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1. AGENCY USE ONLY (Leave blank)__.REOTDE 3 REPORT TYPE AND DATES COVEEI 1990 Final 13 Jun-88. - 12 Jun 89

.TITLE AND SUBTITLE S. FUNDING NUMBERS

Morphology Workshop DA0-8G03

O AUTHOR(S)

Robert M. Haralick (Principal Investigator)

N\ PERFORMING ORGANIZATION NAME(S) AND ADDRESS(ES) 8. PERFORMING ORGANIZATIONREPORT NUMBER

University of WashingtonSeattle, W4A 98195

9. SPONSORING/ MONITORING AGENCY N~AME(S) AND ADDRESS(ES) 10. SPONSORING/I MONITORING

U. S. Army Research Office AEC EOTNME

P. 0. Boxc 12211 ARO 26131.1-EL-CF-Research Triangle Park, NC 27709-2211

111. SUPPLEMENTARY NOTES

The view, opinions and/or findings contained in this report are those of theauthor(s) and should not be construed as an official Department of the Armyposition, policy, or decision, unless so designated by other documentation.-

i2a. DISTRIBUTION /AVAILABILITY STATEMENT I12b. DISTRIA410O "OD '

Approved for public release; distribution unlimited. cTEl

13. ABSTRACT (Maximum 200 words) j"

* Mathematical morphology provides the operations of dilation, erosion, opening andclosing for performing non-linear image analysis for binary or grayscale images. The alge!raof mathematical morphology is as rich as the algebra of convolution and correlation. Thealgebra is n t based on linear combination and has no relation to spatial frequencies. Rather,it has an intrinsic connection to shape due to the primitive matching property inherent inthe opening and closing morphological operations.

Mathematical morphology can be an important component of many of the future smartsensors the Army Is developing. The technology of mathematical morphology has proved

(Abstract continued on reverse side)

14. SUBJECT TERMS 15. NUMBER OF PAGES

Mathematical Morphology, Morphology, Nonlinear Image Analysis1.. PIECDImage Analysis, Smart SEnsors, Workshop 1.PIECD

17. SECURITY CLASSIFICATION 18. SECURITY CLASSIFICATION 19. SECURITY CLASSIFICATION 20. LIMITATION OF ABS7.RACOF REPORr OF THIS PAGE OF ABSTRACT

UNCLASSIFIED I UNCLASSIFIED I UNCLASSIFIED7 ULNSN 7540.01 -280-5500 Standard Form 298 (Rev 2.89)

0,M~r:bod t~ AN~SI SWd Z191

Y.

itself in the manufacturing industry where it is being successfully used on the factory floorfor visual robot guidance, object recognition. inspection, and flaw detection. Almost everycompany manufacturing pixel pushing machine vision boards has one board capable ofperforming mathematical morphology as well as the traditional convolution operations.

It is now time for the Army to benefit from what morphology work has already been doneand to develop a program of what needs to be done. The purpose of the morphology workshopwas to review some of the basic and existing theory of morphology, illustrate how morphologyperforms recognition shape extraction, present new results in mathematical morphology, andmake recommendations to the Army about new research areas in morphology which need tobe developed in order to benefit Army programs. The workshop involved invited speakerswho ar known for the work they have published or lone in mathematical morphology.

* /lico a~I~J. - CF

Morphology Workshop

Final Report

Robert MV. Hara lick

Department of Electrical Engineering, FT-10Universty of Washington

Seattle, WVA 98195

Project P.26131-EL-CF

Grant DAALO3-88-G-0035U.S. Army Research Office

'tscodes

anI orei

al~ 'Je

1. Summary

_ V Mathematical morphology provides the operations of dilation, erosion, opening andclosing for performing non-linear image analysis for binary or grayscale images. The algebraof mathematical morphology is as rich as the'algebra of convolution and correlation. Thealgebra is not based on linear combination and has no relation to spatial frequencies. Rather,it has an intrinsic connection to shape due to the primitive matching property inherent inthe opening and closing morphological operations.

Mathematical morphology can be an important component of many of the future smartsensors the Army is developing. The technology of mathematical morphology has proveditself in the manufacturing industry where it is being successfully used on the factory floorfor visual robot guidance, object recognition, inspection, and flaw detection. Almost everycompany manufacturing pixel pushing machine vision boards has one board capable ofperforming mathematical morphology as well as the traditional convolution operations. ,

It is now time for the Army to benefit from what morphology work has already been doneand to develop a program of what needs to be done. The purpose of the morphology workshopwas to review some of the basic and existing theory of morphology, illustrate how morphologyperforms recognition shape extraction, present new results in mathematical morphology, andmake recommendations to the Army about new research areas in morphology which need tobe developed in order to benefit Army programs. The workshop involved invited speakerswho are known for the work they have published or done in mathematical morphology.

2. Workshop Overview

The two-day workshop was held under the auspices of MICOM at the Tom Bevill Centerof the University of Alabama, Huntsville, on 25 and 26 July 1988. The invited presenterswere

Dr. Robert M. flaralickUniversity of Washington

Dr. Stephen S. WilsonApplied Intelligent Systems, Inc.

Dr. Petros 1faragosHarvard University

Dr. Ronald W. SchaferGeorgia Tech

Seventeen people attended the workshop.

3. Workshop Program

Program

25 July 1988

08:00-09:30 Image Analysis Using Morphology: The Concepts, Robert M. Haralick

09:30-10:30 Applications of Morphology in Industry: Part , Steve Wilson

10:30-10:45 Coffee Break

10:45-11:45 Applications of Morphology in Industry: Part II, Steve Wilson

11:45-13:00 Lunch

13:00-14:30 Image Analysis Using Morphology: The Algebra, Robert M. Haralick

14:30-15:45 Army Needs and Morphology: Panel Session I

15:45-16:00 Coffee Break

16:00-17:00 Morphological Signal Processing Systems: Part I, Ron Schafer

Program26 July 1988

08:00-09:00 Mathematical Morphology Applied to Mulli-Scale ImageRepresentation and Shape Description, Petros - ragos

09:00-09:30 Morphological Signal Processing Systems: Part II, Ron Schafer

09:30-10:30 Army Needs and Morphology: Panel Session H

10:30-10:45 Coffee Break

10:45-11:15 Mathematical Morphology Applied to Multi-Scale ImageRepresentation and Shape Description: Part II, Petros Maragos

11:15-11:30 Closing Remarks

I .I4. Abstracts of Talks

t4

Image Analysis Using Mathematical Morphology

Robert I. HaralickIntelligent Systems Laboratory

Department of Electrical Engineering * FT-10University of Washington

Seattle. WA 98195

ABSTRA CT

For the purposes of object or defect identification required in industrialvision applications, the operations of mathematical morphology are moreuseful than the convo!ution operations employed in zignal processing becausethe morphological operators relate directly to shape. This talk reviews bothbinary morphology and grayscale morphology, covering the operations of

dilation: erosion, opening and closing, their relations and the morphologicalsamplig theorem. Examples are given for each morphological concept andexplanations are given for many of their inter-relationships. A comparisonbetween the algebra of morphology and the algebra of convolution revealssome important similarities which are suggestive of the underlying depth andrichness of the non-linear algebra of morphology.

