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SELECTIVELY FILTERING IMAGEFEATURES USING A

PERCENTAGE OCCUPANCY

HIT-OR-MISS TRANSFORM

Paul Murrayand

Stephen Marshall

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Overview

The Hit-or-Miss Transform (HMT) The Percentage Occupancy Hit-or-Miss Transform

(POHMT)

The Percentage Occupancy Plot (PO Plot) Properties of the PO Plot

A Method for Selectively Filtering Image Features

Examples

Conclusions

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The Hit-or-Miss TransformMorphological transform that can be designed for featuredetection/pattern recognition

Uses two SEs which probe the image in search of a match

One SE searches for places where it fits inside features in the foreground

A second searches for places where it fits around features in the background

A positive result is returned if and only i f both SEs find a match at somepoint in the image

ForegroundProbe

BackgroundProbe

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The Hit-or-Miss Transform

BBG

BFG

BBG

BFG

In some cases, noise prevents the probes from fitting a feature whichshould otherwise be matched

This can be overcome by allowing a percentage P < 100% of the probes tofit the image

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The Percentage Occupancy

Hit-or-Miss Transform

The POHMT may be computed by measuring the extentto which image features occupy the SEs

A feature is detected by the POHMT ifP% of the SEs areoccupied by some feature

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Extent to which BFG

and BBG

are occupied

Intensity

POo

fSEs

POFG

POBG

T=50

T=150

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100

Extent to which BFG

and BBG

are occupied

Intensity

POo

fSEs

POFG

POBG

100P 96P

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The PO Plot

A PO plot is generated by plotting the percentageoccupancy of both probes against each other

The parameter P of the POHMT may be estimated byfinding the value of the critical point in the plot

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The PO Plot and the POHMT

A PO plot may be used to estimate P from training data

before applying the POHMT

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PO P lot

POFG

POBG

Top Left CellTop Right Cell

Bottom Left Cell

Bottom Right CellP=70

One pair of SEs were designed to match all 4 cells in the

image

The PO plot was used to estimate the only parameter, P

The POHMT accurately detects all 4 cells despite thenoise in the image when P = 70%

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Selective Filtering

The PO plot can be used to estimate values ofP such that some featuresare discarded by the POHMT

Increasing the value ofP makes the transform more strict leading to fewercells being detected

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PO Plot

POFG

PO

BG

Top Left Cell

Top Right Cell

Bottom Left Cell

Bottom Right Cell

P=75%

3 cells

P = 96%

1 cell

P = 90%

2 cells

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Selective Filtering

The previous example shows a powerful but simpletechnique for selectively filtering image features

It is obvious that increasing the strictness of thetransform by increasing the value ofP leads to fewerfeatures being detected

However, it is NOT easy to isolate any of the fourcells in the image

The following novel method allows any combination

of the image features to be segmented using justone composite SE

Lets try to isolate the cell in the bottom right of theimage which occupies around 80% of the SEs

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Selective Filtering

Set P low enough to detect the feature of interest

This leads to features other than the desired one to be detected

Overlay the bounding boxes computed for the previous image Set P high enough to exclude the feature of interest Compute a bounding box for each connected component in the

image

Locate any empty bounding boxes these are the locations of the

sought feature Mark the position of any empty bounding boxes in the ouput image

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Selective Filtering - Example

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PO Plot

POFG

POBGP = 95 P = 91 P = 88

P = 84 P = 80 P = 76

A complementary pair of SEs were designed to detect dice in an image

A PO plot was generated for each face of the die using these SEs

The critical points of each SE were computed to allow accurate setting ofparameters for the selective filtering method using bounding boxes

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Selective Filtering - Example

Isolating dice displaying 1 Isolating dice displaying 6

Isolating dice displaying 3 Isolating dice displaying 2 or 5

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Selective Filtering - Example

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PO Plot

POFG

POBG

Noise was added to the imageThe PO plot was regenerated

The selective filtering algorithm was usedto locate dice displaying a value of 2

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Summary

The HMT is a powerful method which can be used for fortemplate matching

The HMT is unreliable for processing noisy data

The POHMT is an extension of the HMT which offersimproved performance for processing noisy data

The PO plot is a novel design tool which can be used toestimate parameters for the POHMT and similar transforms

The PO plot can be exploited to make the POHMT capable ofselectively filtering image features

A novel approach which uses bounding boxes to locatefeatures of interest has been demonstrated

This approach allows features to be isolated in an imagebased on the extent to which they occupy a complementary

pair of SEs

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