flexible shape matching

Flexible Shape Matching

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Index• Template Matching Overview• Deformable Template• Active Contour (Snake)• Greedy Algorithm for Snake

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Template Matching - Problems

• Large number of comparisons.• Exact match of multiple parameters.

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Template Matching - Solution

• Reduce number of matched points.

Still fixed and not adaptable

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Deformable Template –

Exact Match Solution• Rather than using a fixed template with fixed

parameters, more flexible template is used.

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Deformable Template – Many Comparisons

Solution• Use only key edge points to detect object.• These points are discriminant points of the object

which are edge points.

=

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Deformable Template – Dynamic Templates

Generation• The set of parameter values that makes the

template best matches the edge points is the best parameters to use.

{, r}• Deformable templates may not be completely

autonomous.

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Template Energy• Good template parameters is what maximizes the

energy.• The goal is to find parameters that maximize

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More Parameters• More parameters can be used to make results

more accurate.• By a little eye analysis, it is apparent that usually

sclera is white and iris is darker than it.• Adding these parameters can enhance results.

Sclera

Iris

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Combine Parameters• Combining all parameters, result in this final

energy.

• Where, are weighting parameters that control the influence of this parameter over the resultant energy.

• Goal is to maximize E.

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Many Parameters – Problem

• For each parameter, there are a number of values that needs to be tested until maximum energy reached.

• Say 11 parameters selected and each parameter can have 100 values, so there are more than combinations of parameter values needed to be tested.

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Many Parameters – Solution

• This problem can be solved in two ways:o Optimization techniques that not reduce

number of combinations but try to make calculations quickly.

o Techniques to reduce number of parameters such as snakes.

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• An active contour is a set of points that aims to enclose a target object.

Active Contour : Snake

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Active Contour : Snake• Contour is a bounding region of a target object.• It is active because it is a self-learning process to

modify itself until closely bound the target object.• Contour changes like a snake.• Goal of snakes is to find salient image contours

that surround target object.

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Snake Spline• Snake draws a contour surrounding the target

object.• There are many complex objects with complex

boundaries and multiple inflection points. • Snake uses spline to be able to draw complex

shapes using simple shapes.• Spline divides complex shapes into small

segments that are easier to graph.

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Spline• Spline is a polynomial or a set of polynomials to

approximates complex shapes.• Complex shapes has many inflection points

that can be divided into simple segments with fewer inflection points.

• Because cubic polynomial has a maximum of only two inflection points, it will be used to approximate complex shapes.

x(u)=+++y(u)=+++

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Spline• Complex shapes are divided into segments of at

most two inflection points.• These segments are approximated using the

cubic polynomial.• Collection of segments are then connected

together in a smooth manner.

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Contour• Contour is defined in terms of x and y of all spline

cubic polynomial inflection points used to approximate complex shape.

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Snake Process• Snake is similar to deformable templates in which

they may be semiautomatic.• They rely on other mechanisms to place them

near the desired contour.• User specify the initial contour and snake tries to

modify it to find optimal contour.

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Snake Energy Minimization

• Snake changes its contour using different forces:o Internal forceso Image forceso External forces

• To judge contour optimality, snake uses energy minimization techniques.

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Internal Forces – Internal Energy

• Internal forces is used to modify the spline shape.• Internal energy of spline is symbolized that just

depends on spline shape.

• It consists of first- and second-order terms of contour points.

Internal Forces Energy

• Internal energy has two parameters that control snake shape:o α controls amount of snake spline stretching.o β controls amount of snake spline

flexing/smoothing.• The larger α, the more stretch snake contour is.• The larger β, the smoother snake contour.

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Image Forces• How a snake can know we need to detect eye?• Image forces guides the snake to a selected

image portion with certain features.• Examples is to depend on:

o Lineso Edges

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Image Forces Energy• To measure image force optimality, image energy

is calculated.• If only line and edge are the features to guide the

snake, thus line energy and edge energy are calculated.

• There are two parameters used to control image forces:o guides snake to align itself to dark regions.o guides snake to align itself to sharp edges.

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Greedy Algorithm for Snakes

• Greedy algorithm implements the snake energy minimization.

Define snake parameters α,β, and

Select snake point

Check neighborhood points for lower energy

Set new snake point to new minimum

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Greedy Algorithm - Initialization

• Snake parameters are initialized externally and initial contour is found.

• Say there are 10 points in the initial contour, then Greedy algorithm will be applied on all10 points.

Define snake parameters α,β, and

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Greedy Algorithm – Snake Point

NeighborhoodAfter Iteration

1After Iteration

2After Iteration

3

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