Comp Vision Midterm

Question 1

Are orthographic projection of two parallel lines in the world are parallel in the image?

Answer 1

Represents lines in 3D in 2D. No distortion. Lines of sight are parallel rather than converging.

Question 2

Are Perspective projection of two parallel lines are parallel in the image?

Answer 2

No, perspective projection involves projecting 3D points onto a 2D plane through a focal point such as a pinhole camera.
Parallel lines in the world will converge at a vanishing point in the image.

Question 3

Can a 2D rotation be expressed in homography?

Answer 3

Yes, 2D rotation is a linear transformation that can be expressed in homography.

Question 4

what is perspective projection

Answer 4

A type of projection that simulates how an eye or camera captures and projects a 3D scene on a 2D image.

Question 5

What is homography?

Answer 5

A transformation that relates two images of the same planar surface taken from different viewpoints. Transformation can include translation, rotation, and perspective distortion.

Question 6

Is the camera exposure captured by the camera’s intrinsic parameters?

Answer 6

Camera exposure refers to how much light reaches the cameras sensor. Determined by shutter speed, aperture, and ISO. These are not intrinsic parameters, these are camera settings.

Question 7

Definition: Camera intrinsic parameters

Answer 7

Properties of camera related to internal characteristics of the camera itself. Describing how 3D points in the camera coordinate system are projected onto a 2D image plane. Represented by intrinsic matrix.
instrin matrix = K

Question 8

What are the intrinsic cam parameters?

Answer 8

Focal length
Principle points
Skew Coefficient
Pixel Aspect Ratio

Question 9

Focal length

Answer 9

zoom level of cam, distance from camera sensor to the lens where light rays converge to form a focused image.
fx, fy

Question 10

Principle Point

Answer 10

Where the optical axis(line passing through center of lens) intersects the image plane. (Typically center of image plane)
c_x, c_y in pixel coords

Question 11

Skew coefficients

Answer 11

angle between image axes (ideally, x and y axes are perpendicular)
ex. camera sensor not perfectly rectangular.
‘s’

Question 12

Pixel aspect ratio

Answer 12

Ration between width and height of a pixel. Typically pixels are square therefor 1:1.

Question 13

Does correlating a Gaussian with itself yield another Gaussian with double the variance of the original Gaussian.

Answer 13

Yes, correlating or convolving a gaussian function with itself results in another whose variance is 2sig^2. (Double the original)

Question 14

What is a Gaussian?

Answer 14

mathematical function of a bell-shaped curve. AKA normal distribution.
Mean is the center of the curve giving max val.
Std deviation controls how spread out the gaussian is.
Small std.dev gives narrow and concentrated around the mean.

2D gaussian is used to describe intensities or how other quantities vary across a plane.

Question 15

Does Radial distortion affect mostly the pixels close to the centre of an image.

Answer 15

No, radial distortion is caused by the curvature of the camera lens. Mostly affecting pixels at the edge or farther from the center of image.
Distortion increases with distance from the center, leading to barrel distortion or pincushion distortion. (Edges distorted, center okay)

Question 16

Do Points in Cartesian coordinates have a unique representation in homogeneous coordinates.

Answer 16

No, in homogeneous coordinates, cartesian coords can be represented as kx,ky, k, where k is a non-zero scalar. Meaning there are infinitely many homogeneous representations for a given cartesian point.

ex. x,y,1 | 2x, 2y, 2 etc..

Question 17

Why Use Homogeneous Coordinates?

Answer 17

Makes it possible to represent points at infinity or a finite point.
kx, ky, 0 = point at infinity.
Important in perspective geometry for vanish points.
represent transformations in homogeneous matrix, and a simple matrix multiplication of the point

Question 18

Is a weak perspective camera model not suitable for capturing the ground with a camera mounted on a balloon flying at a high altitude?

Answer 18

Not suitable.
Weak perspective camera model assumes a small depth of field variation, such that it can use a simple expression using the depth of field average to reduce complex computations.

Full perspective: uses a pinhole camera. Rays pass through a focal point projecting image onto image plane. Objects farther from the camera appear smaller, preserving depth info (good for large depth variations).

Question 19

Given three parallel lines in the world not in the same plane, will they share the same vanishing point.

