Computer Vision
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The equation of projection

Size illusions

Distant objects are smaller

Parallel lines meet

Vanishing points

Geometric properties of projection

Polyhedra project to polygons

Junctions are constrained

Back to projection

Basic geometric transformations:
Translation

Coordinate rotation

Euler angles

Rotation and translation

Basic transformations
Scaling

Basic transformations
Scaling

Affine Geometric Transforms

A Simple 2-D Example

Matrix representation and Homogeneous coordinates

How to translate a 2D point:

Relationship between 3D homogeneous and inhomogeneous

Matrix representation and Homogeneous coordinates

Geometric Transforms

Geometric Transforms

Rotation about a Specified Axis

Rotation through q about Specified Axis

Comparison:

2. Camera models and projections

The equation of projection

The camera matrix

Camera parameters

Intrinsic Parameters

Example:
A real camera

Relative location
Camera-Laser

In homogeneous coordinates

Full projection model

Result

Orthographic projection

The fundamental model for orthographic projection

Perspective and Orthographic Projection

Weak perspective

The fundamental model for weak perspective projection

Camera Model Structure

Camera Model Structure

History of Perspective

Renaissance
Leonardo da Vinci: The last supper

Other Models

Recall: Intrinsic Parameters

CAMERA CALIBRATION: A WARMUP

Camera calibration

Stereo Vision

Stereo depth calculation:
Simple case, aligned cameras

Epipolar constraint

Stereo measurement example:

How wide is the hallway?
General strategy

How wide is the hallway?
Steps in solution:

Focal length:

How wide…
Depth calculation

How wide…?
Answer:

Visual ambiguity

Ambiguity

Visual ambiguity

Ambiguity

Visual ambiguity

Ambiguity

Camera Models

Visual Invariance