Features, Descriptors and Classical Recognition

Introduction and Context

A digital image contains millions of pixel values, but recognition systems rarely compare every pixel directly. Instead, they identify informative structures—such as edges, corners, textured patches, and distinctive regions—and represent them using compact numerical descriptions called features or descriptors. These representations support tasks including object recognition, image registration, panorama construction, tracking, industrial inspection, and visual search.

Feature-based computer vision was especially important before the widespread adoption of deep convolutional neural networks. It remains valuable because it is interpretable, computationally efficient, useful when training data are limited, and effective in applications where geometric correspondence is required. Classical features also provide conceptual foundations for understanding modern learned representations.

This chapter examines image structure detection, local and global descriptors, feature matching, visual vocabularies, and classical recognition models. It emphasizes the relationship between a visual phenomenon, its mathematical representation, and the recognition task for which that representation is appropriate.

Learning Objectives

By the end of this chapter, a student should be able to:

1. Explain how edges, corners, blobs, and regions are detected.

2. Distinguish keypoints, descriptors, and feature matches.

3. Describe the principles and trade-offs of HOG, SIFT, and ORB.

4. Select suitable distance measures and matching strategies.

5. Construct a bag-of-visual-words representation.

6. Apply classical classifiers to feature-based recognition.

7. Evaluate robustness, efficiency, failure modes, and ethical implications of classical vision systems.

1. What Is a Feature?

A feature is a measurable property of an image that is useful for analysis. It may be a local structure, such as a corner at a window frame, or a global statistic, such as the distribution of edge orientations across a pedestrian image.

Three related terms must be distinguished:

• Feature detector: An algorithm that identifies informative image locations or structures.
• Keypoint: A detected location, often accompanied by scale and orientation.
• Descriptor: A numerical vector that summarizes the appearance around a keypoint or within an image region.

For example, SIFT detects scale-space extrema as keypoints and computes a 128-dimensional descriptor for each keypoint. The detector answers “where is a potentially distinctive point?” The descriptor answers “what does the neighborhood around that point look like?”

A useful feature should ideally have:

• Distinctiveness: Different image regions should produce different representations.
• Repeatability: The same physical point should be detected in different images.
• Invariance: The representation should tolerate expected changes, such as moderate scale, rotation, illumination, or viewpoint changes.
• Efficiency: Detection and comparison should be affordable for the application.
• Locality or spatial coverage: Features should describe enough context to be meaningful but remain localized enough to support correspondence.

No feature is invariant to every transformation. Greater invariance can also reduce discriminative information. Feature design is therefore a problem of matching assumptions to the application.

2. Image Structures and Their Detectors

2.1 Edges

An edge is a location where image intensity changes rapidly. Edges commonly correspond to object boundaries, surface markings, shadows, or depth discontinuities. For a grayscale image represented by intensity function \(I(x,y)\), the image gradient is

\[

\nabla I = \begin{bmatrix} I_x \\ I_y \end{bmatrix},

\]

where \(I_x\) and \(I_y\) are partial derivatives in the horizontal and vertical directions. The gradient magnitude and orientation are

\[

M(x,y)=\sqrt{I_x^2+I_y^2}, \qquad

\theta(x,y)=\operatorname{atan2}(I_y,I_x).

\]

The magnitude measures the rate of intensity change, while the orientation gives the direction of greatest increase. In practice, derivatives are estimated using filters such as Sobel operators. Noise can produce false edges, so smoothing is usually performed before differentiation.

The Canny edge detector is a widely used multi-stage method:

1. Smooth the image, commonly with a Gaussian filter.

2. Compute gradient magnitude and orientation.

3. Apply non-maximum suppression to thin broad edge responses.

4. Use two thresholds to classify strong and weak responses.

5. Link weak edges to strong edges through hysteresis.

Canny detection is effective because it balances localization, noise suppression, and detection of genuine edges. Its results depend strongly on the smoothing scale and thresholds. An edge map alone, however, does not identify objects; it provides structural evidence that later algorithms must interpret.

