GATE Geomatics Engineering Section II Syllabus

Section II syllabus — full chapter and topic list

Expand any chapter to see its topics and sub-topics. This is the whole examinable outline for Section II in GATE Geomatics Engineering, not a summary of it.

1. 1

   Data Quantization and Processing

   4 topics

   • Sampling and quantization theory
   • Principle of Linear System
   • Convolution
   • Continuous and Discrete Fourier Transform
2. 2

   Digital Image Processing

   3 topics

   • Digital image characteristics: image histogram and scattergram and their significance
   • Variance-Covariance matrix
   • Correlation matrix and their significance
3. 3

   Radiometric and Geometric Corrections

   1 topic

   • Registration and Resampling techniques
4. 4

   Image Enhancement

   2 topics

   • Contrast Enhancement: Linear and Non-linear methods
   • Spatial Enhancement: Noise and Spatial filters
5. 5

   Image Transformation

   4 topics

   • Principal Component Analysis (PCA)
   • Discriminant Analysis
   • Color transformations (RGB - IHS, CMYK)
   • Indices (Ratios, NDVI, NDWI)
6. 6

   Image Segmentation and Classification

   1 topic

   • Simple techniques

Section II flashcards for GATE Geomatics Engineering

21 of 60 cards from the Section II deck — real questions with worked answers.

1. What is sampling in the context of digital image acquisition?

   Sampling is the process of discretizing the spatial coordinates of a continuous image, i.e., measuring the image at a finite grid of points (pixels). It converts continuous spatial variables $(x,y)$ into discrete locations.

2. What is quantization in digital image formation?

   Quantization is the process of discretizing the amplitude (brightness/grey-level) values of the sampled image into a finite set of levels. For a $k$-bit image the number of grey levels is $L = 2^{k}$.

3. State the Nyquist sampling theorem.

   To reconstruct a signal without aliasing, the sampling frequency must be at least twice the highest frequency present: $f_{s} \geq 2 f_{max}$. The threshold $f_{s} = 2 f_{max}$ is the Nyquist rate.

4. What is aliasing and how is it avoided?

   Aliasing is the distortion (false low-frequency artefacts) that occurs when a signal is sampled below the Nyquist rate, causing high frequencies to masquerade as low frequencies. It is avoided by low-pass (anti-aliasing) filtering before sampling or by increasing the sampling rate.

5. How many bits are needed to store an image of size $M \times N$ with $L = 2^{k}$ grey levels?

   The number of bits is $b = M \times N \times k$, where $k = \log_{2} L$.

6. Define a linear system in terms of its response properties.

   A system is linear if it satisfies superposition: additivity and homogeneity. For inputs $f_{1}, f_{2}$ and scalars $a, b$, $H\{a f_{1} + b f_{2}\} = a\,H\{f_{1}\} + b\,H\{f_{2}\}$.

7. What additional property defines a Linear Shift-Invariant (LSI) system?

   Shift (position) invariance: a spatial shift of the input produces an identical shift of the output. If $H\{f(x,y)\} = g(x,y)$, then $H\{f(x-x_{0}, y-y_{0})\} = g(x-x_{0}, y-y_{0})$.

8. What characterizes an LSI system completely, and what is the output expressed as?

   An LSI system is completely characterized by its impulse response (point spread function) $h$. The output is the convolution of the input with $h$: $g = f * h$.

9. Write the definition of 1-D continuous convolution.

   $$ (f * h)(x) = \int_{-\infty}^{\infty} f(\tau)\, h(x - \tau)\, d\tau $$

10. Write the definition of 2-D discrete convolution for image processing.

    $$ g(x,y) = \sum_{s=-a}^{a} \sum_{t=-b}^{b} f(x-s,\, y-t)\, h(s,t) $$ where $h$ is the kernel (mask).

11. State the convolution theorem relating spatial and frequency domains.

    Convolution in the spatial domain equals multiplication in the frequency domain (and vice versa): $f * h \;\Leftrightarrow\; F \cdot H$, and $f \cdot h \;\Leftrightarrow\; F * H$.

12. List the commutative, associative, and distributive properties of convolution.

    Commutative: $f * h = h * f$. Associative: $(f * h) * g = f * (h * g)$. Distributive: $f * (h + g) = f * h + f * g$.

13. Write the 1-D Continuous Fourier Transform and its inverse.

    Forward: $$ F(u) = \int_{-\infty}^{\infty} f(x)\, e^{-j 2\pi u x}\, dx $$ Inverse: $$ f(x) = \int_{-\infty}^{\infty} F(u)\, e^{\, j 2\pi u x}\, du $$

14. Write the 1-D Discrete Fourier Transform (DFT) for a sequence of length $N$.

    $$ F(u) = \sum_{x=0}^{N-1} f(x)\, e^{-j 2\pi u x / N}, \quad u = 0,1,\dots,N-1 $$

15. Write the 2-D Discrete Fourier Transform of an $M \times N$ image.

    $$ F(u,v) = \sum_{x=0}^{M-1} \sum_{y=0}^{N-1} f(x,y)\, e^{-j 2\pi \left( \frac{ux}{M} + \frac{vy}{N} \right)} $$

16. What does the value $F(0,0)$ of the 2-D DFT represent?

    $F(0,0)$ is the DC component, proportional to the average grey level of the image: $F(0,0) = \sum_{x}\sum_{y} f(x,y) = MN \cdot \bar{f}$ (the sum / mean intensity).

17. What is the separability property of the 2-D DFT and its computational benefit?

    The 2-D DFT can be computed as two successive 1-D DFTs (along rows then columns) because the kernel is separable. This reduces complexity and allows use of the FFT, lowering cost from $O(N^{2})$ to $O(N \log N)$ per dimension.

18. What is an image histogram?

    An image histogram is a graph/discrete function $h(r_{k}) = n_{k}$ giving the number of pixels $n_{k}$ having each grey level $r_{k}$. It shows the frequency distribution of brightness values but contains no spatial information.

19. What does the shape of a histogram tell you about image contrast?

    A histogram spread across the full range indicates high contrast; one concentrated in a narrow range indicates low contrast. Clustering at the low end means a dark image; at the high end, a bright image.

20. What is a scattergram (scatterplot / feature-space plot) in multispectral image analysis?

    A scattergram is a 2-D (or n-D) plot of pixel grey values in one band against another band, where each axis is a band. It reveals the correlation/relationship between bands and the clustering of land-cover classes in feature space.

21. What does the spread and orientation of a scattergram indicate?

    A tight, elongated diagonal cloud indicates high correlation (redundancy) between the two bands; a circular/diffuse spread indicates low correlation. Distinct clusters correspond to separable spectral classes.

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