as the fundamental matrix and the trilinear tensors to reproject image pixels from a small number of reference images to a given viewpoint.
Chen et al. [9] represented the whole set of original images as a graph structure. Each node in the graph contained a source image, the camera parameters and apriori known corresponding range data. Arcs connecting adjacent nodes represent directional morph maps (optical flow) obtained from the dense correspondences. A similar approach has been proposed in [8] where instead, a stereo algorithm has been used to compute approximate depth maps.
To synthesise views in-between a pair of images the displacement vectors are linearly interpolated and the pixels in the reference images are moved by the interpolated vector to their destination. However, linear interpolation only yields a valid reprojection if the source and the new image planes are parallel.
To overcome this limitation Seitz et al. [52] proposed a three step algorithm. Initially they prewarp (rectify) the source images so that their image planes are aligned. By linearly interpolating positions and colours on the reference images a new intermediate view along the line segment connecting the two camera centres is generated. A postwarping process finally transforms the image plane of the new view to its desired position and orientation. The principal restriction on this technique rely on the configuration of the two basis views which must satisfy the monotonicity constraint.
Generation of new views from rectilinear source images has been extended to cylindrical panoramic images. McMillan et al. [38] reconstruct panoramic views by stitching together images acquired from a purely rotated camera and describe a geometric constraint for cylindrical projections that determines the possible positions of a point given its location in some other cylinder. This constraint has been used to establish correspondences between cylindrical reference pairs which gives a dense disparity map. A warp function subsequently combines the transformation of the disparity values from the known reference pair to the new cylinder and its reprojection as a planar image for viewing. Similar work using stereo pairs of planar images has been proposed in [32].
The introduction of the cylindrical epipolar geometry was the novel aspect of [38]. However, a more stable geometric constraint than the epipolar geometry is the trilinear tensor [55]. The use of trilinearities as a warping function from model views to novel synthesised images has been presented in [2]. A seed tensor is computed from three reference images. For every new view with known camera motion parameters relative to one of the reference images, a tensor is computed between the remaining two images and this new view. The tensor is subsequently used to render the image.
The relatively small number of reference images required by view interpolation together with the absence of explicit geometry are their principal characteristics. However, all such techniques rely on establishing correspondence between image pixels in the source views. Although, several geometric constraints have been imposed to solve this problem, in practice accuracy depends on the system calibration which is itself a challenging problem. Furthermore, when stereo correspondence estimation algorithms are used the small base line requirement, imposes limitations on the reference image configuration while the aperture problem limits the applicability of correlation techniques.