2.2 Corners

A corner is a local image region with significant intensity variation in more than one direction. A straight edge changes strongly in one direction but weakly along the edge. A corner changes under movement in many directions and is therefore more suitable for matching.

The Harris corner detector examines the change in image intensity caused by a small displacement \((u,v)\). A local approximation is

\[

E(u,v)=\sum_{(x,y)\in W} w(x,y)[I(x+u,y+v)-I(x,y)]^2,

\]

where \(W\) is a neighborhood and \(w(x,y)\) is an optional weighting function, often Gaussian. Using a first-order Taylor approximation gives

\[

E(u,v)\approx \begin{bmatrix}u&v\end{bmatrix}M\begin{bmatrix}u\\v\end{bmatrix},

\]

where the second-moment matrix is

\[

M=\sum_{(x,y)\in W}w(x,y)

\begin{bmatrix}

I_x^2&I_xI_y\\

I_xI_y&I_y^2

\end{bmatrix}.

\]

Let the eigenvalues of \(M\) be \(\lambda_1\) and \(\lambda_2\). If both are small, the region is approximately flat. If one is large and the other small, it resembles an edge. If both are large, it is corner-like. The Harris response is commonly written as

\[

R=\det(M)-k[\operatorname{trace}(M)]^2,

\]

where \(k\) is an empirical sensitivity parameter. Large positive values indicate corner candidates. The formula assumes locally meaningful intensity derivatives and is sensitive to image scale; multi-scale methods are needed when object size varies substantially.

The Shi–Tomasi detector uses the smaller eigenvalue, \(\min(\lambda_1,\lambda_2)\), as its quality measure. It is often described as a “good features to track” detector because points with strong variation in both directions support stable optical-flow tracking.

2.3 Blobs and Scale Space

A blob is a region that differs from its surrounding neighborhood, such as a bright spot, dark spot, or textured circular structure. Blob detection is useful when corners are absent but region contrast is distinctive.

A central challenge is scale. A feature that appears as a small blob in one image may appear larger after zooming. Scale-space theory represents an image at multiple smoothing scales:

\[

L(x,y,\sigma)=G(x,y,\sigma)*I(x,y),

\]

where \(G(x,y,\sigma)\) is a Gaussian kernel with standard deviation \(\sigma\), * denotes convolution, and \(I\) is the original image. Increasing \(\sigma\) suppresses finer structures.

The Laplacian of Gaussian (LoG), \(\nabla^2L\), responds strongly to blob-like structures. In practical systems, the difference of Gaussians (DoG) approximates scale-normalized LoG efficiently:

\[

D(x,y,\sigma)=L(x,y,k\sigma)-L(x,y,\sigma),

\]

where \(k>1\) is the ratio between adjacent scales. Local extrema across spatial position and scale become candidate keypoints. SIFT uses this DoG scale-space construction.

3. Descriptors: Turning Appearance into Vectors

A detector supplies locations; a descriptor supplies comparable data. A descriptor is a vector \(\mathbf{d}\in\mathbb{R}^n\), and similarity is estimated using a distance or similarity function.

For real-valued descriptors, the Euclidean distance is

\[

d_2(\mathbf{a},\mathbf{b})=\sqrt{\sum_{i=1}^{n}(a_i-b_i)^2}.

\]

The squared Euclidean distance may be used when only ranking is required because the square root does not change the ordering. For binary descriptors, the appropriate measure is commonly Hamming distance, the number of bit positions at which two descriptors differ. It can be computed efficiently using bitwise XOR followed by a population count.

Descriptor normalization matters. If one region produces vectors with unusually large magnitude because of contrast, direct comparison may be misleading. Normalization, clipping, or illumination preprocessing can improve robustness, but may also remove useful information.

