Computer Vision — Question Bank (CV1–CV7)

Questions extracted and expanded from the AIMLCZG525 Computer Vision lecture decks CV1–CV7 — questions only, no answers. Use these for active recall before checking the Computer Vision vault and the formula sheet.

CV1 — Course intro, goals, applications & why vision is hard

State the three course objectives for AIMLCZG525 Computer Vision and map each objective to one practical skill a student should demonstrate.
What is the broad goal of computer vision when a slide says every image tells a story?
List at least four world properties that a computer vision system may try to compute from an image.
Why can computers be better than humans at some easy visual tasks but still worse at many hard perceptual tasks?
What is in here? How would you reason from limited visual evidence when only a small or degraded image patch is available?
Differentiate image enhancement, computational photography, image recognition, 3D shape recovery and image synthesis as computer vision goals.
Face detection is now available in nearly all cameras in real time — why is face detection useful before capture?
Who is she? What makes face recognition and iris-based biometrics different from generic face detection?
Which face is real? What visual cues might a human or algorithm use to detect synthetic faces?
List five application areas of computer vision shown in the introduction deck and state the key visual task in each.
Explain why viewpoint variation, illumination variation and scale variation make recognition difficult.
Explain how intra-class variation, background clutter, motion and occlusion create ambiguity in computer vision.
What is meant by local ambiguity in images? Give one example where the same 2D evidence can correspond to different 3D scenes.
Why is perception called an inherently ambiguous problem?
Why do computer vision systems need prior knowledge about the world's structure?
What are 3D vision tasks and what algorithmic components would you expect in a 3D vision pipeline?

CV2 — Digital image fundamentals, image formation, sampling & transforms

Draw and explain the pinhole camera model, including why the image is inverted on the image plane.
Slide quiz: Why do we use lenses when we have pin-hole camera? Consider these slide options: cameras with lenses are easier to manufacture when compared to pin-hole cameras; lenses gather more light than pinhole cameras, reducing exposure time; lenses can be stacked to produce a clear image of the scene; lenses keep parallel lines from the scene parallel in the image.
Define an image as a two-dimensional function \(f(x,y)\). What does the value of \(f\) represent in a monochrome image?
In the simple image formation model, explain the roles of illumination \(i(x,y)\) and reflectance \(r(x,y)\).
What do the reflectance limits 0 and 1 represent physically?
For a grayscale image with intensity range \([0,L-1]\), what do the lowest, highest and intermediate values represent?
Differentiate sampling from quantization in the digitization of a continuous image.
How does a sensor array convert a projected continuous image into a sampled and quantized digital image?
Represent a digital image as a matrix and explain the meaning of row index, column index and pixel value.
Distinguish spatial resolution from intensity resolution.
What visual changes occur when spatial resolution decreases from 930 dpi to 72 dpi?
What visual changes occur when intensity resolution decreases from 256 levels to 2 levels at fixed spatial resolution?
What is an un-normalized histogram and what is a normalized histogram?
Why must the sum of all normalized histogram probabilities \(p(r_k)\) equal 1?
Write the negative intensity transformation for an \(L\)-level image and describe when it is useful.
Write the log transformation form and state why it is useful for displaying Fourier spectra.
Write the power-law transformation \(s=cr^\gamma\) and explain what changing \(\gamma\) does.
Why is gamma correction needed for CRT-like display devices whose response follows a power function?
Differentiate contrast stretching, thresholding and intensity-level slicing.
For a low-contrast medical image, which elementary intensity transformations would you try first and what should each reveal?

