JAWAHARLAL NEHRU TECHNOLOGICAL UNIVERSITY HYDERABAD
JAWAHARLAL NEHRU TECHNOLOGICAL UNIVERSITY HYDERABAD B.Tech IV Year COMPUTER VISION Previous Question Paper (July - 2021 - R16)
Answer any Five Questions. All Questions Carry Equal Marks.
Main
Discuss the limiting effect of repeatedly applying a 2 × 2 low-pass spatial filter to a digital image. Ignore border effects. Is this effect different from applying 4 × 4 filter.
Answer
Repeatedly applying a 2 × 2 low-pass filter, such as a box filter where each coefficient is 1/4, results in a cumulative smoothing effect. Mathematically, this is equivalent to convolving the image with the filter kernel multiple times. If the kernel is denoted as H, applying it n times is equivalent to convolving the image with Hn, where Hn represents the kernel convolved with itself n times.
As the number of iterations increases, the effective kernel size grows and its shape converges toward a Gaussian distribution due to the Central Limit Theorem. The limiting effect is a severe loss of high-frequency components, leading to significant blurring and a reduction in image resolution.
Applying a 4 × 4 filter is not equivalent to applying a 2 × 2 filter twice. A 4 × 4 filter has a larger spatial support and a different frequency response. While both are low-pass filters, the 4 × 4 filter provides a single-pass smoothing operation with a specific kernel structure (e.g., a 1/16 uniform average), whereas two passes of a 2 × 2 filter result in a 3 × 3 effective kernel with a pyramid-shaped weight distribution. Thus, the resulting image characteristics, such as the degree of blur and the preservation of edges, will differ significantly.
Discuss in detail about Corner detection algorithms.
Answer
Corner detection is a fundamental technique in computer vision used to identify points of interest where the local intensity changes significantly in two or more directions. These points are typically invariant to rotation and translation.
1. Harris Corner Detector: This algorithm relies on the local auto-correlation function. It computes a Structure Tensor (or second-moment matrix) M over a window:
where Ix and Iy are image gradients. The corner response function R is defined as:
Points where R exceeds a threshold are identified as corners. A large positive R indicates a corner, while a large negative R indicates an edge.
2. Shi-Tomasi Corner Detector: This is a variation of the Harris detector that simplifies the selection criteria. Instead of using the determinant and trace, it directly uses the minimum eigenvalue of the matrix M:
If the minimum eigenvalue is greater than a threshold, the point is classified as a corner. This approach is often more robust for tracking applications.
3. FAST (Features from Accelerated Segment Test): This algorithm is designed for real-time performance. It examines a circle of 16 pixels around a candidate point p. If a set of n contiguous pixels in the circle are all brighter or all darker than the intensity of p by a threshold, the point is considered a corner. It uses a high-speed decision tree to classify points, making it computationally efficient for video processing.
Devise an efficient algorithm to compute the distance transform. The algorithm should take a binary image and return at each pixel the city block distance to the nearest non-zero element of the original image. The city block distance d between pixels (x1, y1) and pixel (x2, y2) is defined as:
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Explain the method of Active Contours. What underlying trade-off governs the solutions they generate? How is that trade-off controlled? What mathematical methods are deployed in the computational implementation of deformable models?
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Describe the use of the Hough transform for circular object detection, assuming that object size is known in advance. Show also how a method for detecting ellipses could be adapted for detecting circles of unknown size.
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Discuss how an increase in the complexity of curve under detection increases the computations in an exponential way in Hough transform.
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Discuss how cutting down the possible number of positions in gradient space for a given point on the surface of the object is done.
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A cube is viewed in orthographic projection. Show that although the cube is opaque, it is easy to compute the theoretical position of its centroid in the image. Show also that the orientation of the cube can be deduced by considering the apparent areas of its faces.
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Discuss in detail about In-vehicle vision system.
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When visually inferring a 3D representation of a face, it is useful to extract separately both a shape model, and a texture model. Explain the purposes of these steps, their use in morphable models for pose-invariant face recognition, and how the shape and texture models are extracted and later re-combined.
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Prove that if the histogram of an image is uniform over all possible intensity levels, the basic global thresholding algorithm converges to average intensity of the image (L-1)/2.
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Discuss in detail about mathematical morphology.
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Show that if only two Fourier descriptors are used to reconstruct a boundary, the result will be a circle.
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Find the differential chain code of i) Hexagon ii) Quadrilateral and iii) Octogon.
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What information about the shape and orientation of an object can be inferred, and how, from the extraction of texture descriptors; and what is the role of prior assumptions in making such inferences from texture?
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Show how a GHT version of the spatial matched filter can be devised to detect an equilateral triangle, leading to a star-shaped transform that peaks at the center of the triangle.
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