3.1 Histogram of Oriented Gradients (HOG)

HOG represents an image region using local distributions of gradient orientations. It is particularly effective for objects whose shape is expressed through contours, such as pedestrians.

A typical HOG pipeline is:

1. Compute horizontal and vertical gradients.

2. Divide the image into small cells.

3. Accumulate gradient magnitudes into orientation bins within each cell.

4. Group neighboring cells into blocks.

5. Normalize the concatenated histogram within each block.

6. Concatenate all normalized block vectors.

A gradient contribution is often assigned to orientation bins by interpolation, so nearby orientations do not create abrupt changes. A common block normalization is L2-Hys: first normalize a block vector, clip values above a threshold, then renormalize. The exact dimensionality depends on image size, cell size, number of orientation bins, block size, and block stride.

HOG is relatively robust to small illumination changes because it emphasizes local orientation rather than absolute intensity. It is not inherently invariant to large rotations, scale changes, or significant viewpoint changes. HOG is a region descriptor rather than a sparse keypoint descriptor; it is usually computed on detection windows or regularly sampled regions.

3.2 SIFT

Scale-Invariant Feature Transform (SIFT) combines scale-space keypoint detection with a locally normalized gradient descriptor. Its classical stages are:

1. Construct a Gaussian scale space and DoG pyramid.

2. Detect extrema over neighboring spatial and scale samples.

3. Refine keypoint location and reject low-contrast or edge-like unstable points.

4. Assign one or more orientations using local gradient distributions.

5. Form a descriptor from gradient orientation histograms in a grid around the keypoint.

The standard SIFT descriptor has 128 components: a 4-by-4 array of spatial cells, each containing an 8-bin orientation histogram. The descriptor is normalized to reduce sensitivity to contrast and illumination changes.

SIFT is robust to image scaling and in-plane rotation and tolerates moderate affine distortion, illumination variation, and viewpoint change. Its disadvantages include greater computational cost and a relatively large floating-point descriptor. SIFT matching is often highly effective in textured scenes, but it may generate few reliable points in textureless areas.

3.3 ORB

ORB (Oriented FAST and Rotated BRIEF) combines the FAST corner detector with an orientation-aware version of the BRIEF binary descriptor. FAST identifies corners by testing intensity comparisons on a circle around a candidate pixel. ORB estimates a dominant local orientation using the intensity centroid, rotates the BRIEF sampling pattern, and produces a compact binary descriptor.

Because ORB descriptors are binary, Hamming distance is appropriate. ORB is substantially faster and more memory-efficient than many floating-point descriptors, making it attractive for embedded systems, mobile robotics, and real-time applications. Its limitations include reduced robustness under large viewpoint changes, severe scale changes, blur, or difficult illumination conditions compared with strong scale-space methods.

3.4 Comparison of Common Representations

HOG is appropriate when the task depends on the overall distribution of local shape gradients in a fixed or normalized window. SIFT is suitable when sparse, repeatable local correspondence is required across scale and rotation changes. ORB is suitable when speed, low memory use, and binary matching are priorities. The “best” descriptor is therefore task-dependent rather than universal.

4. Feature Matching and Geometric Verification

Given descriptors from two images, a matcher seeks likely correspondences. Brute-force matching compares each descriptor in one image with descriptors in the other. Approximate nearest-neighbor methods, such as tree-based or graph-based indexing, reduce search time for large databases.

A common procedure is the ratio test. For a descriptor in image A, let \(d_1\) and \(d_2\) be the distances to its nearest and second-nearest candidates in image B. Accept the match when

\[

\frac{d_1}{d_2}<\tau,

\]

where \(\tau\) is selected empirically. The condition is meaningful only when the descriptor distance is appropriate and the nearest candidate is genuinely more distinctive than alternatives. It should not be treated as a universal probability threshold.

