18-Geom-A5 Remote Sensing and Image Analysis · May 2015
Nivaar worked solution (AI-drafted; not reviewed by a licensed engineer)
National Exams — May 2015 — 04-Geom-A5 Remote Sensing and Image Analysis. Closed-book; one approved Casio or Sharp calculator permitted. Format: five questions of equal value (20 marks each), all of which must be answered (total 100 marks). Questions 1–4 are essay-format; Question 5 is a short quantitative comparison of two covariance matrices. Radiometric and image-processing conventions follow standard North-American digital-image-processing practice (8-bit Landsat/ETM+ imagery).
Reference texts: J. R. Jensen, Introductory Digital Image Processing: A Remote Sensing Perspective (4th ed., Pearson, 2016); Lillesand, Kiefer & Chipman, Remote Sensing and Image Interpretation (7th ed., Wiley, 2015); J. A. Richards, Remote Sensing Digital Image Analysis (5th ed., Springer, 2013); J. R. Schott, Remote Sensing: The Image Chain Approach (2nd ed., Oxford, 2007).
Question text not reproduced: the examination questions are © Engineers and Geoscientists BC. Open the official past paper (linked at the top of this page) to read the question, then follow the worked solution below.
Geometric rectification maps each output (map-grid) pixel back into the input image, where its computed location almost never falls exactly on an integer pixel centre. An intensity-interpolation (resampling) rule is therefore needed to assign that output pixel a brightness value from the surrounding input pixels. The three standard methods, in order of increasing sophistication, are nearest-neighbour, bilinear interpolation, and cubic convolution.
The output pixel is simply assigned the digital number (DN) of the single input pixel whose centre is closest to the back-projected location; no arithmetic is performed on the brightness values.
Advantages. It is the fastest and computationally simplest method, and — crucially — it transfers original DN values unchanged, creating no new (synthetic) brightness values and preserving the original radiometry and the extremes of the histogram. This makes it the only choice when the pixel values must retain their exact original meaning.
Disadvantages. Because whole pixels are duplicated or dropped, features can be shifted by up to half a pixel, and linear features (roads, field edges) acquire a characteristic blocky, "staircase" appearance. The output looks spatially rough, and the geometric fidelity of individual pixels is the poorest of the three.
The output value is a distance-weighted average of the four (2 × 2) input pixels surrounding the back-projected point, interpolating first in one direction and then the other.
Advantages. It is a good compromise between speed and quality: the result is geometrically more accurate than nearest-neighbour and visually much smoother, with the staircase artefacts largely removed.
Disadvantages. Because it averages four pixels, it creates new DN values that were not in the original image and acts as a low-pass (smoothing) filter — it blurs sharp edges and suppresses high-frequency detail and the histogram extremes. The altered radiometry makes it unsuitable where the original DNs must be preserved.
The output value is a weighted combination of the surrounding sixteen (4 × 4) input pixels, using a cubic weighting function that approximates the ideal (sinc) reconstruction kernel.
Advantages. It generally gives the most visually pleasing result — the sharpest and least blurred of the three — and the highest geometric/radiometric accuracy for continuous-tone display, because the cubic kernel reconstructs gradients better than a linear average.
Disadvantages. It is by far the most computationally expensive (sixteen inputs per output pixel), and like bilinear it synthesizes new DN values; the cubic kernel can even overshoot near strong edges, producing values slightly outside the original data range. The original brightness values are again not preserved.
For an application in which the original digital numbers must survive the resampling unchanged — most importantly before a spectral classification, but also before any quantitative analysis that depends on the raw radiometry — the correct choice is nearest-neighbour interpolation. It is the only one of the three that assigns each output pixel an actual input DN rather than a computed average, so no new (non-physical) brightness values are introduced and the class-defining spectral values are carried through intact. Bilinear and cubic convolution both blend neighbouring pixels and would corrupt the very DN values the classifier relies on (and would blur class boundaries), so they are avoided when radiometric integrity matters and reserved for producing visually smooth imagery for display or interpretation.