Applications of Morphology in Industry

Steve WilsonApplied Intelligent Systems, Inc.

Ann Arbor, MI 48103

ABSTRA CT

Morphology has been successfully used in a number of applications inindustrial machine vision. This session will outline vision principles involved inthe application of morphology to several different real world image processingproblems such as classification of different objects, location and dimensionalmeasurement of objects to subpixel accuracy, and texture analysis such asflaws in machined or painted surfaces. Familiarity with image processing willbe helpful but not necessary.

This session will not involve a rigorous math approach, but instead itsemphasis will be on gaining an intuition on how the application of variousgrayscale and binary technique can successfully handle images encountered inadverse envirionments where conditions cannot be well controlled.

Many of today's machine vision hardware systems can be programmed totake advantage of the methods discussed, which will range from simple appli-cations involving erosion*, dilation, and skeletonizing to newer morphologicaltechniques involving vector correlation and majority voting logic. Other topicsto be covered will include applications where binary morphology fails, wherelinear methods will fail, how to do thresholding and segmentation correctly,tradeoffs between processing time and robustne5s, how to handle movingimages, variation in illumination levels and textured backgrounds, findingvarious image features, and the transition from morphology to higher levelprocessing concepts.

For each of the important application categoris, a number of Side will beshown illustrating step by step morphology processing from the input cameraimage to the final recognition.

Morphological Signal Processing Systems

C. H. Richardson arid R. W. SchaferGeorgia Institute of TechnologySchool of Electrical Engineering

Atlanta. Georgia 30332

ABSTRA CT

This talk will begin by reviewing some important relationships betweenmorphological systems and a variety of signal processing transformations thatwere originally developed outside the framework of morphological systemtheory. This discussion is intended to highlight the need for a systematicapproach to the design of signal processing systems that are based on theprinciples and fundamental representational theorems of mathematical mor-phology. A second aspect of the talk will be concerned with some applicationsof morphological signal processing systems. The talk will conciude with ageneral discussion of the some of the fundamental problems in computer-aided design and analysis of morphological systems. Specifically discussedwill be preliminary research on developing a LISP-based signal processingenvironment for the representation of discrete signals and systems for bothsymbolic and numeric manipulations of morphological systems.

t

Mathematical Morphology Applied to Multi-ScaleImage Representation and Shape Description

Petros MaragosDivision of Applied Sciences

Harvard UniversityCambridge. MA 02138

ABSTRA CT

Two fundamental problems in computer vision are how to represent imageobjects at multiple scales and how to describe their shapes. Mathematicalmorphology is a formal and quantitative methodology to image analysis, whichdirectly extracts information about the shape and size of image objects. Assuch, it can offer a systematic approach to solving the above two problems.Specifically we will discuss the use of morphological skeletons for a very gen-eral and versatile multi-scale image representation transform; morphologicalopenings for nonlinear multi-scale image smoothing and a derived shape-sizedescriptor, the pattern spectrum; a shape-size approach for a symbolic imagemodeling by parts; and the use of morphological skeletonization for modelingfractal images.

Through successive erosions and openings of an image with respect to anarbitrary structuring element, a sequence of small critical image parts can beobtained, called skeleton components, whose superposition is Lhe morphologi-cal skeleton. The ensemble of all skelet_ n components can exactly reconstructthe image through dilations. Elimination of some components is equivalent tomorphological opening (smoothing) the image at a scale equal to the number ofeliminated components. By also varying the structuring element, multi-shapemulti-scale structural distributions in images can be modeled by skeletons andopenings with direct applications to data. compression and progressive imagetransmission.

The openings can also complement linear smoothing filters used in multi-scale image analysis, because openings can suppress noise ,vfh'mu. sh1i "ng r

blirring image edges and axiomatize the concept of scale. In addition, areasof differences among successive openings create a useful shape-size descriptor,the pattern spectrum, which can detect critical scales in images.

Morphological concepts can be used to rigorously formulate a symbolicimage modeling problem. Here the image is modeled as a nonlinear super-position of simpler parts (the "symbols"), which are translated and scaledshape patterns (structuring elements) drawn from a finite collection. Then

2

the model parameters can be found by using the information from openingsand pattern spectrum, and via local searches at points of generalized skeletons.This symbolic modeling appears promising in bridging the gap between low-level image processing operations and high-level vision tasks such as objectrecognition.

Finally, in the theory of iterated function systems, a fractal image can bemodeled arbitrarily closely as the attractor of a finite set of affine maps. We usethe morphological skeleton to efficiently extract the parameters of these affinemaps. This technique has appiicatkuns for fractal image analysis/syrthesis.computer graphics. and coding.

L

5. Discussion at Workshop

~4

Remarks on Morphology Workshop Panel Discussionby Stephen Dow

The morphology workshop panel discussion brought out anumber of issues relating morphology to Army image processingapplications. Some of the general types of processing wheremorphology was identified as being applicable are imageenhancement or filtering, shape feature extraction, and datacompression. Some concern was expressed that the shapedetection capabilities of the morphological operations may bemore applicable to images from manufacturing applications thanto those from Army applications because in the former casethe shapes of interest tend to be more predictable and well-defined than in the latter. It may be the case that thecomplex imagery involved in automatic target recognitionapplications precludes the free-form, interactive selectionof morphological operations and structuring elements which willextract desired objects; techniques for automated selection andoptimization may be necessary. It was pointed out thatmathematical morphology is not a stand-alone method but a setof tools to be used along with other methods. Even ifmorphological operations cannot directly extract the objects ofinterest there are probably portions of the processing whichcan be aided by these operations and by the algebraicmethodology morphology provides.

There was also some discussion relating to the existenceand availability of image data bases and criteria forperformance evaluation. These factors are important to theresearch community's ability to develop, test, and demonstatethe applicability of morphological methods to Army imagery.

APPLICATIONS OF MORPHOLOGY IN INDUSTRY

Stephen S. Wilson, Applied Intelligent Systems, Inc.

