18-Geom-A5 Remote Sensing and Image Analysis · May 2014
Nivaar worked solution (AI-drafted; not reviewed by a licensed engineer)
National Exams — May 2014 — 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); most require essay-format answers, and all five are solved in full below. 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.
Supervised classification requires the analyst to delineate representative training samples for each information class in advance, which presumes reliable prior knowledge of the area and adequate ground reference. Unsupervised classification (for example ISODATA or $k$-means) instead lets the algorithm find the natural spectral clusters in the data, which the analyst labels afterward. One therefore prefers unsupervised classification when:
• little or no reliable ground-truth or training data is available, or fieldwork/reference maps for the scene are lacking;
• the analyst is unfamiliar with the area and cannot confidently identify or locate the classes to train on;
• the number and identity of distinct classes are not known a priori, and the goal is to discover the natural spectral groupings present;
• the work is an exploratory / reconnaissance first pass, or an objective, analyst-bias-free partition of the spectral space is wanted;
• the scene is spectrally complex and one wants the data themselves to reveal how many separable classes actually exist before committing to training sites.
In short, unsupervised methods trade the analyst's up-front knowledge for the data's own structure, which is exactly the right trade when that knowledge or reference data is missing.
A minimum-distance-to-means classifier assigns a pixel to the class whose mean spectral vector is nearest (usually in Euclidean distance); it uses only the class means and ignores how the classes are spread or correlated. A maximum-likelihood (ML) classifier models each class by its full mean vector and variance–covariance matrix and assigns the pixel to the class of highest probability density. One therefore chooses maximum-likelihood when:
• the classes have unequal variances / different spectral spread, so a class that is inherently more variable should be allowed a wider acceptance region — which min-distance cannot represent;
• the spectral bands are correlated and the class clusters are elongated or tilted in feature space (non-circular), so the covariance orientation matters;
• the class distributions overlap, where accounting for each class's probability density resolves the ambiguous pixels far better than nearest-mean;
• there are enough training pixels per class (rule of thumb: more than about $10n$–$100n$ for $n$ bands) to estimate the covariance matrices reliably.
Conversely, the simpler minimum-distance classifier is preferable when training samples are too few to estimate covariances stably, when classes are well separated with similar spread, or when computational speed is at a premium. ML is more accurate precisely because it uses the second-order (covariance) statistics that min-distance discards — but only if enough training data exist to estimate them.