Matching alone is insufficient. Repeated textures, background regions, and accidental descriptor similarities produce outliers. Geometric verification tests whether accepted matches are consistent with a common transformation. For approximately planar scenes or camera motion dominated by rotation, a homography can relate corresponding image points:

\[

\mathbf{x}'\sim H\mathbf{x},

\]

where \(H\) is a 3-by-3 projective matrix and \(\sim\) denotes equality up to a nonzero scale factor in homogeneous coordinates.

For general scenes under camera motion, the fundamental matrix relation is

\[

\mathbf{x}'^{T}F\mathbf{x}=0.

\]

The RANSAC algorithm repeatedly samples a minimal subset, estimates a model, counts inliers within a geometric error threshold, and returns the model supported by the largest consistent set. RANSAC is effective when most tentative matches are correct, but results depend on the inlier ratio, sampling budget, and threshold. It does not guarantee a correct model when the scene is degenerate or the data contain too many outliers.

5. Bag of Visual Words

Local descriptors are variable in number, but many classifiers require fixed-length vectors. The bag-of-visual-words (BoVW) model solves this by quantizing local descriptors into a learned vocabulary.

The process is:

1. Extract local descriptors from training images.

2. Pool descriptors into a large training set.

3. Cluster them, commonly with k-means.

4. Treat each cluster center as a visual word.

5. Assign each image descriptor to its nearest visual word.

6. Count word assignments to form a histogram.

7. Use the histogram as input to a classifier.

If the vocabulary contains \(K\) words, an image is represented by a histogram \(\mathbf{h}=(h_1,\ldots,h_K)\), where \(h_j\) is the number of descriptors assigned to word \(j\). A normalized frequency is

\[

\hat h_j=\frac{h_j}{\sum_{i=1}^{K}h_i},

\]

provided that the image contains at least one descriptor. A common alternative is TF–IDF weighting, which reduces the influence of words occurring in many images:

\[

\operatorname{tfidf}_{j}=\operatorname{tf}_{j}\log\left(\frac{N}{n_j}\right),

\]

where \(N\) is the number of training images and \(n_j\) is the number containing word \(j\). Definitions of term frequency vary, so the chosen convention must be documented.

BoVW discards most precise spatial arrangement. A car and a building may share similar local textures even when their word histograms differ only weakly. Spatial pyramids partially address this limitation by computing histograms over the whole image and progressively finer spatial regions, then concatenating them.

The vocabulary must be learned using training data only. If descriptors from validation or test images influence clustering, information leaks into evaluation and produces an overly optimistic result.

6. Classical Recognition Models

Once features are extracted, recognition becomes a supervised or unsupervised learning problem.

Support Vector Machines

A linear SVM seeks a separating hyperplane with a large margin. For labeled examples \((\mathbf{x}_i,y_i)\), where \(y_i\in\{-1,+1\}\), a soft-margin formulation minimizes

\[

\frac{1}{2}\|\mathbf{w}\|^2+C\sum_i\xi_i

\]

subject to

\[

y_i(\mathbf{w}^{T}\mathbf{x}_i+b)\geq 1-\xi_i,\qquad \xi_i\geq0.

\]

Here \(\mathbf{w}\) and \(b\) define the classifier, \(\xi_i\) are slack variables, and \(C\) controls the trade-off between margin size and training errors. The formulation assumes a chosen feature space and labels; it does not guarantee probabilistic outputs. Kernel SVMs can model nonlinear boundaries but usually require greater computational cost.

k-Nearest Neighbors

k-NN assigns a new example the majority class among its k closest training examples. It is simple and requires little training, but prediction can be slow and highly sensitive to feature scaling and the distance metric. Small k values are sensitive to noise; large k values smooth class boundaries.

Decision Trees and Random Forests

A decision tree recursively partitions feature space using thresholds. A random forest combines many randomized trees and averages or votes over their predictions. Forests can model nonlinear relationships and provide useful baselines, although histogram features may be high-dimensional and correlated.