Many of the tools of morphology have been successfully applied inindustrial applications. The erosion, dilation opening and closingoperations are useful for noise filtering and for recognizing and locatingsimple shapes defined by a structuring element. Also, a wide variety ofmore complex but useful tools fall under the heading of "hit or miss"operations such as topological filters, convex hull, skeletonizing,feature finding, conditional dilation, and directional filtering.Generalization of the above operations to fuzzy logic is one way ofextending the morphology concepts so that they can be directly applied togrey level images. Other generalizations such as majority voting logicare useful when applied to noisy images.

Vector correlation is similar to the usual concept of correlation, butwhere the picture and kernel are vectors multiplied using the innerproduct. In morphology, a vector structuring element can be defined wherethe basis of the vector space is a number of feature bit planes. Thus,morphology can be used for relating features to classify objects.

Industrial applications largely fall into five application categories:1. Classification, such as character recognition using vector morphology,2. Location; finding overlapping parts to subpixel accuracy using vectorcorrelation,3. Texture defects, such as finding flaws in TV screens by directlyapplying openings and closings,4. Dimensional measurement, where morphology is used to locate positionswhere measurement is to take place, and5. Flaw detection, such as missing, or improperly punched holes in metalparts.

There are two broad classes of parallel computer architecture used inmorphological image processing: MIMD (Multiple Instruction, Multiple Data)systems which are coarse grained, and SIMD (Single Instruction, MultipleData) systems which have fine grained processing elements. The mostpopular types of MIMD systems are pipeline processors where a large numberof functional modules can be interconnected to form a real time imageprocessing system. Examples of these systems are the ERIM Cytocomputer,and a large variety of cards manufactured by Datacube which can beconfigured using their proprietary Maxvideo buss. However, these syst.emscan be bulky and expensive, and difficult to configure in the field.

The most popular type of SIMD architecture is the mesh connected systemwhere a large number of simple processing elements are connected in an NxNtwo dimensional grid such as in the GAPP chip manufactured by NCR.Although these systems are superb at morphology; the data I/0 tends to bequite complex, and existing systems are large and expensive. The AppliedIntelligent Systems Inc. AIS-5000 is an industrial system with a onedimensional array of moderately complex processors. The Centipede is anevolution of the AIS-5000 which is small, low cost, and more powerful, andis a candidate for an automatic target recognition system.

6. Letters

,I Aeronautics andS-- a Administration

George C. Matshall Space Flight CenterMarshall Space Flight Center, Alabama35812

ReplytoA,,nof Mail Stop EB44

MSFC, AL 35812

August 1, 1988

Dr. Robert M. HaralickBoeing Clairmont Egtvedt ProfessorDepartment of Electrical EngineeringUniversity of Washington402 Electrical Engineering Building FT-10Seattle, Washington 98195

Dear Dr. Haralick,

The workshop last week has aroused interest in the potentialthat morphology shows for use on several NASA programs. Projectsat the Marshall Center that may benefit from its applicationinclude: vision sensor driven off-line programming of a robot forSolid Rocket Booster refurbishment; vision guided rendezvous anddocking for an autonomous satellite service vehicle; and thecapture of a CAD data base via the use of 3D Computed TomographyCT data. The last application, in particular, is interestingsince it would require the extension of morphological techniquesto 3D images, and it could have widespread use in industry.

Thanks again for organizing such an interesting and timely

conference. I look forward to receiving the post-workshop report.

Sincerely

ikc -f,.. I -

Ken Fernandez, Ph/D.Information and ElectronicSystems Laboratory

TECHNICAL. LETTER KN11-ADVTEC-HV-143080 MTLYTNBROWN ENIGNEERING

Contract DASG6O-87-C-OO'42TA 150CDRL A001

TO: Advanced Technology DiLrectorateU.S. Army Strategic Defense CommandP.O. Box 1500Huntsville, Alabama 35807

Attention: Mr. Doyce Satterfield, CSSD-H-V

FROM: Teledyne Brown EngineeringSETAC Project OfficeCummings Research ParkHuntsville, Alabama 35807

Author: Wendell A. Childs

UBJECT: Morphology Workshop

ATE: 1 August 1988

1) On 25 and 26 July I attended the Morphology Workshop at the

Beville Center, University of Alabama in Huntsville. The handout

material from the Workshop is attached. Additional material to include

a copy of viewgraphs used in the workshop and list of attendees will be

supplied at a later (late.

2) Morphology in a nonlinear mathematical formalism that is

.aptable to parallel digital processing. It has potential for

?plications in image analysis, target recognition and discrimination.

Work is needed to determine just how well it can satisfy the

requirements of these applications. Examples of the use of morphology

to good advantage in industry were described during the Workshop and

were very impressive. If the opportunity should arise it appears using

morphology algorithms in the discrimination process would be a fertile

area for investigation.

enidell A. 'c~hidsLdvacedTechnology

THE VIEWS, OPINIONS, AI#O/ON FINOINGS C dTAINEO INTHIS REPORT ARE T"0111 OF THE AUTHORISI AND SHOULDNOT S CONSTRUED AS ANd OFFICIAL DEPARTMENT OfTHE AWAY POSITION. POLICY. OR DECISION, UNLESS SO0DESIGNAT1Ely5 OTHERX OFFICIAL OOCUMEINTATION.

WAWN HSDOCUIENT CONTAINS TECHNICAL DATAWiIixOTIS RESTRICTED SY THE ARMS CX0OIIT

CONTROL ACT (TITLE 22. U.SC.. SEC. 2751 ET SCOI OR~Cf V(ORDER 12470 VIOL.ATION OF TIIUTXFORT- ~RETTO SEVERE CRIMINAL. PENAL TIES,

7. Recommendations

It is clear from the discussions at the workshop that mathematical morphology is animportant image analysis tool that has applications not only in industry but also in smartsensor systems. This is confirmed by the letters of section 6. It would be worthwhile forsome basic and DOD applied research to be sponsored in this area.

