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be applied to scenes like the room in Figure below.
Discrete relaxation assigns all possible labels to each object and iteratively removes all the
labels which may not be assigned to an object without violating the constraints.
Labels : W Wall, F – Floor, C – Ceiling, D – Door, etc.. Assign all possible labels to each object
REPEAT
FOR each scene object
Faculty of Engineering Robotics Technology MECH 4041 12
B. Eng (Hons.) Mechatronics S. Venkannah Mechanical and Production Engineering Department Delete inconsistent labels on the basis
constraints
Delete inconsistent labels on the basis
constraints
UNTIL (any object has no label) OR (no updating possible)
IF (any object unlabelled) THEN return no solution
ELSE return current solution of unary of Nary The current solution may be a complete consistent labeling, as with Figure 1, or ambiguities may
still remain. There may be more than one consistent labeling.. unary properties:
A window is circular
A table is rectangular
A drawer is rectangular
A floor is chequered
Binary constraints :
A window is above a table
A phone is above a table
A drawer is inside a table
Background is adjacent to image border
A table is above a floor 13
Faculty of Engineering Robotics Technology MECH 4041 B. Eng (Hons.) Mechatronics S. Venkannah Mechanical and Production Engineering Department As an alternative to discrete relaxation, probabilistic relaxation allows each scene object to
have associated with it not only a set of component labels, but also a weighting assigned to each
label in the range 0 1. In general, these weighting are considered as probabilities, and so the sum
of the label probabilities should be equal to 1.0. There are several approaches to linear and nonlinear probabilistic relaxation schemes
For example, if a given region of a room image is chequered there is a high condition probability
that it is a floor, P(floorchequered)  0.8, say, however, it might be a tablecloth.
P(clothchequered)  0.2.
Have already seen some applications of relaxation labeling
Relaxation labeling for model based matching is no different.
is
Matching is posed as a labeling problem, where a model primitive
mi
labeled with (i.e. matched to) a scene primitive εi
Region based measurements of both a numerical and topological nature used.
Each primitive is given a quality measurement, normally a probability, for the
likelihood of it labeling each model primitive.
Starting from these initial measurements, the goal of the relaxation technique is to
reduce iteratively the ambiguity and disagreement of the initial labels by
employing a coherence measure for the set of matches.
The compatibility of each primitive with its neighborhood is used, and iteratively
increasing the size of the neighborhood.
14
Faculty of Engineering Robotics Technology MECH 4041 B. Eng (Hons.) Mechatronics S. Venkannah Mechanical and Production Engineering Department
Relaxation labeling problems may be easily visualized as graph labeling
problems. Graph Searching
The aim is to decide whether the reality represented by an image matches prior knowledge about
the image incorporated into the graphical models. In object recognition problem, the object
graph must match the object model graph exactly. If the problem is to find an object
(represented by the model graph) in the graphical representation of the image, the model must
match a subgraph in the image graph exactly. An exact match is called graph isomorphism.
It is possible to represent object models by a directed or undirected graph structure in which the
set of nodes,
, represents labeled features of the model and the set of arcs, ,
represents relationships between them. Examples of directed arcs are
relationships such as greater than, less than, whereas undirected arcs include
relationships such as parallel and connected, equivalent to ordered and unordered relations
respectively. In its purest form, two
graphs,
and
are isomorphic if there is a onetoone mapping, f, such that In other words, there is a correspondence between the nodes of
and
that
preserves the arc relationships. However, in order to determine if two object models are
equivalent, it is not sufficient to determine solely that the two graphs are isomorphic, but that the
labeling of the arcs and nodes is also equivalent. In practical scene identification, each of the arcs
and nodes generally assumes a value within a continuum, a line of length x pixels for example,
and the elegance of the approach is sometimes lost. 15
Faculty of Engineering Robotics Technology MECH 4041 B. Eng (Hons.) Mechatronics S. Venkannah Mechanical and Production Engineering Department Figure 5: Graphs for the triangle problem The graph isomorphism problem is of little practical use in scene analysis because it is not
expected that the scene segmentation will be perfect. In addition to the problem of false or
missing features, and hence node data, it is common that a multiple object scene is matched
against single object models. One approach to scene interpretation using att...
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This document was uploaded on 03/12/2014 for the course MECHANICAL 214 at University of Manchester.
 Spring '14
 Mechatronics

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