Answer 19

No
Vanishing points are created by projecting parallel lines in 3D onto a 2D plane. (Same plane)
Else, it is very unlikely they will share the same vanish point if on different planes

Question 20

Camera extrinsic transformation

Answer 20

Describes the transformation from world to camera coordinates. Includes rotation and translation, also expressing how the camera is oriented and positioned in the world.

Question 21

Does the camera extrinsic transformation result in points expressed in pixels?

Answer 21

No
Results in points expressed in camera coordinate system, not pixels. Applying Intrinsic transformation takes camera to pixel coords.

Question 22

Are all convolution filters separable filters?

Answer 22

No
It is separable if it can be broken down into a series of 1D convolutions.
ex. Gaussian can be applied in the x and y direction separately.
Not all can do this, such as laplacian filters.

Question 23

What is a convolution filter?

Answer 23

Mathematical operation that modifies pixel values based on the values of its neighboring pixels via kernel grid.
Applies a filter to an image
Kernel slides across image, kernal value multiplied with corresponding pixels and summed and applied to center pixel.

Question 24

Is the perspective projection operation an invertible transformation?

Answer 24

No
Transforms a 3D points into a 2D point by projecting onto an image plane. This process loses depth information, as multiple 3D points can project to the same 2D point.

Question 25

Describe the Hysteresis Thresholding Process Used in the Canny Edge Detector

Answer 25

Final step in Canny edge detector alg.
Refines edge map by categorizing detected edges based on pixel strength and connectivity.
Aims to keep most significant edges, and remove noisy edges.
(Gradient magnitude for pixel strength and thresholding)
Edge linking -> BFS on strong edges, weak edge pixels connected to strong edge is promoted to strong edge for continuity.
All other weak edges not connected are suppressed.

Question 26

List the Camera Parameters that Control the Depth-of-Field

Answer 26

Aperture size (f-stop): Controls amount of light entering lens, represented by f-stop values
Focal Length: dist from cam sensor to lens.
Distance to the subject: shallower depth of field for closer objects

Question 27

What is Depth of field?

Answer 27

Range of distance in a scene that appears acceptably sharp in an image.

Question 28

Aperture

Answer 28

Aperture size (f-stop): Controls amount of light entering lens, represented by f-stop values
ex. f/2.8, f/8
Larger aperture (smaller f-stop value)-> shallow depth, more blur in the background/foreground.
Smaller aperture (larger f-stop value)-> deep depth of field, more of the scene in focus.

Question 29

For a Shallow Depth of Field, Should the Camera Aperture Be Small or Large?

Answer 29

To obtain a shallow depth of field, we need more light in the camera.
Larger aperture(smaller f-stop) will create a shallow depth of field.

Question 30

What is warping?

Answer 30

Changes shape or orientation of an image.
Forward warping: each pixel mapped to a new location source to des. images
Backward warping: each pixel in output image is mapped back source image

Question 31

what is foreshortening?

Answer 31

Natural effect where rays passing through camera center/lens form objects that appear smaller the farther they are.

Question 32

Which of the Following Image Projection Models—Perspective, Orthographic, and Weak-Perspective—Do the World Points Pass Through the Origin as Part of the Projection Process?

Answer 32

Perspective projection have rays pass that converge to a single point passing through the origin.

Weak and orthographic rays are parallel or nearly parallel

Question 33

What is a circle of confusion?

Answer 33

CoC is the blur spot that forms when light from a point source does not converge to a single point on the image sensor or film.
It forms a small circle that blurs.
Depth of field relates to CoC.

Question 34

thin lens equation

Answer 34

relates the distance between a lens, object viewed, and resulting image.
Explains how lenses focus light and form images.

Question 35

Template matching

Answer 35

Template matching: small portion of an image compared to larger target image to find location where template best matches a section of the target image.
Templates slides across all pixels and applies Sum of squared differences or normalized cross correlation to measure similarity.

Question 36

Sobel

Answer 36

Sobel operator calculates x, and y gradient.
Uses two 3x3 convolution kernels
Direction of gradient -> theta = tan-1(gy/gx)

Question 37

Correlation

Answer 37

Measures similarity of two images.
Cross-correlation : creates a coefficient as template slides as a metric of measurement.

Question 38

Gaussian noise

Answer 38

Follows norm dist, intensity values of the noise are distributed around a mean. Pixel intensities are randomly altered based on the distribution