I

I

I

1'II

8. List of Attendees

III

I

I

J.S. Bennett Stephen WilsonMICOM/AMSMI-RD-RE Applied Intelligent Systems, Inc.U.S. Army Missile Command 110 Parkland PlazaRedstone Arsenal, AL 35898-5253 Ann Arbor, MI 48103(205) 876-1623 (313) 663-8051

J.L Johnson Petros MaragosMICOM/AMSMI-RD-RE-op Harvard UniversityU.S. Army Missile Command Division of Applied SciencesRedstone Arsenal, AL 35898-5253 Cambridge, MA 02138(205) 876-3820 (617) 495-4390

Scott Speigle Craig RichardsonMICOM/AMSMI-RD-GC-C Georgia TechU.S. Army Missile Command P.O. Box 31431Redstone Arsenal, AL 35898-5253 Atlanta, GA 30332(205) 876-8281 (404) 894-2910 X- 1

Judy Denton Ronald W. SchaferNASA/EB44 Georgia TechMSFC. AL 35812 School of Electrical Engineering(205) 544-3831 Atlanta, GA 30332

(404) 894-2917Stephen Dow

Department of Mathematics Ken FemandexUniversity of Alabama NASA-EB44Huntsville, AL 35899 MSFC, AL 35812(205) 895-6470 (205) 544-3825

C.C. Sung Jim EppersonDepartment of Physics Department of MathematicsUniversity of Alabama University of AlabamaHuntsville, AL 35899 Hunstville, AL 35899(205) 895-6117 (205) 895-6611

Wendell Childs Richard SimsTeledyne Brown Engineering MICOM/AMSMI-RD-AS-SS300 Sparkman Drive U.S. Army Missile CommandHuntsville, AL 35807 Redstone Arsenal, AL 35898-5253(205) 532-8435 (205) 876-1648/1879

William Pittman Larry Z. KennedyMICOM/AMSMI-RD-AS-PM Applied Research, Inc.U.S. Army Missile Command P.O. Box 11220Redstone Arsenal, AL 35898-5253 Huntsville, AL 35814(205) 876-1778 (205) 837-8600(AV) 746-1778

Henry C. HollmanCSSD-H-SAIU.S. Army SDCP.O. Box 1500Hunstville, AL 35807(205) 895-5459

Morphological Signal ProcessingSystems

Craig H. Richardson and Ronald W. Schafer

Georgia Institute of Technology

School of Electrical Engineering

Atlanta, Georgia 30332

-- . -. .. l ..

Signal Processing

Signal

I Processing -

waveform System waveformor or

imag-e image

S i g n a l _________________________________________________

Interpretationwaveform System symbols

orimage

0 Design of signal processing systems miay be facilitated bv

symbolic manipulation of signal processing expressions.

Basic Set Operations

Shifted Set: (X)b = {Z Z=X+b; X}

Complement Set: (X)C = {z X}

Symmetric Set: B = {z• z = -b; b G B}

Minkowski Sum:

Xe B = {z:z=x+b;xEX,bEB}

= U(X)b= U (B)x = X e BbEB xEX

= {.X n (B)z # }

Minkowski Difference:

X B = (X ED B)- n (X)bbEB

= {z: ( )zC X} = {z. z-bEX;b -B}

Duality: X G B = (XCG B)C; X G B = (Xc e B)c

Basic Morphological Systems

Dilation: P(XB) =XO3 {z "X n(B)z / 0}

Erosion: E(XB) = xe B {z: (B)> C X}

Duality:

E(.X, B) = X 13 = (XC P) -- [D(Xc B) "c

D(XB) = X 3 = (Xc 1) c = [p(X',B)]c

Opening: O(X,B) =(X @ B)O B =P((XB),B)

Closing: C(XB) =(X E',h) B =&(V(X, B),/1)

Duality: O(XB) [C(Xc,B)]Ic C(X,B) = [O(Xc ,B)]c

Open-Closing: OC(XB) - C(O(XB),B)

Close-Opening: CO(XB) = O(C(X, B). B)

,N~. P 'n,r crmm ritr-r cfri irtirncr Pomont P P --. wR cn

drop the " and all definitions of morphological operators give

the same results.)

Properties of Morphological

Systems

Increasing: For example,

If X, C X9, then E(XiB) C E(X 2,B)

Translation Invariant: For Example,

9((X)z, B) =[(XB)]z

Extensive/Antiextensive:

(X, B) c O(XB) C X C C(XB) C D(X,B)

Idempotence:

(O(X.B).B) - C(X.B)

C(C(X,B),B) =C(XI B)

Systems for Thinning- T

Hit or Miss Operator:

Assume B - (B 1, B2) where B, and B 2 are disjoint sets.

4(X. B) = (X G f.)/(X e f 2 )

= {z :z e (X eCB,) and z 0 (X B.2)}

= (X e/fi) n (X f- 2 ) c = (X e 1 ) n (X B 2)

= (X,B1) n E(XC, B2)

The hit or miss operator selects the set of points for which B,

is inside the image and B2 is inside the background.

I Filter

MoiregratingT

.304 k8 ~stainlesssteel

N1 61filler

I Base

- Filler

Base

245 MPaFigure 7b. Moire interferometry displacementfield of a lack of fuison weld defect. Thenet in-plane displacement per fringe is 0.4microns.

dL

Systems for Thinning - II

Skeleton:

The skeleton S(X) of a binary image is defined as

S, (X) = E(X, nB)/O(E(X, nB),B)

for n = 0, 1,..., N.

NS(X) = U Sn(X)

n=0

The original image can be reconstructed from the skeleton sub-

sets by

N

X= U D(Sn(X),n)n=O

ORIGINALIMAGES

_- I

ORIGINAL I ,\... jSKELETONS " I

€1

SKELETONS,

rigu 6-. Images, skeletons, and globally ininimal skeletons (stmic. elm3ent-k SQUARE).

Representing Functions by Sets

* Functions can be represented by sets.

F UNCTION CROSS - SECTIO0N Ul{R

f *

Xt~f ~ Ti Iit g,

*min and max are isomorphic to intersection and union.

(f A g) (Y) = min f f(x), g (x)] Uz U(f ) Ug

f (X) g(x) Vz U Uf) U (g)

Morphological Systems for Functions

Minkowski Sum:

(f E g)( x) = ma[f/(z) + g(x - z)'

Minkowski Difference:

(f e g)(z) = min[f(z) g(x - z)]

Dilation:

V(f, g)(x) = (f E> )(x) =max[f(z) t g(z - x)]

(x) = g(-x) (reflected function)

Erosion:

(f, 9)(r) --7 (f G 9^)(X) = rnn[f (z) -gz -X)I]

Opening and Closing:

O(f,g) = D V(Yf9),9) CUf9) =1

Morphological Filtering

e Morphological systems can be used to smooth functions.

OICINAL. FU'JCTION

A I

%i t ItIit IA A ,ii

OPENING BY SET B C 181S) CLO..SINC BY ET B CIBIS)

I

ItI

Morphological Signal Analysis

Top Hat Operator:

T(f,B)(x) = f( ) - O(f,rnB)(x)

cnICXNAL FLINCTICN

Q -

EROSON BY SET B C 151=5) OInATION BY SET B CIBI-S)

A

fil I f

/ i ,,,. ,,,

O i

N14 N

, I III, 1i

// I/ I , ,,I i ,I I I a "

.1 12

I . ~I !

