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Computer Vision. Mubarak Shah Computer Vision Lab University of Central Florida Orlando, FL 32816. Computer Vision. The ability of computers to see. Image Understanding Machine Vision Robot Vision Image Analysis Video Understanding. A picture is worth a thousand words.

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computer vision

Computer Vision

Mubarak Shah

Computer Vision Lab

University of Central Florida

Orlando, FL 32816

computer vision1
Computer Vision
  • The ability of computers to see.
    • Image Understanding
    • Machine Vision
    • Robot Vision
    • Image Analysis
    • Video Understanding
image
Image
  • 2-D array of numbers (intensity values, gray levels)
  • Gray levels 0 (black) to 255 (white)
  • Color image is 3 2-D arrays of numbers
    • Red
    • Green
    • Blue
  • Resolution (number of rows and columns)
    • 128X128
    • 256X256
    • 512X512
    • 640X480
image formats
Image Formats
  • TIF
  • PGM
  • PBM
  • GIF
  • JPEG
video
Video
  • Sequence of frames
  • 30 frames per second
  • Formats
    • AVI
    • MPEG
    • Quick Time
digitization
Digitization
  • TV camera is analog, need
    • A to D converter
    • Frame grabber
  • Digital Cameras do not need digitization
    • JVC (MPEG through fire wire, USB)
    • Sony (MPEG through fire wire, USB)
    • ---
simple approach
Simple Approach
  • Recognize faces (mug shots) using gray levels (appearance)
  • Each image is mapped to a long vector of gray levels
  • Several views of each person are collected in the model-base during training
  • During recognition a vector corresponding to an unknown face is compared with all vectors in the model-base
  • The face from model-base, which is closest to the unknown face is declared as a recognized face.
problems and solution
Problems and Solution
  • Problems :
    • Dimensionality of each face vector will be very large (250,000 for a 512X512 image!)
    • Raw gray levels are sensitive to noise, and lighting conditions.
  • Solution:
    • Reduce dimensionality of face space by finding principal components (eigen vectors) to span the face space
    • Only a few most significant eigen vectors can be used to represent a face, thus reducing the dimensionality
eigen vectors and eigen values
Eigen Vectors and Eigen Values

The eigen vector, x, of a matrix A is a special vector, with the following property

Where  is called eigen value

To find eigen values of a matrix A first find the roots of:

Then solve the following linear system for each eigen value to find corresponding eigen vector

example
Example

Eigen Values

Eigen Vectors

face recognition1
Face Recognition

Collect all gray levels in a long vector u:

Collect n samples (views) of each of p persons in matrix A

(MN X pn):

Form a correlation matrix L (MN X MN):

Compute eigen vectors, , of L, which form a bases for whole face space

face recognition2
Face Recognition

Each face, u, can now be represented as a linear combination of eigen vectors

Eigen vectors for a symmetric matrix are orthonormal:

face recognition4
Face Recognition

L is a large matrix, computing eigen vectors of a large matrix is time consuming. Therefore compute eigen vectors of a smaller matrix, C:

Let be eigen vectors of C, then are the eigen vectors of L:

training
Training
  • Create A matrix from training images
  • Compute C matrix from A.
  • Compute eigenvectors of C.
  • Compute eigenvectors of L from eigenvectors of C.
  • Select few most significant eigenvectors of L for face recognition.
  • Compute coefficient vectors corresponding to each training image.
  • For each person, coefficients will form a cluster, compute the mean of cluster.
recognition
Recognition
  • Create a vector u for the image to be recognized.
  • Compute coefficient vector for this u.
  • Decide which person this image belongs to, based on the distance from the cluster mean for each person.