CV3 — Low-level vision: histograms, equalization, filtering, smoothing & color

How is histogram shape related to image appearance?
Why do poorly exposed images often fail to use the full grayscale range?
State the objective of histogram equalization in one sentence.
For the slide string 4444434543355533454344444, list the gray levels present and formulate the histogram-counting task.
In the slide's 3-bit histogram-equalization example, why is \(L=8\) and why is the multiplier \(L-1=7\)?
Given pixel counts \(n_k\), how do you compute the PDF, CDF, transformation \(s_k=(L-1)\sum_{j=0}^{k}p(r_j)\), and rounded output gray level?
In continuous histogram equalization, why does choosing \(s=T(r)=\int_0^r p_r(w)dw\) lead to a uniform output density?
Why does a digital image need a discrete mapping rather than a continuous transformation function?
Differentiate correlation and convolution in spatial filtering.
Why is the origin of a spatial kernel usually placed at the center of the kernel?
What are the two components of a spatial filter?
Write the general expression for linear spatial filtering of an \(M\times N\) image with an \(m\times n\) filter.
Compare a box kernel and a Gaussian kernel for image smoothing.
What happens as the size of a box filter increases from \(3\times3\) to \(21\times21\)?
How does Gaussian smoothing depend on \(\sigma\) and kernel size?
Why can low-pass filtering help estimate slow shading patterns in an image?
What is color, and why do we see reflected or transmitted light rather than objects directly?
List the three factors that determine perceived object color: source spectrum, object reflectance and sensor characteristics.
What is trichromacy, and what are the approximate peak sensitivities of S, M and L cones?
Differentiate primary colors of light from secondary colors of light.
What is a color model, and why does it provide a coordinate system for colors?
Classify RGB, CMYK, YCbCr and HSV/HSI as device-based or perception-based color spaces.
For an 8-bit-per-channel RGB image, compute the total number of possible colors.
Explain why CMY is subtractive and complementary to RGB.
Why does CMYK introduce a black channel \(K\), and how is \(K\) related to \(C,M,Y\)?
Define hue, saturation and intensity/brightness.
Why are YIQ, YUV and YCbCr useful in television, video and compression?
Using the slide formula, frame the task of converting an RGB pixel to YCbCr without computing the final values.

CV4 — Edge and line detection: edge profiles, gradients, Prewitt & Sobel

Define edge detection as the task of converting a 2D image into a set of curves made of edges.
Compare step edge, ramp edge and roof edge profiles.
How do Gaussian noise levels affect first-derivative and second-derivative edge responses?
List the three main steps of the edge detection approach: smoothing, edge-point detection and edge localization.
How can we differentiate a digital image \(F[x,y]\)? Compare reconstructing a continuous image with finite differences.
What does the gradient vector point toward at pixel \((x,y)\)?
How are edge magnitude and edge orientation related to gradient magnitude and gradient direction?
In the slide example with shaded pixels as 0 and white pixels as 2, formulate how to compute partial derivatives by subtracting rows and columns.
Why is the direction of an edge orthogonal to the gradient vector at that point?
Slide to-do: For a \(3\times3\) region with intensities \(z_1\) to \(z_9\), compute the gradient at \(z_5\) using the difference form shown in the lecture.
Slide to-do: For the same \(3\times3\) region, compute the gradient at \(z_5\) using Prewitt operators.
Slide to-do: For the same \(3\times3\) region, compute the gradient at \(z_5\) using Sobel operators.
Why might an image be smoothed with a \(5\times5\) averaging kernel before applying Sobel edge detection?
State the three objectives of edge detection: good detection, good localization and single response.
What performance requirements should an edge operator satisfy?
What kinds of physical scene changes can cause edges in images?
Why do edges look like steep cliffs when images are treated as functions?
Why can first derivatives detect edge locations, and what role can second derivatives play?