A ' l,t I~ I;!, I ''''

pl _ _ _ _ _ _ __'_ _ _ _ _

I f _ _ _ _ _ _ _ _ _ _ _I_

Systems for Thinning - III

Edge Detection:

The edges of a binary image can be extracted using an operator

of the form

F(X, nB) = X/(X, nB)

where B is a small symmetric structuring element.

For greyscale images, the corresponding operator is

"(f, nB) = f - E (f, nB)

U C7

Rank-Order Systems - I

Consider a system with input f(x) such that the output signal

Rk(f, B)(x) is obtained by sorting the values of the input subset

{f(z) :z E Bx} and assigning the kth number in the resulting

list as the output value. (Assume N is the number of points in

the set B.) Then

R1(fB)(x) = min[f(z)] = $(f,B)(x)

kN(f,B)(x) = max(f(z)] = P(f,B)(x)

R (N+1)/2(f, B(x) = median [f(z) for z C B,]

Rank-order systems are increasing and translation-invariant.

Rank-Order Systems - II

The kth rank-order system with structuring set B (window)

is equivalent to a union of erosions by all the subsets of B

containing k points. For example, consider a 3-point median

filter.

M 3(f,B)(x) - median [f(x- 1),f(x),f(x + 1)]

min[f(x - 1), f(X)]

- max min[f(x- 1),f(x+ 1)]

min[f(X), f(x + 1)J

Rank-Order Systems - III

Relations to other morphological systems:

ORICINA. FIJ4CtIO' OPEN - O..OSINC BY L CILI=3)

o wr

-LO OPENINC BY LC 1L1ux3) MEDZAN ROOT W.R.TO 8 (181z5)

vi v

o 2 ~0 645 264 M7 Z3

SAMLESnML

Kernel Representations- I

Consider an increasing translation-invariant system I(X). The

kernel of this system is defined to be the collection of sets

Kern(T) = {A :0 e IF (A)}

where 0 is the origin.

Any increasing translation-invariant system can be exactly rep-

resented as a union of erosions by all its kernel elements: i.e..

S(X) U(XB)BEKe:n(91)

In general the kernel may contain an infinite number of ele-

ments, but sometimes it is possible to represent a system with

only a finite subset (basis) of the kernel elements.

Kernel Representations - II

For function processing systems, the analogous result is

V(f,g)(x) = max [(f,g)(x)]gEKern(O)

Recall the example of the previous 3-point median filter.

M3(f,B)(x) = median [f(x - 1),f(x),f(x + 1)]

min[f(x - 1), f(x)]

= max min[f(x- 1),f(x + 1)]

min[f (x), f(x + 1.)]

= max[E(f,BI)(x)]B%

where B = {-1,0, 1}, B 1 = {-1, }, B 2 = {-1, 1}, and B 3 =

6A.C15

{0, 1}. Thus the kernelhof the 3-point median filter is

Kern(,M 3) = {B 1, B2, B3}

Kernel Representations - III

Which systems have finite kernels?

* Basic morpholo' a! systems - erosion, dilation, opening.

and closing.

a Rank-order systems including median filters.

* An interesting class of linear shift-.invariant systems.

@ Wilcoxon filters - combination of median and linear filters

(Crinon).

9 Shape recognition window transformations (Crimmins and

Brown).

Design of Morphological Systems

e Powerful theory - much structure.

* How do you specify a desired system?

e How do you synthesize a system meeting given specifica-

tions?

• Can you find a kernel basis?

* How do you find the most efficient implementation for a

given architecture?

Morphological Signal Processing Systems: Part II

* Application of morphology to FLIR images

* Concerns of computer aided morphology

* Introduction to LISP

* Numeric and symbolic processing of morpho-

logical expressions

Forward Looking Infra Red (FLIR) images arecharacterized by:

* compact light (concentrated heat) regionscorresponding to man-made objects

* darker (cooler) background

* light distractions such as a forest or trees

* poor contrast

" no precise geometrical cues

" unknown object size

The top hat transformation is defined as:

ftopL( 7 ) - (f - max{fnLo, fnLgo})( )

where n is an integer multiplier and L0 and L 9 0 are

horizontal and vertical line structuring elements,

respectively, centered at the origin and having

overall length equal to 3, i.e., IL0 -- IIL9 011 = 3.

t

I

To exploit the high contrast of the man-made

object a simple approximation to the gradient is

defined as:

G(Y) - (f G B)(Y) - (f eB )(Y)

where a rhombus of size 1 was used for B.

The top hat transformation with:

I1nLoII = IIinL 9o = 2n + 1

separates the compact areas, whose largestdimension (height or width) is less than 2n + 1,

from the larger non-compact areas such as ahorizontal band or a forest.

The object location is found by taking the mean ofthe grey scale maximum locations of the gradient

M

k= 1

where Mv is the number of times the maximum grey

scale value is found, xk is the location of the kthmaximum and X is the desired location. If there isonly one maximum in the image then a point on

the edge of the object is acceptable.

I

By using a slightly different top hat

transformation of the form:

(ftopL) () = (f-max{fnLo, fnL9 0 , frnL 45 , f&L 135 })( )

one may suppress some of the noise in the top hat

images-- since this step more cleanly separates the

object from the whole image, making the

subsequent gradient processing less susceptible to

false peaks.

The processing steps for the FLIR data were:

* Close with rhombus of size 1

" Sequence of Top Hat Transformations

* Find maximum of gradient

" Average maximum locations to find object

SUMMARY

* sequence of top hai transformations coupled

with gradient processing able to locate single

man-made object

* by changing the method of object location

selection one can locate an arbitrary number

of obje-cts

* FLIR object detection can not be solved using

solely these methods

* require additional information for more

complete solution

.. ... .. .. ...

Computer Aided Morphology - CAM

How does one select the sequences of operations to

perform a task?