Naive Bayes and Linear Models

Naive Bayes models class-conditional feature distributions under a conditional independence assumption. Although the assumption is often false for visual features, the method can be efficient. Logistic regression and linear discriminant methods are also useful when features are informative and approximately linearly separable.

Evaluation

Accuracy is suitable when classes are balanced and error costs are similar. For imbalanced recognition, precision, recall, and F1-score are more informative:

\[

\text{precision}=\frac{TP}{TP+FP},\qquad

\text{recall}=\frac{TP}{TP+FN},

\]

\[

F1=2\frac{\text{precision}\cdot\text{recall}}{\text{precision}+\text{recall}}.

\]

Here TP, FP, and FN denote true positives, false positives, and false negatives. Evaluation must use an image-level or subject-level split that prevents near-duplicate images from appearing in both training and test sets.

Worked Example: Building a Small Visual Vocabulary

Suppose four one-dimensional descriptors are \(2,3,10,11\), and k-means with \(K=2\) is initialized with centers 2 and 10. Assignment gives the first two descriptors to center 2 and the last two to center 10. The updated centers are

\[

\mu_1=\frac{2+3}{2}=2.5,\qquad \mu_2=\frac{10+11}{2}=10.5.

\]

The assignments remain unchanged, so the algorithm has converged for this dataset. An image containing descriptors 3, 11, and 10 maps to visual words \((1,2,2)\), producing the histogram \((1,2)\). Its normalized frequency histogram is

\[

\left(\frac{1}{3},\frac{2}{3}\right).

\]

This example illustrates quantization and normalization, but real descriptors are high-dimensional and k-means may depend on initialization. Multiple restarts and validation of vocabulary size are therefore common best practices.

Applied Case: Illustrative Industrial Surface Inspection

Background

Consider an illustrative manufacturing system that inspects ceramic tiles for cracks, missing patterns, and severe surface defects. The camera is fixed above a conveyor, and lighting is controlled but not perfectly constant.

Problem

The system must classify each tile as acceptable or defective at production speed. A pixel-template comparison fails when tile position shifts slightly or brightness changes. A deep model is not initially feasible because only a modest labeled dataset is available and the embedded processor has limited resources.

Analysis

Cracks produce elongated edges, while printed patterns create repeatable local corners and blobs. The system therefore requires both shape-sensitive information and tolerance to small translations. False negatives are more costly than false positives because defective tiles may reach customers.

Approach

The engineering team first calibrates the camera and crops each tile to a standardized region. HOG features describe overall edge structure, while ORB keypoints describe local pattern consistency. A random forest combines engineered summary features with HOG measurements. For tiles with known reference geometry, ORB matches are verified with a geometric consistency test. Thresholds are selected using a validation set weighted toward high recall.

The dataset is split by production batch rather than by neighboring frames, preventing nearly identical tiles from appearing in both training and test sets. Performance is reported using recall for defects, precision, false-alarm rate, processing time, and memory consumption.

Outcome

The classical system provides an auditable baseline, operates within the embedded processor budget, and identifies common defects. It performs poorly on hairline cracks with low contrast and on previously unseen decorative patterns. These limitations motivate improved illumination, higher-resolution imaging, or later transition to a learned detector when additional labeled data become available.

Learning Points

The case demonstrates that feature selection must follow image formation and operational constraints. A detector should not be judged only by accuracy: latency, false-negative costs, data leakage, maintainability, and failure coverage also matter. Hybrid systems can be practical when local descriptors, global shape features, and geometric checks complement one another.

Challenges, Limitations, and Best Practices

Classical features are sensitive to image quality, blur, occlusion, repeated patterns, severe perspective changes, and textureless surfaces. Descriptor invariance is always limited. A system designed for one camera and lighting setup may fail after deployment elsewhere.

