GATE Geomatics Engineering Section II Flashcards

24 sample cards from the Section II deck

Sampled from the end of the deck, so these are different cards from the ones shown on the syllabus page.

1. What is a percentage / saturation linear stretch and why is it used?

   A percentage (saturation) linear stretch clips a small percentage of extreme pixels (e.g., 2% at each tail) and stretches the remaining values linearly. It prevents outliers from compressing the stretch, giving better contrast for the bulk of pixels.

2. Name three non-linear contrast enhancement methods.

   Histogram equalization, logarithmic (and exponential) stretch, and Gaussian stretch. (Piecewise-linear is intermediate.)

3. What is histogram equalization and its effect?

   Histogram equalization is a non-linear stretch that redistributes pixel values so the output histogram is approximately uniform, using the cumulative distribution function as the transformation. It assigns more display range to the most frequently occurring grey levels, maximizing global contrast.

4. In histogram equalization, what transformation function is applied to grey level $r$?

   The CDF-based transformation: $$ s = T(r) = (L-1) \int_{0}^{r} p_{r}(w)\, dw $$ (continuous), or $s_{k} = (L-1)\sum_{j=0}^{k} \frac{n_{j}}{N}$ (discrete).

5. What is spatial (spatial-domain) enhancement and what image property does it operate on?

   Spatial enhancement modifies pixel values based on the values of neighbouring pixels (using filters/convolution kernels). It operates on spatial frequency — the rate of change of brightness over distance — rather than on individual pixel statistics.

6. What is a low-pass (smoothing) spatial filter and its effect?

   A low-pass filter averages or weights neighbourhood pixels (e.g., a mean filter) to attenuate high spatial frequencies. It smooths the image, reduces noise, but blurs edges and fine detail.

7. Write a $3\times3$ mean (box) smoothing kernel.

   $$ \frac{1}{9} \begin{pmatrix} 1 & 1 & 1 \\ 1 & 1 & 1 \\ 1 & 1 & 1 \end{pmatrix} $$

8. What is a median filter and what type of noise is it best at removing?

   A median filter is a non-linear filter that replaces each pixel with the median of its neighbourhood values. It is highly effective at removing salt-and-pepper (impulse) noise while preserving edges better than a mean filter.

9. What is a high-pass (sharpening) spatial filter and its effect?

   A high-pass filter emphasizes high spatial frequencies (edges, fine detail) by subtracting a smoothed version or using a kernel with a positive centre and negative surround. It sharpens/enhances edges but also amplifies noise.

10. Name common types of image noise.

    Gaussian (additive) noise, salt-and-pepper (impulse) noise, speckle (multiplicative, common in radar), and periodic noise.

11. What is Principal Component Analysis (PCA) in remote sensing?

    PCA is a linear transformation that converts correlated multispectral bands into a new set of uncorrelated variables (principal components), ordered by decreasing variance. It concentrates information into fewer bands and is used for dimensionality reduction and decorrelation.

12. How are the principal components mathematically derived?

    PCs are obtained from the eigenvalues and eigenvectors of the variance-covariance (or correlation) matrix $\Sigma$. The eigenvectors give the transformation axes (loadings) and the eigenvalues give the variance carried by each component; the PC with the largest eigenvalue holds the most variance.

13. What is the variance and correlation structure of the principal components produced by PCA?

    The principal components are mutually uncorrelated (orthogonal), so the covariance matrix of the PCs is diagonal. The variance of the $i$-th PC equals the $i$-th eigenvalue $\lambda_{i}$, with $\lambda_{1} \geq \lambda_{2} \geq \dots$

14. What is Discriminant Analysis and how does its objective differ from PCA?

    Discriminant analysis (e.g., Fisher's LDA) finds linear combinations of variables that best separate predefined classes. Unlike PCA (unsupervised, maximizes total variance), LDA is supervised and maximizes between-class separation relative to within-class scatter.

15. What criterion does Fisher's Linear Discriminant maximize?

    It maximizes the ratio of between-class scatter to within-class scatter: $$ J(w) = \frac{w^{T} S_{B}\, w}{w^{T} S_{W}\, w} $$ where $S_{B}$ is the between-class and $S_{W}$ the within-class scatter matrix.

16. What is the RGB to IHS colour transformation used for?

    It converts the Red-Green-Blue colour space into Intensity, Hue, and Saturation components. It is used for colour enhancement and especially for image (data) fusion — e.g., replacing intensity with a high-resolution panchromatic band, then transforming back (pan-sharpening).

17. Define the Intensity, Hue, and Saturation components in the IHS model.

    Intensity = overall brightness (total energy), e.g., $I = \frac{R+G+B}{3}$. Hue = dominant wavelength / pure colour (the attribute we name a colour). Saturation = purity or amount of white light mixed with the hue (how vivid vs. pastel).

18. What does the CMYK colour model represent and how does it relate to RGB?

    CMYK (Cyan, Magenta, Yellow, blacK) is a subtractive model used in colour printing; inks subtract light from white. Its primaries are the complements of the additive RGB primaries: cyan = white $-$ red, magenta = white $-$ green, yellow = white $-$ blue.

19. What is a band ratio and one benefit of using it?

    A band ratio divides the DN of one band by another, pixel by pixel: $R = \frac{DN_{i}}{DN_{j}}$. It enhances spectral differences (slopes), suppresses topographic/illumination effects, and highlights specific materials.

20. Write the formula and value range for NDVI.

    $$ NDVI = \frac{NIR - Red}{NIR + Red} $$ Range is $-1$ to $+1$; high positive values ($\approx 0.6$–$0.9$) indicate dense healthy vegetation.

21. Why is NDVI a normalized index rather than a simple ratio, and what does it exploit about vegetation?

    Normalization to $[-1,1]$ reduces sensor/illumination/topographic effects and bounds the values. It exploits that healthy vegetation strongly reflects NIR (high) and strongly absorbs red light (low) due to chlorophyll, giving a large difference.

22. Write the formula for NDWI (McFeeters, water-detection form).

    $$ NDWI = \frac{Green - NIR}{Green + NIR} $$ Positive values indicate water bodies (water reflects green, absorbs NIR); vegetation and soil give negative values.

23. In a typical NDVI image, what values do water, bare soil, and clouds/snow tend to show?

    Water and clouds/snow give negative or near-zero NDVI (sometimes negative), bare soil gives small positive values (~0.1–0.2), and dense vegetation gives high positive values (~0.6–0.9).

24. What is the key difference between point operations and neighbourhood (spatial) operations in image enhancement?

    Point operations (e.g., contrast stretch, histogram equalization) compute each output pixel from the single corresponding input pixel value only. Neighbourhood (spatial) operations (e.g., smoothing, sharpening filters) compute each output pixel from a window of surrounding input pixels.

What this deck covers

Section II flashcards FAQ