Serra suggests five rules for organizing sequences

of morphological operations:

* Review possible modes for information

reduction (i.e. reducing a structure)

* Order commutative processes so the largest

simplification is made first

* Determine groupings of useful interconnected

operations

o Minimize the effects of interaction of sequen-

tial operations

* Remember that it is possible to back-track to

regain lost information

Requirements for computer aided morphology in-

clude:

* Representation of reference properties of

operations

Method of selecting operations based on

assessment, of properties

* Means of interpreting user's requirements

* Heuristic knowledge of operations and

structuring elements

Introduction to List Programming

(Common LISP)

* Fundamental structures are word-like objects

called atoms

" Groups of atoms form sentance-like objects called

lists

* Atoms and lists, collectively, are called

symbolic expressions

" Compound data objects and procedures arelists and can be used interchangably

Symbolic Expression Examples

Atoms may be numbers or symbols:

* 3.1415, ATOM, SYMMETRIC-STRUCTEL

Lists consist of a left parenthesis, followed by zeroor more atoms or lists, followed by a right

parenthesis:

* (THIS IS A (LIST)), (3.1415)

Expressions are typically lists whose first elementis the name of a procedure to be evaluated, or

executed:

* (+ (/ 4 2) (- 7 3)), (MAX POINT1 POINT2)

Built in features of LISP include:

* Numeric primitive operations such as

+, -, x, ...

* Floating point and integer arithmetic

capabilities

* Symbolic primitives for list processing such as

CAR, CDR

* Ability to evaluate arbitrary lists

Symbolic and Numeric Manipulations of

Morphology Expressions

Features that a system for manipulating

expressions should possess include:

* Numeric processing of expressions

(i.e. computation of an erosion)

* Symbolic manipulation of an expression (i.e.

simplification of sequence of operations)

In our work the symbolic system surrounds the

numeric processing core.

The numeric manipulation of expressions requires:

# Natural signal representation (abstract data

obj ects)

* Inquiry operations for extracting signalinformation

• Functional specification of useful operators (i.e.

erosion, dilation, ...

A representation of signals for numerical process-

ing should be based on the following observations

of signals:

" Signals are immutable

" Signals are identified and distinguished by their

region of support and sample values.

" Signals are organized into signal classes

* Signals exhibit deferred evaluation

By considering a sine wave to be a function of three

variables ( w, p, and N) we can define the class of

sinusoids by:

xwcp,N[rL] = sin (w -n + o) n =N,

Any particular sinusoid may be formed by bindingparameters with actual values:

27r"_ 7r

Setting w = , - -, and N 10 generates

7 42,7r 7sin( n + 7r-)"n - ,. ,10

The notion of signal classes naturally leads to sub-

classes, generating a hierarchy of signal classes.

As an example, zero-phase sinusoids form a sub-

class of sinusoids:

xw,N[L] =sin (w n) :n = ,..,N

Specification of a signal class requires:

" Name for the class (i.e. sine-wave)

" Parameters for distinguishing specific signal

instances

• Functional specification for computing

samples

" Parent type for property inheritance

" A signal finder for creating specific signals

Annotated terminal gession defining the CONSTANT signal class:

(1) : (defsigtype constant :parameters (length sample-value)

:a-kind-of basic-signal

:finder signal-constant

:init (dimension length)

:fetch ((n) sample-value) )

==> CONSTANT ; returns the class name

(2) : (signal-constant 10 1) ; create a signal instance

=> SIGNAL-i ; returns unique name

(3) : (signal-fetch signal-1 3) ; request sample at n = 3

==> 1 ; value of sample at n 3

(4) (signal-what signal-i) ; inquire about signal-1

==> (signal-constant 10 1) ; returns the definition

(5) : (signal-constant 10 1) ; re-specify the signal

==> SIGNAL-i ; signal name is unique

Symbolic Manipulations

Rule based systems provide a flexible mechanism

for representing morphological knowledge for:

" Expression simplification

* Generation of equivalent forms

Sample manipulation rules

(Open-Idempotence ; Rule name

(:FORM If the input matches this form

(OPEN (OPEN ?IMAGE ?SE1) ?SE2) )

(:TEST and satisfies this condition

(SE1 OPEN WR/T SE2) )

(:RESULT ; Then replace input with result

(OPEN IMAGE SEl) ) )

(Erosion-of-structel-union

(:FORM ; The input form

(ERODE ?IMAGE (UNION ?SE1 ?SE2)) )

(:RESULT ; The equivalent output form

(INTERSECT (ERODE IMAGE SEl) (ERODE IMAGE SE2)) )

Simplification Example

(1) (SIMPLIFY '(CLOSE

(OPEN

(OPEN SIGNAL-i LINOOO)

VECOOO )RHOMBUS ) )

(FOUND RULE - OPEN-IDEMPOTENCE)

System has found a rule and applied it

==> (CLOSE (OPEN SiGNAL-i LINOOO) RHOMBUS)

Evaluate the expression

(2) (EVAL '(CLOSE (OPEN SIGNAL-i LINO00)))

Return the resulting signal object

SIGNAL-3

APPLICATIONS OF MORPHOLOGY

IN INDUSTRY

STEPHEN S. WILSON

APPLIED INTELLIGENT SYSTEMS, INC.

110 PARKLAND PLAZA

ANN ARBOR, MI 48103

90 08 28 025I-

I . 0

MATHEMATICAL MORPHOLOGY

IS A MATHEMATICAL MODEL ADDRESSING THE NEED TOANALYZE PICTURES TO GAIN KNOWLEDGE.

IT IS A SET OF TOOLS. FOR A PARTICULAR PROBLEM,THE METHOD WILL SELDOM TELL YOU EXACTLY WHAT TODO, OR HOW TO DO IT - THE USER MUST GAIN ANINTUITION FOR THE STRENGTHS AND WEAKNESSES OF THEMETHOD, AND DECIDE FOR HIMSELF WHICH TOOLS TO USE.

1. C

THE FIRST OBJECTIVE OF THIS COURSE IS TO FOCUS ONTHE VARIOUS TOOLS FROM AN INTUITIVE POINT OF VIEW.A RIGOROUS MATHEMATICAL INSIGHT IS OPTIONAL IN USINGTHESE TOOLS, BUT CAN COME LATER BY STUDYING THELITERATURE ON THE SUBJECT. A KNOWLEDGE OF SETTHEORY AND BOOLEAN ALGEBRA WOULD BE REQUIRED.

A SECOND OBJECTIVE IS TO UNDERSTAND HOW THE TOOLSCAN BE APPLIED TO VARIOUS CATEGORIES OFAPPLICATIONS - FOR SPECIFIC APPLICATIONS, WHICHTOOLS WORK WELL, AND WHICH DO NOT.

1.0

THERE ARE SOME APPLICATIONS WHERE THE TOOLS OFMATHEMATICAL MORPHOLOGY ARE NOT APPROPRIATE.WE WILL FOCUS ON THOSE APPLICATIONS THAT DO WORK.

