1. CS262 – Computer Vision Lect 4 - Image Formation
John Magee
25 January, 2017
Slides courtesy of Diane H. Theriault

2. Question of the Day:
Why is Computer Vision hard?

3. All this effort to make sure the LIGHTING is good for a movie
All this effort to make sure the LIGHTING is good for a movie. Why is more light needed for a good quality movie? What factors affect how much light reaches the film or image sensor? Why does your cell phone take such lousy pictures at a party? How does this all affect Computer Vision?

4. How are images formed Light is emitted from a light source
Light hits a surface
Light interacts with the surface
Reflected light enters camera aperture
Sensor of camera interprets light
Szeliski Ch 2.2 Don’t worry about all the details of the math
Shapiro & Stockman Ch. 6, Ch. 2 (

5. Light is emitted
Point light sources radiates (emits) light uniformly in all directions
Properties of light:
Color spectrum (Wavelength distribution)
Intensity (Watts / Area * Solid Angle)
Note: A solid angle is like a cone
Note: “Area” light sources, like fluorescent lights, are a little different

6. Light hits a surface
Surface orientation is very important for determining the amount of incident light!
The amount of incident light that falls on a surface (irradiated light)
size of the surface
solid angle of light subtended by the surface
depends on distance to light and orientation of surface
Distance: 5 m
Orientation: 0 degrees
Solid angle: 16.4 degrees
attenuation
Distance: 2.5 m
Solid angle: 22.6 degrees
Distance: ≈2.5 m
Orientation: 45 degrees
Solid angle: 11.4 degrees
foreshortening

7. Light Interacts with a surface
Some light absorbed due to surface color
What happens to the rest?
The orientation of a surface is defined by its “normal vector” which sticks straight up out of the surface.
Simplified BRDF modeled with two components:
“Lambertian”, “flat” or “matte” component : light radiated equally in all directions
“Specular”, “shiny”, or “highlight” component: radiated light is reflected across the normal from the incoming light
Bi-direction reflectance function: “BRDF” expresses :
the amount, direction, and color spectrum of reflected light
depending on
the amount, direction, and color spectrum of incoming light

8. Reflected light enters a camera
Pinhole Model
Object location
focal distance /
focal length
Optical axis
focal plane / image plane
Scene Depth
Center of Projection
Image location
Red triangle (behind camera) and blue triangle (in front of camera) are similar: therefore:
Given any three terms, you can determine the fourth

9. Reflected light enters a camera
For given focal length, “Lens Equation leads to
A “blur circle” or “circle of confusion” results when projections of objects are not focused on the image plane. The size of the blur circle depends on the distance to the object and the size of the aperture.
The allowable size of the blur circle (e.g. a pixel) determines the allowable range of depths in the scene (“depth of field”)
Note: The “F number” or “f stop” commonly used in photography is the ratio of focal length to aperture size. (

10. Camera sensor interprets light
Image is quantized into pixels to go from physical size of projection to pixel coordinates
Szeliski 2.3, Shapiro & Stockman 2.2

11. Now what?
Interaction between light, objects, and the camera leads to images
The way image values change hopefully tells us something about the objects, the light, and the camera

12. Image Gradients
“the way image values change”  image derivative
“Gradient” at a particular point (x, y) is a vector that points in the direction of largest change
Gradient can be in Cartesian (x, y) or Polar (magnitude, angle) coordinates
Every point in an image may have a different gradient vector
Friday’s lab and this week’s homework will be devoted to image gradients and edges.

13. Discussion Questions:
What influences are mixed together when we observe the light reflected from a surface?
In order to infer surface orientation, what assumptions do we need to make? Can we construct restricted imaging conditions that make this job easier?
In order to infer surface properties, what assumptions do we need to make? Can we construct restricted imaging conditions that make this job easier?
What are some things we would like to know about objects that we can’t directly observe, even if we could correctly reconstruct surface orientation, color, texture, and reflectance properties? (hint: clothes) What steps could we take to try to understand those things, given the image information
Think of some ways that we could define the scope of some tasks that we might be able to do, even if all we have is the image appearance and we can’t infer scene structure and surface orientation and properties.

14. Light incident on a surface
The amount of light that falls on a surface (irradiated light)
size of the surface
solid angle of light subtended by the surface
Surfaces that are further away from the light subtend a smaller solid angle  attenuation
Surfaces that are turned away from the light subtend a smaller solid angle  foreshortening

15. Image Gradients
The gradient is a vector like any other vector. It just happens to represent the way the values of the image are changing.
One way to compute gradient: “finite differences”: Just compute the difference between each pixel and the previous one (horizontally and vertically).
Switching from the Cartesian representation (x,y) to the polar representation (magnitude, direction) is often helpful, and very, very important.
Friday’s lab and this week’s homework will be devoted to image gradients and edges.