CV5 — Canny edge detection & Hough line transform

List the four steps in Canny's edge detection pipeline.
Why is Gaussian smoothing the first step of Canny edge detection?
Slide question: Where is the edge when the gradient magnitude is spread by noise?
After smoothing, how are gradient magnitude and gradient angle images computed?
Slide question: Can we make use of angle to locate the edge better?
What does non-maxima suppression check along the gradient direction?
In non-maxima suppression, what do the directions \(d_1,d_2,d_3,d_4\) represent?
Why does non-maxima suppression return an image of the same size as the original?
What is hysteresis thresholding?
Why does Canny use two thresholds \(T_L\) and \(T_H\), and why is the high-to-low threshold ratio often in the range 2:1 to 3:1?
Define strong edge pixels, weak edge pixels and valid edge pixels in the double-thresholding stage.
State the edge-linking rule: when should a weak edge be kept?
Why is Canny described as the course's first complete computer vision pipeline?
Slide question: Many objects are characterized by straight lines; wait, why aren't we done just by running edge detection?
List the line-fitting difficulties caused by clutter, missing edge parts and noisy edge measurements.
Explain the role of voting in line fitting.
What questions does the Hough transform answer: what is the line, how many lines are there, and which points belong to which lines?
In \((m,b)\) Hough space, what does a line in image space correspond to?
For an image point \((x_0,y_0)\), what curve does it map to in \((m,b)\) parameter space?
How do two image points determine line parameters in Hough space?
Why do we accumulate votes in discrete bins rather than continuous parameter space?
Why is the polar representation \((\rho,\theta)\) often preferred over \((m,b)\) for vertical lines?
Slide numerical: Determine if \((1,2)\), \((2,3)\) and \((3,4)\) are in the same line using Hough transformation and the relation \(c=-mx+y\).

CV6 — Harris corner detector, HoG & applications

What is corner detection, and why do corners usually occur near intersections of two edges?
Why are corners useful for object recognition, image matching, feature tracking, camera calibration and 3D reconstruction?
Compare flat regions, edge regions and corner regions using the change observed when a small window is shifted.
What is meant by a local measure of uniqueness?
State the basic Harris idea: shifting a window in any direction should cause what kind of intensity change?
What matrix \(M\) is used in the Harris detector, and what image-gradient quantities contribute to it?
Write the Harris corner response form \(R=\det(M)-k\operatorname{trace}(M)^2\) and state the typical range of \(k\).
How do the eigenvalues \(\lambda_1\) and \(\lambda_2\) of \(M\) distinguish flat regions, edges and corners?
Why is \(R\) large for corners, negative with large magnitude for edges, and small in magnitude for flat regions?
List the Harris detector algorithm steps: compute response, threshold response, then keep local maxima.
Slide numerical: Given local image gradients in a window, compute \(M\), \(\det(M)\), \(\operatorname{trace}(M)\), and the Harris response \(R\).
Slide numerical: Use kernel logic to compute image gradients required for a Harris corner response.
Slide numerical: Use a Sobel kernel to compute gradients before evaluating whether the central pixel is a corner.
What is Histogram of Oriented Gradients (HoG), and why is it called a feature descriptor?
List applications of HoG in feature extraction, object detection, image classification, face recognition and surveillance.
Define gradient, cells, blocks and orientation histograms in HoG.
For the standard \(64\times128\) HoG window, how many \(8\times8\) cells are present along width and height?
Why are cells grouped into overlapping \(2\times2\) blocks for normalization?
Explain the dimension calculation \(15\times7\times4\times9=3780\) for the HoG feature vector.
How are gradient magnitude and orientation computed from \(g_x\) and \(g_y\)?
How are gradient orientations quantized into 9 bins over \(0^\circ\) to \(180^\circ\)?
Why does HoG weight orientation-bin votes by gradient magnitude?
Why is block normalization crucial for robustness to lighting changes?
Slide numerical: For the given \(5\times5\) grayscale image patch, compute central \(3\times3\) \(G_x\), \(G_y\), gradient magnitudes, gradient angles and the 9-bin cell histogram.