MORPHOLOGY, AT ITS BEST IS MIXED WITH OTHERTECHNIQUES. THESE OTHER TECHNIQUES WILL BEDISCUSSED WHEN THEY HAVE RELEVANCE TO THEPRINCIPLES OF MORPHOLOGY.

2

P4C-5 3- 7

2.1

EROSIONS

r E

I = image S structuring element

Erosion: I :> S = , I-C.S; ES

note: subscript means translate

Image I eroded by structuring element S means

wherever S fits in I, mart the center of S on I.

2. 1

DILATIONS

I-,

1- I

Dilation I ® S = U Iss. rS

A A

Wherever the center of S hits I, mark S on I

or wherever S to ,ches I, mark the center of

S on I.

iDi A

DILATION EXAMPLESFICTITIOUS PROGRAM

SYSTEM- INITDOTLOOK

DTLOOK

DOTD+

LOOKDOT

D.LOOKDOTDILOOKDOT

D-LOOKDOTD-0

.. ./ LOOK

D* D* D* D*LOOK -DOT

D+ D+ D+ D+LOOKDOT

D+ D+ D* D*LOOKDOT

D+ D+ D* D*D+ D-O

LOOK-4/ DOT

D+ D* DI DILOOK-

END

I0

1

Ci p j'Xe4 r~j t4 ~&Qt: ~S 1:; .u t "'A

'. Ah t';~~.3

it

EROSION EXAMPLESFICTITIOUS PROGRA~M

______ SYSTEM-INIT_____________BLACK-DOT

___ ___ __- LOOK _ _

__________ E+_ _ _ _ _ _

LOOKBLACK- DOT

_________ E-0 _ _ _ _

__________ LOOK_ _ _ _ _ _

___ BLACK-DOT- ~ E+ E* E+ E*

__________E+ E-O0_____

LOOK _____ _

BOX~-LOOK

__ El ElI ELOOKBOX

E+ E+ E+,,LOOK

E+ E+ E+ E+E+ E+

LOOKEND

LX12-

1~

&1 ~

lir2f~ "~2~ 2

L3 -cL4-

OPENING OR SHAPE INCLUSION EXAMPLES

SYSTEM-INIT

ACQUIRE CAMERA

12 SILHOUETTE

IMAGE STORE

LOOK

E* E* E* E*

LOOK

D* D* D* D*

LOOK -

IMAGE LOAD

E+ E+ E+ E+

,-- LOOK

D+ D+ D+ D+

LOOK

IAGE LOAD

E+ E* E-0

D+ D* D-0 -

LOOK

END

____________________ S F-P PE i NCL UEO F* E h E

OA

-z0

N ib-~-

2.4

OTHER OPERATIONS- Hit or miss (Serra 19e2)

Two structuring elements:

H "Hit" cM = "Miss "

I CS { i:HCI; MCI= J

i.e. the transformed pixel is "I"if H is included in the object foreground

and M is included in the object baclkground.

Thus, erosions only use AND operations,dilations only use OR operations,

hit or miss uses both operations.

There are many important examples.

17

2.4.1

TOPOLOGICAL FILTERS

A "PLUG" will cause a kind of dilation, but itwill dilate preferentially into areas for whichwhite is concave on black. These figures show theeffect of PLUG on swiss cheese: the holes are

filled up while the outer dimensions of the cheesestays the same.

Formula: PLUG(I) = C OR ( AND N)

neigh

SYSTEM-INIT

AQU I RE-CAMERA

S ILHOUETTE

LOOK

PLUG

PLUGI

LOOK -

PLUG

PLUGLOOK __ _ _ _ _ _ _ _ _ _ _

END

18

CONVEX HULL

Put a rubber-band around the object.

CONVEX HULL SIMPLIFIED

The plug operation repeated enough times will puta box around the object.

I

44

SKELETONIZE OR THINNING

A type of erosion except the last dot or thinnestline does not erode away completely.(i.e. maintain the connectivity )

Features such as end points and tee connections

become apparent.

Cannot be done in one 3x3 structuring element.Must use 4 elements in succession: thin N, S, E,and W. Must be repeated depending on thethickness of the object.

F'E

Kb0

Tj~

2.4.4

FEATURE FINDING FUNCTIONS

Blank out image except where there is thespecified feature. Useful after skeletonizingoperations.

Find dot - there is an isolated pixel.

yes-- r 4- o- -

Find line - the middle of a line segment.s-4 n"-'o- k

Find end point - of a line segment.yes-* J no-p JE-T __

Find tee connection.

yes- , 'no-.

Find four connection.

yes-4- no-*--

More complex finding functions can be combinationsof the above.e.g. fipd line OR end ooint.

2.4.5

COVARI ANCE

This is a large field. We will not go into

details in this course. Need a knowledge of

statistics.

Ex amp l es.

mi ss -

Chords of size N. E Ethit

Set covariance of size N -

- hit /

Use various angles and sizes. Tally results.Look at statistics.Good for classifying textures such as in polished

mineral cross-sections, or wood grain.

22

-. 4.6

CONDITIONAL DILA~TION

Two bitpianes are involved:A "mask" or condition plane which will

not be altered.

A~n "object" plane where pixels are to be

dilated.

The object is5 generally smaller than the mask.

The transformation: dilate the object plane

under the conditioni that it dOes not grow outside

tebounds of the mask.

23

3&AAfk'

ej,.

Ulu

PRINTED CIRCUIT BOARD INSPECTION

t -open mouse bite /void

short / - -,,-

under-etched)

Inspection by rule.To look at lead quality, open with a small disk.

To look at spacing between leads, close with asmall disk.

C~C,

2.5.4

DIRECTIONAL FILTERING

Problem: Thresholding after edge detection of a

low contrast noisy picture results in a noisybinary image. Raising the threshold causes a lossof the image along with intended loss of noise.

r Morphological filtering by opening or closingfails because of the noise density.

An effective solution:

Create separate bit planes for the eight differentedge directions.

Threshold them separately with the same threshold.The density of pixels around edges remainsconstant for the corresponding direction plane.The density of random noise drops by a factor

of eight so that morphological filtering is

now more effective.

Filter each direction plane separately.

Combine into one plane if desired by an OR of the

eight direction planes.

27

DIRECTIONAL FILTERING EXAMPLES

to's~- 'a

_ _ _ _ _ _ _ -A -

- - - -- aj

A2Q4

3.1

FUZZY LOGIC

First, Aristotelian logic:

Two values - true or false 1 or 0.

