3. Image Formation

Basic:

We have 2 types of images:

• Intensity
  • light intensity
• Range (depth)
  • shape and distance

Elements of a real imaging device:

Why Lenses?

Adding a lens:

• all parallel rays converge to one point on a plane located at the focal length f.

• points “in focus” (red line) are projected to one point on the film
  • others are projected to a “circle of confuion” (blurring) in the image
• Changing the shape of the lens changes this distance

Thin Lens Model:

Thin Lenses Equation:

• is the distance of the object from lens
• is the distance of the in focus image plane
• f is the focal length of the lens
• if increases, decreases, and vice versa

**

Depth of Field:

• The range of Z that is in focus is called the depth of field.
• Changes with lens focal length f and image plane distance

In this picture, object is on the right:

• pin hole camera has infinite DoF
• Thin lens implies there is always a finite DoF
• Change change DoF by changing lens or aperture size
  • Larger aperture means smaller DoF, more light

The distance between 2 lines before and after the tree is DoF

f-stop number:

• f-stop number = f / D
  • f is focal length
  • D is diameter of the pin hole
• if f-stop number ↑
  • the image is darker
  • DoF is greater
• if f-stop number ↓
  • the image is brighter
  • DoF is smaller

Field of View:

• FOV depends on Focal Length (f)
  • 

Effect of change in focal length:

strong perspective and weak perspective:

small f = strong perspective = parallel lines seem not parallel
large f = weak perspective = not parallel lines might seem parallel

Specularity:

• The changes in appearance of a surface point defines the specularity
  • Plain sheet of paper is non-specular (no change)
  • Desktop is semi-specular (some change)
  • Mirror is very specular (a great deal of change)

Image Digitization:

• Sampling – measuring the value of an image at a finite number of points.
• Quantization – representing the measured value at the sampled point, by an integer.
• Pixel – picture element, usually in the range [0,255]

Grayscale Image:

A digital image is represented by an integer array E of m-by-n. E(i,j), a pixel, is an integer in the range [0, 255].

Color Image:

3 channels of a color image - blue, green, and red.
Those 3 colors can be mixed into other colors.

Geometric Model of Camera:

• 3D -> 2D
• P is the point of object, p is the corresponding image point

Reference:

• wikipedia
• handout of COMP4102: Introduction to Computer Vision from Carleton University School of Computer Science, 2019