Vision - Computer Science and...

Wang: Suvery of Artificial Intelligence

1

Vision

From image to visual description

An interdisciplinary field

• Computational vision (computer/robot vision)

• Visual physiology

• Receptive fields• Orientation and other feature detectors• Retinotopic organization

• Visual perception


2

Three Levels of Analysis (Marr)

1. Computational Theory

Goals of computation, Appropriateness of the goal,General strategies

2. Representation/Algorithm

• How to represent the input and the output• Algorithms for transforming from one representation to

another

3. Implementation

How can the representation and algorithm be realizedPhysically (architecture, hardware)?


3

Image Example

A photograph

Closer look


4

Marrian Representational Framework

Input: Images as intensity distribution

• Primal Sketch

Intensity changes,geometrical distribution of line segments

• 2 12 -D Sketch

Orientation and rough depth of visual surfaces, and thecontours of discontinuities between surfaces, in a viewer-centered coordinate frame

• 3-D Model

Shapes and their spatial organization in an object-centeredcoordinate frame


5

Primal Sketch

Lines and contours from gray level images

• Edge Detection by finding discontinuities

• Edge segments are lined up and glued together

• Similar curves are combined to form contours


6

Edge Detection

• Different kinds of edges


7

Edge Detection (cont.)

• One-dimensional (1D) edges


8


• Convolution with linear filters: h = f * g

• 1D

• Continuous

h x f u g x u du( ) ( ) ( )= −−∞

+∞∫

• Discrete

h x f u g x u( ) ( ) ( )= −−∞

+∞

∑

• 2D - straightforward extension


9


• Canny edge detector

• Smoothing by convolving with a Gaussian

G x ex

σσ

πσ( ) =

−1

2

2

22

• Differentiate with the equality: ( f * g)' = f * g'And

′ = −−

G xx

ex

σσ

πσ( )

2 32

2

2

• Overall three-step algorithm

• Convolve an image I with ′Gσ to get R• Find the absolute value ||R||• Mark those peaks in ||R|| that are above a threshold

Tn, in order to reduce noise effects. Results are edgeelements


10

Smoothing Examples

y

x

W

© 1998 Morgan Kaufmann Publishers 2D Gaussian

(a) Original image (b) Width of Gaussian = 2 pixels

(c) Width of Gaussian = 4 pixels (d) Width of Gaussian = 8 pixels

© 1998 Morgan Kaufman Publishers

Smoothing with different Gaussian widths


11


• LOG: Laplacian of Gaussian

• Smoothing using a Gaussian kernel• Edge detection using the Laplacian operator• Edge elements are zero crossings

2D Gaussian and LOG function

G x y ex y

σσ

πσ( , )

( )

=− +

12 2

2

2 2

2

LOG x yx y

G x yσ σ∂∂

∂∂

( , ) ( ) ( , )= +2

2

2

2


12

LOG - 1D

“Positive” partof window

“Negative” partof window

© 1998 Morgan Kaufman Publishers A step edge

1 2 3 4 5 6

0.5

1

1.5

2

1 2 3 4 5 6

0.20.40.60.8

1

1 2 3 4 5 6

–1

–0.5

0.5

1

Image intensity, I(x)

dI/dx

d2I/dx2

© 1998 Morgan Kaufman Publishers LOG operation


13

LOG - A 2D Function

W

y

x

+

–

© 1998 Morgan Kaufman Publishers

Laplacian of a 2D Gaussian

• 2D LOG examples


14

Region Growing for Surface Detection

Input Image (unclassified pixels)=>

Disjoint Regions of Pixels

• Goal

Let X be the set of all pixels in the input image

Partition X into subsets (R1, R2, ..., Rn) such that

• The sets are disjoint• The union of the Ri's is X

• Similarity Measure

H Ri( ) =

TRUE if is homogeneous, or Max( ) – Min( ) <

FALSE if otherwise

R R Ri i i θ


15

Region Growing for Surface Detection

• Some Algorithms

• Merging - Bottom-up method. Starting with allindividual pixels

• Splitting - Top-down method. Starting with the entireimage

• A Sample Example (region growing)

1. Choose all pixels as seeds, Si, i = 1, 2, ..., N. N is thenumber of pixels. Each seed forms an initial region

2. Pick up two unchecked neighboring regions, check thesimilarity criterion

• If yes, merge• If no, mark them as separate regions

3. Goto Step 2 until all regions are marked


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3-D Model (or Model-based Vision)

Describing Shapes in Object-centered Coordinates

• Organization of 3-D shapes in a hierarchy

• Cylinder-based representation: Components, spatialrelations, and relative sizes

• Derive 3-D model

- Based on previous analysis (primal sketch, 2 12 D sketch)

- Recognition as matching between the representedimage and catalogued (stored) models


17

Vision

Summary

1. Computationally expensive, thus high demand onparallel algorithms

2. Computational vision is difficult

- Low level vision (primal sketch): There exist goodalgorithms.

- Medium level vision (2 12 - D sketch): There are

some reasonable algorithms.

- High level vision (3-D model): Invariant patternrecognition and image understanding (Sceneinterpretation), Few good algorithms.

These levels are intertwined together, making the wholeproblem most challenging.

3. Currently active field

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