Transformations and Viewing
Operations
1
Transformation
Transformation operations are usually involved in modeling
objects (points, lines, 3D models) in CAD
2
Cartesian Coordinate
- 2D space in Cartesian coordinates (x, y)
- 3D space in Cartesian coordina
3D Reconstruction
1
3D Reconstruction
Problem
Given xixi
Compute P, P and Xi such that
x i = PX i
xi = PXi
Reconstruction method
Compute F from correspondences
2. Compute camera matrices from F
3. Compute 3D point for each pair of corresponding points
Motion Analysis
1
Motion Related Problems
Motion detection
Registers any detected motion
For security
Single camera
Moving object detection and location
Relative motion between object and camera
Trajectory of its motion
Prediction of future trajec
Image Processing
1
Image
Processing
Operation
Original
Increased contrast
Change in Hue
Posturized
Blurred
2
Rotated
Image Processing
Image Processing
Processing of a 2D picture by a computer
Image enhancement
Image restoration
Image compression
Point o
Two View Geometry
1
Structure
(i)
Correspondence geometry: Given an image point x in
the first view, how does this constrain the position of the
corresponding point x in the second image?
(ii) Camera geometry (motion): Given a set of corresponding
image p
Image Formation
1
Image Formation
Discrete color
Intensity
2
Reflection and Shading
Light scattered and reflected when it hits an objects surface
objects
Bidirectional reflectance distribution function (BRDF)
General model of light scattering
4D function
Camera Calibration
1
Introduction
Estimating the camera projection matrix
Xi x i
P?
Computation of camera matrix is known as resectioning
From sufficient corresponding world and image lines
2
Basic Equations
x i = PX i
By using the direct linear trans
Camera Models
1
Finite Cameras
Camera is a mapping between 3D world and a 2D image
Basic pinhole model
Euclidean coordinate system (a general space defined by 3 axes)
Projection of points in the space onto a plane
A point in space with coordinates X
2D Projective Geometry
1
Projective Geometry
Points, lines & conics (planar and projective geometry)
Homogeneous representation of lines
ax + by + c = 0
(a,b,c)T
same
( ka) x + ( kb) y + kc = 0, "k 0
(a,b,c)T ~ k (a,b,c)T
Two vectors are related by an
MAEG 5720
Computer Vision in Practice
Lecturer: Dr.YM Tang
Email: mfymtang@polyu.edu.hk
1
Assessment Scheme
Projects
Tests
T t
Final examination
2
Course Outline
Computer vision
Transformations and viewing operation
T f
ti
d i i
ti
2D and 3D transformatio
Segmentation
1
Segmentation
Finding shape and size of image object
Important in the analysis of image data
Thresholding
Segment object and background
It is the transformation of an image f to an output binary image g
1 for f (i, j ) T
g (i, j ) =
0