Learning Object Representation

Andrej Lúčny

Department of Applied Informatics

Faculty of Mathematics, Physics and Informatics

Comenius University, Bratislava

andy@microstep-mis.com

www.microstep-mis.com/~andy

Regular objects

few parameters fully describe the object

recognize object = specify its parameters

Regular objects

e.g. Hough transformConversion of image to parameters

Image

Three arrays r[h,w], g[h,w], b[h,w], values 0..255 corresponding to color ingredients

Red ingredient

Green ingredient

Blue ingredient

Intensity map

bw[i,j] = 0.3*r[i,j] + 0.59*g[i,j] + 0.11*b[i,j]

• Looking for edges:one line can be represented as a function

column

inte

nsit

y

• Edges corresponds to sharp sectors

Sobel operator

ai-1,j-1 ai-1,j ai-1,j+1

ai,j-1 ai,j ai,j+1

ai+1,j-1 ai+1,j ai+1,j+1

bi,j

-1 0 1

-2 0 2

-1 0 1

º =

dxi,j = ai-1,j+1 + 2ai,j+1 + ai+1,j+1 - ai-1,j-1 - 2ai,j-1 - ai+1,j-1

ai-1,j-1 ai-1,j ai-1,j+1

ai,j-1 ai,j ai,j+1

ai+1,j-1 ai+1,j ai+1,j+1

bi,j

-1 -2 -1

0 0 0

1 2 1

º =

dyi,j = ai+1,j-1 + 2ai+1,j + ai+1,j+1 - ai-1,j-1 - 2ai-1,j – ai-1,j+1

Sobel operator approximated image derivation (gradient)Concerning a threshold Sobel operator indicates us edges

threshold

Sobel operator

|dx| |dy|

Sobel operator

|grad| = √ (dx + dy )2 2

Binary image

Thinning

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Thinning

Hough transform

Example: Circle

Task: how to turn thinned image to circle parameters

Paramaters:• center x-coordinate • center y-coordinate• radius

x

y

r

Hough transform

Each parameter has a particular range

E.g. for image with resolution 320 x 240 :• Range of center x-coordinate is 0..319• Range of center y-coordinate is 0..239• Range of radius is 10..200

We evaluate probability of each tupple (x,y,r)

from the given range

Hough transform

x

y

• The probability P[x,y,r] is given by number of witnesses, i.e. white pixels on thinned image which would be white if one draws circle with parameters x,y,r.

r

Hough transform

Circle is recognized !

Irregular objects

Parameters of irregular objects are not clear !

It is better look an universal method how to learn their representation

Irregularobjects

e.g. Dominant orientation templates

How such objects are

represented?

• Simple but fast and efficient method

Dominant orientation templates (DOT)

Motivation

template

image dealing with thinned edges

Edges detector Canny

intensity

|gradient| orientations

|dx|

thinned edges

|dy|

Orientations

(dx, dy)

01

23456

7

Template

• based on the orientations

Template

• object is covered by non-overlapping regions

Template• We concern orientation of any pixel in region,

which lies on edge

Template• We select set of dominant (prevailing)

orientations

Template• We have such set of few dominant

templates for each region

Template• The sets of dominant orientations form the

representation of the object

How to use the template• We cover image by regions and select one most

dominant orientation for each region

template

image

How to use template• Object is found if for the most of regions the dominant

orientation from image is an element of the set of dominant orientations in template

template image

Basic formal expression

I – current imageO – image from which the template is createdc – position on the image IR – region c + R – corresponding region put to position cDO(O,R) : set of (maximally k) dominant orientations in region R in template, i.e. on the image Odo(I,R) : dominant orientation in region R in the current image I do(X, R ) = DO(X, R ) for k = 1 δ(x) = x ? 1 : 0 where x is true or false

Does it work ?• Yes, if we put region R to proper position c• No, otherwise

Therefore we will need more templates for various positioning of regions

templates

positions…

Advanced formal expression

I – current imageO – image from which the template is createdw(O,M) – image O shifted by Mc – position on the image IR – region, c + R – corresponding region put to position cDO(O,R) : set of (maximally k) dominant orientations in region R in template, i.e. on the image Odo(I,R) : dominant orientation in region R in the current image Iδ(x) = x ? 1 : 0 where x is true or false

More effective but less precise approach• We can summarize more overlapping templates to one.• We simply add orientations from overlapping regions.• Such template must fit regardless shifting, but can detect also phantoms

integrated templatetemplates

…

Formalism of the efficient approach

I – current imageO – image from which the template is createdw(O,M) – image O shifted by Mc – position on the image IR – region, c + R – corresponding region put to position cDO(O,R) : set of (maximally k) dominant orientations in region R in template, i.e. on the image Odo(I,R) : dominant orientation in region R in the current image Iδ(x) = x ? 1 : 0 where x is true or false

=

More viewpoints• Still one template represents the object from one viewpoint only• Therefore we need to create more templates from various viewpoints• Again we can integrate more templates which are similar enough to one (in

the same way as shifted templates)

DOT efficiency• Belonging of orientation to a template can be represented by bits

0 or 1 and all DOT can be expressed in form of bit operations • Therefore DOT is very fast and running in real time

Object border• DOT can provide also approximate border of the object.• It is created by those edge pixels for which we have found

their orientation in the template

How to get template?

• Scan object put to contrast scene by camera from various viewpoints (i.e. not in the natural scene but under specific conditions)

or• separate object from scene by another method (e.g. by movement detector)

Failure of recognition

pattern

1.

2.

Failure or creativity ?

phantom

Further study

Hinterstoisser, S. - Lepetit, V. - Ilic, S. - Fua, P. - Navab, N.: Dominant Orientation Templates for Real-Time Detection of Texture-Less Objects. IEEE Computer Society Conference on Computer Vision and Pattern Recognition (CVPR), San Francisco, California (USA), June 2010

Thank you !

Andrej LúčnyDepartment of Applied Informatics

Faculty of Mathematics, Physics and Informatics

Comenius University, Bratislava

andy@microstep-mis.com

www.microstep-mis.com/~andy