CV7 — SIFT, feature matching, invariance & RANSAC

Why do automatic panoramas need local feature extraction, feature matching and image alignment?
What makes image matching harder when images differ by viewpoint, scale, rotation, illumination or scene content?
How are SIFT feature matches useful in NASA Mars Rover images, object search and visual SLAM?
Define geometric invariance and photometric invariance for local feature descriptors.
List the advantages of local features: locality, quantity, distinctiveness and efficiency.
State the three main components of a local-feature system: detection, description and matching.
What does SIFT stand for, and what does it mean to transform image data into scale-invariant coordinates?
What invariances and robustness properties does SIFT aim for: scale, rotation, affine distortion, 3D viewpoint, noise and illumination?
Why is raw image matching less reliable than descriptor-based matching?
What is the role of Gaussian blurring in SIFT scale-space construction?
How does variation in scale \(\sigma\) help identify structures at different characteristic scales?
What is a blob in scale space, and why do local extrema in \((x,\sigma)\)-space represent blobs?
What is the Difference of Gaussian (DoG), and why is it used for SIFT keypoint detection?
What happens during SIFT keypoint localization after DoG extrema are found?
What information is encoded in the SIFT keypoint descriptor?
How does SIFT achieve scale invariance?
How does SIFT achieve rotation invariance?
In image alignment, what could go wrong after matching features between images A and B?
Differentiate inliers and outliers in feature matching.
State the RANSAC algorithm steps for line fitting or translation estimation.
Why does RANSAC rely on the idea that all inliers agree with one another while outliers disagree?
What does the slide claim about RANSAC guarantees when outliers are below 50%?
How is the final least-squares fit computed after RANSAC has selected inliers?
How are the inlier threshold and the number of RANSAC rounds related to expected noise, expected outlier percentage and desired success probability?
List the pros and cons of RANSAC.
Slide question: HOG: where is the final bin? Explain why there is no single final bin per pixel before all cell votes and block normalization are complete.

Exam focus: The decks emphasize theory plus numericals. Practice writing the pipeline, formula, matrix and voting steps from memory before checking any solved notes.

Long & Exercise Questions

Multi-part derivation, numerical and trace questions for subjective answers — still questions only. Show all intermediate steps when you attempt them.

