Computer Vision: Geometry of Pinhole Projection

Podcast

Play an AI-generated podcast conversation about this lesson

Questions and Answers

What is the origin of the coordinate system (O, i, j, k) attached to?

Pinhole of the camera (correct)

Optical axis

Scene

Image plane

What is the distance of the image plane from the pinhole?

Negative distance f

Positive distance f 0 (correct)

Variable distance

Zero distance

What is the point C 0 in the context of the pinhole projection?

Optical axis

Pinhole

Scene point

Image center (correct)

What is the line perpendicular to the image plane and passing through O called?

Optical axis Signup and view all the answers

What is the relationship between the origin O and the pinhole?

The origin O coincides with the pinhole Signup and view all the answers

What is the purpose of the coordinate system (O, i, j, k) in the context of the pinhole projection?

To describe the pinhole camera Signup and view all the answers

What is the main disadvantage of the pinhole principle in camera systems?

Not enough light is gathered from the scene. Signup and view all the answers

What is the assumption made in the weak perspective projection model?

Scene points have approximately identical distances. Signup and view all the answers

What is the purpose of using a lens in camera systems?

To gather more light from the scene and keep the image in focus. Signup and view all the answers

What is the relationship between the coordinates of scene and image points in the perspective projection model?

x0 = f0x/z Signup and view all the answers

What is the effect of increasing the size of the pinhole in a camera system?

The image gets more and more blurred. Signup and view all the answers

What is the main factor that defines the behavior of lenses in camera systems?

Geometric optics. Signup and view all the answers

What is the condition for point P0 to lie in the image plane?

z0 = 0 Signup and view all the answers

What is the relationship between λ and OP?

λ = OP Signup and view all the answers

What can be said about the points P, O, and P0?

They are colinear Signup and view all the answers

What is the expression for x0 in terms of x, y, z, and f?

x0 = f*x/z Signup and view all the answers

What can be said about the coordinates of scene point P?

x, y, and z are all non-zero Signup and view all the answers

What is the assumption about the angles between light rays passing through a lens and the interface normal?

They are always zero or very small Signup and view all the answers

What is the relationship between the angles α1 and γ according to the law of refraction?

α1 = γ + β1 Signup and view all the answers

What is the derived relationship between scene and image points?

x/x0 = y/y0 = f/z0 Signup and view all the answers

What is the shape of the boundary of a lens according to the assumptions?

Circular Signup and view all the answers

What is the approximate relationship between the angle γ and the height h of the light ray?

γ ≈ h/R Signup and view all the answers

What is the relationship between the angles β1 and β2 according to the law of refraction?

β1 = γ - β2 Signup and view all the answers

What is the condition for paraxial refraction to be applicable?

Angles are always small Signup and view all the answers

What is the focal point of a lens?

The point at a distance f from O Signup and view all the answers

What is the relationship between the object and image distance in a thin lens?

1/z - 1/z0 = 1/f Signup and view all the answers

What happens to rays through O in a thin lens?

They are not refracted Signup and view all the answers

Study Notes

Pinhole Camera Model and Perspective Projection

The coordinate system (O, i, j, k) is attached to the pinhole in a pinhole camera model.
The distance of the image plane from the pinhole is denoted by f.
The point C0 represents the projection of the scene point P onto the image plane.
The line perpendicular to the image plane and passing through O is called the optical axis.
The origin O coincides with the pinhole.
The coordinate system (O, i, j, k) is used to describe the position of scene points and their projections on the image plane.
The main disadvantage of the pinhole principle is its low light sensitivity, resulting in blurry images.
The weak perspective projection model assumes that all scene points are equidistant from the camera.
Lenses in camera systems are used to focus light onto the image plane, improving image quality.
In the perspective projection model, the coordinates of the scene point P (x, y, z) and its image point P0 (x0, y0, 0) are related by a linear transformation.
Increasing the size of the pinhole in a camera system results in increased blur.
The refractive index of the lens material defines the behavior of lenses.
Point P0 lies in the image plane when z0 is equal to 0.
λ is proportional to the distance OP.
Points P, O, and P0 are collinear.
The x-coordinate of the image point P0 (x0) can be expressed as x0 = (f * x) / z.
The coordinates of the scene point P (x, y, z) are relative to the pinhole.
In paraxial refraction, the angles between the light rays and the interface normal are assumed to be small.
According to the law of refraction, the angles α1 and γ are related by the Snell's law.
The relationship between scene and image points is derived from the geometric principles of perspective projection.
The lens boundary is assumed to be spherical in the paraxial approximation.
Angle γ is approximately proportional to the height h of the light ray.
According to the law of refraction, the angles β1 and β2 are related by Snell's law.
Paraxial refraction is applicable when the angles of incidence and refraction are small.
The focal point of a lens is the point where parallel rays converge.
The object and image distances in a thin lens are related by the lens equation.
Rays passing through O in a thin lens are undeviated.

Studying That Suits You

Use AI to generate personalized quizzes and flashcards to suit your learning preferences.

Description

This quiz covers the fundamental concepts of pinhole projection in computer vision, including the coordinate system, image plane, and optical axis. Test your understanding of the geometry involved in this key concept. Learn about the relationship between the pinhole, image plane, and optical axis.