Recommended practices include:

• Normalize image acquisition through calibration and controlled illumination where possible.
• Select detector scale and descriptor type according to expected object size and motion.
• Use descriptor-specific distances: Hamming for binary descriptors and Euclidean-type distances for many floating-point descriptors.
• Remove ambiguous matches and verify geometric consistency.
• Tune thresholds on validation data, not on the test set.
• Report class-wise metrics and operational costs.
• Preserve reproducibility by recording preprocessing, vocabulary construction, random seeds, and hyperparameters.
• Test on changes in camera, environment, object supplier, and time period.
• Inspect false positives and false negatives rather than relying solely on aggregate scores.

Ethical, Governance, and Security Considerations

Feature-based recognition can be used in surveillance, biometric identification, access control, and workplace monitoring. Even when the algorithm is classical, the social risks remain. Systems should have a clearly defined purpose, data minimization, access controls, retention limits, and human oversight for consequential decisions.

Performance may differ across demographic groups or environments if image quality, clothing, lighting, or representation varies. Evaluation should therefore examine relevant subgroups and deployment conditions. Security teams should consider adversarial physical patterns, replayed images, and template theft. Feature descriptors may reveal information about faces, locations, or objects, so they should be protected as potentially sensitive data.

Contemporary Developments

Modern vision systems often learn features end-to-end with convolutional or transformer architectures. Nevertheless, classical descriptors remain useful for low-data settings, geometric matching, visual odometry, embedded deployment, explainable baselines, and hybrid pipelines. Learned local features and learned matchers increasingly combine the repeatability goals of classical methods with data-driven adaptation. Classical algorithms also remain valuable teaching tools because their assumptions—gradient structure, locality, normalization, quantization, and geometric consistency—are explicit and testable.

Chapter Summary

Features convert raw pixels into representations that emphasize useful visual structure. Edges are detected through intensity gradients; corners through variation in multiple directions; and blobs through multi-scale local extrema. Detectors identify locations, whereas descriptors encode local or regional appearance.

HOG summarizes gradient orientation distributions and is effective for shape-based detection in normalized windows. SIFT provides scale- and rotation-aware local descriptors with strong matching performance but higher computational cost. ORB offers fast binary descriptors and efficient Hamming-distance matching. Matching should be strengthened through ratio tests and geometric verification, often using RANSAC.

Bag-of-visual-words converts variable collections of local descriptors into fixed-length histograms through clustering and quantization. These representations can be classified using SVMs, k-NN, trees, forests, and other classical models. Reliable evaluation requires appropriate metrics, leakage-free data splits, and analysis of deployment constraints. Despite the growth of deep learning, classical features remain important for interpretation, efficiency, geometry, and limited-data applications.

Key Terms

Feature: A measurable image property useful for analysis.

Feature detector: An algorithm that identifies informative image locations or structures.

Keypoint: A distinctive detected location, often with scale and orientation.

Descriptor: A numerical representation of image appearance around a feature.

Gradient: The vector of spatial intensity derivatives.

Edge: A location of rapid image-intensity change.

Corner: A region with strong intensity variation in multiple directions.

Blob: A locally distinct region differing from its surroundings.

Scale space: A multi-resolution representation formed by smoothing an image at different scales.

Harris detector: A corner detector based on the second-moment matrix.

HOG: A descriptor based on histograms of oriented image gradients.

SIFT: A scale- and rotation-aware local feature method using DoG detection and gradient descriptors.

ORB: A fast method combining oriented FAST keypoints with binary BRIEF-like descriptors.

Hamming distance: The number of differing bit positions between binary vectors.

Ratio test: A match-filtering rule comparing nearest and second-nearest descriptor distances.

RANSAC: A robust model-fitting method that handles outliers through random sampling.

Visual word: A cluster center representing a group of similar local descriptors.

Bag of visual words: A histogram representation formed by assigning descriptors to visual words.

Inlier: A data point consistent with an estimated geometric model.

Descriptor invariance: Stability of a representation under specified image transformations.