L1 · Image formation and digitization. A monochrome scene has illumination \(i(x,y)\), reflectance \(r(x,y)\) and image intensity \(f(x,y)=i(x,y)r(x,y)\). Explain the physical meaning of each term, then describe how sampling and quantization convert \(f(x,y)\) into an \(M\times N\) digital image with \(L\) gray levels.
L2 · Resolution trade-off. Suppose the same image is stored at four spatial resolutions and four intensity resolutions. Design a comparison that isolates the effect of spatial resolution from intensity resolution, and state the visual artifacts you would look for in each case.
L3 · Histogram equalization from the slide string. For the 3-bit sequence 4444434543355533454344444, compute the un-normalized histogram, normalized histogram, CDF, equalization mapping using \(s_k=\operatorname{round}((L-1)\operatorname{CDF}(r_k))\), and the transformed output sequence.
L4 · Histogram equalization for a \(64\times64\) image. A 3-bit image has \(MN=4096\) pixels and gray levels \(0\) to \(7\). Given a table of counts \(n_0,\ldots,n_7\), derive the PDF, CDF, transformation function and equalized histogram, and discuss what happens if multiple input gray levels map to the same output gray level.
L5 · Intensity transformations. For an \(L=256\) image, compare negative, log, power-law, contrast-stretching, thresholding and intensity-level-slicing transformations. For each, write the transformation form and construct one exam-style use case.
L6 · Spatial filtering by hand. Given a \(5\times5\) image patch and a \(3\times3\) averaging kernel, compute the filtered value at the center using correlation, then repeat using convolution with a non-symmetric kernel and explain the difference.
L7 · Gaussian smoothing design. Choose two Gaussian filters with different \(\sigma\) values and kernel sizes for removing noise before edge detection. Explain the trade-off between noise reduction, edge blurring and computational cost.
L8 · RGB, CMY, CMYK and YCbCr conversion. For a pixel \((R,G,B)=(120,80,200)\), formulate the conversion to CMY, CMYK and YCbCr using the lecture formulas, and explain which representation is more suitable for display, printing and video compression.
L9 · Sobel gradient computation. Given the patch \(\begin{bmatrix}10&20&30\\20&40&60\\30&60&90\end{bmatrix}\), apply Sobel \(G_x\) and \(G_y\), compute gradient magnitude, gradient direction and edge direction at the central pixel.
L10 · Prewitt versus Sobel. For the same \(3\times3\) patch, compute gradients using Prewitt and Sobel operators, compare the results, and explain why Sobel gives more weight to the center row or center column.
L11 · Trace the Canny pipeline. For a noisy image patch with a visible ramp edge, describe every Canny step: Gaussian smoothing, derivative computation, magnitude/orientation calculation, non-maxima suppression, double thresholding and hysteresis linking.
L12 · Non-maxima suppression. Given a \(3\times3\) gradient-magnitude neighborhood and the center pixel orientation quantized to horizontal, vertical, \(+45^\circ\) or \(-45^\circ\), decide whether the center pixel survives non-maxima suppression for each possible orientation.
L13 · Hysteresis thresholding. Given gradient magnitudes and thresholds \(T_L=40\), \(T_H=100\), classify pixels as strong, weak or non-edge, then decide which weak pixels survive under 8-neighbor connectivity to strong edges.
L14 · Hough voting in \((m,c)\) space. For points \((1,2)\), \((2,3)\), \((3,4)\) and \((3,2)\), write each point's parameter-space line \(c=-mx+y\), find intersections that receive multiple votes, and identify candidate image-space lines.
L15 · Hough voting in polar space. For edge points \((x_i,y_i)\), construct the polar voting equation \(\rho=x_i\cos\theta+y_i\sin\theta\), choose bins for \(\rho\) and \(\theta\), and describe how peaks identify lines even when edge points are missing.
L16 · Harris response derivation. Starting from the shifted-window intensity-change idea, derive the second-moment matrix \(M\), then derive the corner response \(R=\det(M)-k\operatorname{trace}(M)^2\) and interpret it using \(\lambda_1\) and \(\lambda_2\).
L17 · Harris numerical. A window has \(\sum I_x^2=120\), \(\sum I_y^2=90\), \(\sum I_xI_y=20\) and \(k=0.05\). Form \(M\), compute \(\det(M)\), \(\operatorname{trace}(M)\), \(R\), and classify the point as flat, edge or corner using a stated threshold.
L18 · HoG descriptor construction. For a \(64\times128\) detection window with \(8\times8\) cells, \(2\times2\) overlapping blocks and 9 orientation bins, compute the number of cells, number of blocks, values per block and total descriptor length.
L19 · HoG mini-patch numerical. Using the lecture's \(5\times5\) grayscale patch, compute \(G_x\), \(G_y\), magnitude, angle, 9-bin histogram and an L2-normalized vector for the central \(3\times3\) cell.
L20 · HoG bilinear bin voting. For pixels with \((\theta,|g|)=(45^\circ,14.14)\) and \((63.43^\circ,22.36)\), distribute votes into 20-degree bins centered at 40, 60 and 80 degrees using bilinear interpolation, then state the resulting histogram entries.
L21 · SIFT scale-space pipeline. Starting with an input image, describe Gaussian scale-space construction, Difference-of-Gaussian computation, extrema detection, keypoint localization, orientation assignment and descriptor construction.
L22 · SIFT invariance. Explain how SIFT obtains invariance or robustness to translation, rotation, scale, affine distortion, illumination change and noise, and identify which parts of the pipeline contribute to each property.
L23 · Feature matching and outliers. Given two images with matched SIFT descriptors, propose a pipeline for matching, detecting outliers, computing a homography and aligning images into a panorama.
L24 · RANSAC rounds. Suppose 20% of matches are outliers and a minimal sample of 2 points is needed. Derive the formula for the number of RANSAC trials required to obtain 99% success probability, then set up the numerical substitution.
L25 · RANSAC line fitting trace. Given a set of 2D points with inliers and outliers, run three RANSAC iterations by hand: sample two points, fit a line, count inliers within distance threshold \(d\), choose the best model and refit using all inliers.

Computer Vision — question bank, no answers.