A Comparison of Bilinear Interpolation, Cubic Convolution, and
Brownian Interpolation with Least Squares Matching
Data for Numerical Experiment
The SUBURB dataset released by the Working Group III/3 of International Society for Photogrammetry and Remote Sensing (ISPRS), is used in this study. This dataset consists of a digitized b/w stereopair and a DTM. The scene of this stereopair is primarily a group of single-family, one- to three-floor suburban homes surrounded by gardens and trees. The DTM was derived with MATCH-T (INPHO-GmbH, Stuttgart, Germany), from this stereopair.
The right and left images are named SUBURB_R.PGM and SUBURB_L.PGM respectively. The images are in epipolar geometry, and both sizes are 1000*1000 pixels The file name of the DTM is SUBURB.DTM, containing three-dimensional coordinates in the terrain system. The planimetric spatial resolution of this DTM is one meter.
Image Data Preprocessing
The Fractal Factors and Image Reduction
The fractal property is examined with Equation (2) in all directions and shown in Table1.
Table 1 Parameter H estimated for different sampling schemes
| Sampling type vs. reduction ratio |
Range of pair distance |
Decimation sampling |
Averaging sampling |
| H |
R2 |
H |
R2 |
| Original |
(1-23) |
0.5544 |
0.9922 |
- |
- |
| Reduction ratio 1/2 |
(1-12) |
0.5108 |
0.9944 |
0.5689 |
0.9915 |
| Reduction ratio 1/4 |
(1-6) |
0.4714 |
0.9964 |
0.5633 |
0.9938 |
| Reduction ratio 1/8 |
(1-4) |
0.4231 |
0.9982 |
0.5537 |
0.9965 |
| Reduction ratio 1/16 |
(1-11) |
0.0618 |
0.9614 |
0.0881 |
0.9729 |
The stereo-pair's left image is selected for reduction. The reduction ratios are chosen to be 1/2, 1/4, and 1/8. Both the decimation and averaging scheme are adopted. The six reduced images, three for each sampling scheme, are then interpolated back to the original image size with the afore-mentioned four interpolation schemes.
Target Points of Least Matching
The data points in the DTM dataset SUBURB.DTM are transformed into an epipolar coordinate system and then to a row and column system. After transformation, each point in SUBURB.DTM corresponds to a stereo-point pair located on the left and right images. Let the point on the left image be a target point. The point on the right image would then be the conjugate point for correct matching. In this study, 849 points well-distributed around the center of the left original image are selected as the target points. Results obtained from image matching are transformed to ground coordinates and then compared with the ground truth in the SUBURB.DTM file .The RMSE of the coordinates between the results from image matching and ground truth function as the index of positioning accuracy.