Review Questions

Short Answer Questions

1. Distinguish a feature detector from a feature descriptor.

2. Why are corners generally more useful for matching than points on a straight edge?

3. What type of distance is commonly used for ORB descriptors, and why?

4. State the main stages of the Canny edge detector.

5. What problem does the bag-of-visual-words model solve?

Long Answer Questions

1. Explain the Harris corner detector using the second-moment matrix and its eigenvalues.

2. Compare HOG, SIFT, and ORB in terms of representation, invariance, computational cost, and applications.

3. Describe a complete feature-matching pipeline, including descriptor extraction, tentative matching, outlier rejection, and geometric verification.

4. Explain how a visual vocabulary is constructed and how it is used for image classification.

5. Discuss the limitations of classical feature-based recognition compared with modern learned representations.

Analytical / Application Questions

1. You must recognize book covers photographed at different scales and rotations using a mobile processor. Choose a feature method, distance measure, and verification strategy, and justify each choice.

2. A defect classifier has 98% accuracy but misses 15% of defective products. Explain why accuracy is insufficient and propose a better evaluation and threshold-selection procedure.

3. A BoVW system performs well on laboratory images but poorly on images from a new factory camera. Analyze possible causes and design an investigation to determine whether the failure arises from acquisition, vocabulary construction, feature instability, or classifier shift.

Multiple Choice Questions with Answers

Question 1

Which image structure typically exhibits strong intensity variation in two directions?

A. A flat region

B. A straight edge

C. A corner

D. Uniform sensor noise

Correct Answer: C. A corner

Question 2

Which distance is most appropriate for comparing standard binary ORB descriptors?

A. Hamming distance

B. Cosine distance only

C. Mahalanobis distance with image intensities

D. Manhattan distance on raw pixels

Correct Answer: A. Hamming distance

Question 3

What is the primary purpose of the ratio test in feature matching?

A. To normalize image brightness

B. To reject ambiguous nearest-neighbor matches

C. To compute a visual vocabulary

D. To estimate gradient orientation

Correct Answer: B. To reject ambiguous nearest-neighbor matches

Question 4

Which descriptor is organized around histograms of local gradient orientations?

A. HOG

B. ORB

C. Harris response

D. RANSAC

Correct Answer: A. HOG

Question 5

In a bag-of-visual-words model, what usually represents a visual word?

A. A raw image pixel

B. A camera calibration matrix

C. A cluster center of local descriptors

D. A classifier confidence score

Correct Answer: C. A cluster center of local descriptors

Question 6

If an image has visual-word counts (2, 1, 1) and no other words, what is its normalized histogram?

A. (2, 1, 1)

B. (1/2, 1/4, 1/4)

C. (1/4, 1/2, 1/2)

D. (2/3, 1/3, 1/3)

Correct Answer: B. (1/2, 1/4, 1/4)

Question 7

What is the main role of RANSAC in feature-based recognition?

A. To smooth every image pixel

B. To fit a geometric model while tolerating outlier matches

C. To convert grayscale images to color

D. To replace descriptor extraction

Correct Answer: B. To fit a geometric model while tolerating outlier matches

Question 8

In the Harris response R = det(M) - k[trace(M)]², what does a large positive response generally indicate?

A. A corner-like region

B. A completely flat region

C. A saturated image boundary only

D. An image with no gradients

Correct Answer: A. A corner-like region

Question 9

Which evaluation measure is especially important when missing a defective product is costly?

A. Recall for the defective class

B. Number of visual words only

C. Descriptor dimensionality

D. Training-set size alone

Correct Answer: A. Recall for the defective class

Question 10

Which statement best describes a limitation of bag-of-visual-words?

A. It cannot use local descriptors

B. It always requires deep neural networks

C. It largely discards precise spatial arrangement

D. It cannot produce fixed-length representations

Correct Answer: C. It largely discards precise spatial arrangement