A IB ANDI OR A NOT A0 0 0 0 C) 1C) 1 0 111 0 0 11 1 1

]ruth tables

Fuzzy logic - continuous values 00 False

.2 I doubt it

.5 - Maybe, maybe not

.8 I think so1. - You're darn right

Operation Replacement

A AND B MINIMUM(A,B)A OR B - MAXIMUM(A,B)g- NOTA -A 1 - A

De Morgan's rule still works

Binary: T ANDB = AOR BFuzzy: MIN(1-A,I-B) = i - MAX(A,B)

All other common theorems in boolean logicalso hold with the above replacements.

3o

FUZZY LOGIC APPLIED TO MORPHOLOGY

The grey level intensity is a fuzzy logic state.

Binary morphology operations have a direct

fuzzy counterpart.

Dilate: OR(nbhd) - MAX(nbhd)Erode: AND(nbhd) - MIN(nbhd)Plug: cen OR AND(nbhd) - MAX(cen,MIN(nbhd))

What is a "fuzzy threshold?

3.1

IMPORTANT ISOMORPHISM

fuzzy ops threshold

grey image vw-grey image -- ,binary image

threshold binary opsgrey image sbinary image -binary image

The resulting binary image is the same in

both cases!

Fuzzy logic is usefulwhen the threshold is adaptive or uncertain;when combined with arithmetic operations.

3'

32 -3q

4.. C

BEYOND MORPHOLO9Y

The following operations strictly do not belong ina discussion of morphology. However, someprinciples are related, and they are oftennecessary to use along wi.tr_ morphology in order tosuccessfully develop solutions to some imageprocessing problems.

4.1

IMAGE ALGEBRA

Supportad by the Air Force and DARPA.Under ,evelopment at the University of Florida.The objective is to be able to express all greyleve) image-to-imaoe transformations,

35

4.2

MAJORITY VOTING LOGIC

Similar to 2-D erosions.

/0

/ 4

Object with Structuring element

pixel dropouts will not fit.

This object will not be detected with an opening.

Majority vote:Allow a 95% fit of the structuring element to vote

for a hit.

Noise dropouts can then be tolerated.

The percentage vote is a variable to be adjusted

to give good performance.

A 100% vote is equivalent to an erosion.

Lu

0

LUJ- -- - OcrT

z C -- a. wL

a- a-4 a- a --

O a- 333 3

a- a- a-V

- -L (L CLa (

x % ZW=1I U' UN0C

+i +. + Wu.3z

- -I 000

Lii 3fI. IN

37

+ + z

Lu zC

z Uu(D wU

0 0 0 C4NL

m mNcl N QLO C-i N r-4 CQ1

C

o re) N C4 OC' 0.0. N0 N N

m Ci J N N ~ '

t. IT

LuL

1- -i +J~

J~ 0aL

38

*11.J

46

0IiUa >

cc. C4 N N~ W W w

w ~~ I- I 1wZ~

z Q W> C Z

w -a.- ow

.4 W4wZ

C I Q 0 CL

iL --j a:Zg3f

0 (nUWz .4- I-I-

4v u r

aW ".cc ED w

x x ww

0 C

W W 4 "4 "4 V-41- W' M41 IC

it W- i" -bW. LLCDW

W W4 '4 ' 4 ' ' 43 ZC LL

Ct 4 ' '4 '4 W4 '4ED -0 c4~ - Ct CLL (n "-

'4~ '4 '44 '4 'U4 W-O -n - 1Ww m (:r CL'4~~i '4 '4 ' 4 Z

4-3

>zCJC

z~~~ Mzta '0q it 0- N o- V V LZa

0 - -n - -- - w w'

> N V) N % -a N- LL. X--- - w ZZ

N: 03 MD 0.-CD " CD a. 0 W1-N O0 N '-O (' ui Im

Znq- a r-. P . - x: -WN:~~~~~ z x- ~ N N - (4L-~~~~~C I) N N t) ''WL cflC

-, zj4Z~~~~~~~ w D- C - ~ C ~~

CX ~- ~ CD -' C ~ 4 ~Z b4CD~ - zz o

z u

'-4 - '' -~ (lIfl

• "

IPUY

?4u

14

zz

w > - z CC.fay D-4 EDa a

C- z Cz ELw (a(n (:r az

t~iic x 4

W (0

30 WOa.(

Ow

C aL

0L0

z U) U , x ua

Er W U__ _ X_ _ ____ EW Z x u--J

a0 I- Z 0 :4 <C(:LI 0.4 ). -j '-

0 u) cn F- W CL aa: I- a!nt I cr

0 u ;I. W - W Z w tQa. 0 (nl

<c '- 0: tC-~~ r- 0 E.--4 '-LI W 0 (f)

a. W 0r C3W~w u

LMNEM]LMAGE

CORMEATION ___________________

KERNfELGRADIENT OF ]Y.AG

VECTOR CORRMEATION

I II

2~v c-4 orr

xCr C-1

RELATED CONCEPTS

UniformUniform Convolutions

Convolutions

Binary IGray

SO

0 __

0- 0)

~o

E-4 4.4 p.d \-,--jp.

'-4~ to'4 '4C) r4 0tot

4- 4-) M ii-.

q- - 0 $ qI4

$4 C 4 ~ *4-) )o 0 *r40 0 E-4-

WV ~ i WLS

5.0

PROCESSING TECHNIQUES USING MORPHOLOGYOR OTHER RELATED OPERATIONS

image

noise filter

edge high-passdetection filter( ,histogram

linearv 3-D morphological

average

gauss -flat-top fuzzy shapedopening filters 3-Dclosing opening

magnitude closing

magnitudeand direction

threshol ding

absolute constant constantfraction fraction with

noise removal

2-D morphology

w m mm q ~ ~m m m mu mw mM wm mm !mmm6L

DLAfl P

THRESHOLDSFIXED THRESHOLD./

Set threshol djust above noise

.7.....L.

A~ blurred image gives -

an illumination oL -

dependent width. -*''

Non-linear filtering would help by allowing alower threshold.Linear filtering would cause more blurring.

- _ _

-n-I--

5.3

THRESHOLDCONSTANT FRACTION

Assume a 3:1 ratio of reflectivity of objects tobackground.

Image A

Background afterlow-pass filter. -.

Normalized image -- /\ -

andbackground. -

Thresholded ima.ge

The threshold has the same relative position fordifferent illumination levels.

For other reflectivities, first multiply the

background by a constant.

To prevent noise from being thresholded, replace

background by:MAX (noise threshold, background)

Noise does not obey the laws of reflectivity!

7o.

5.3

THRESHOLDADAPTIVE CONSTANT FRACTION

What if reflectivity differenceis small

is not knownchanges over the image.

Image afterbackgroundnormalI iz--at ion

DilIate

imaae - . . . .

Divide dilatedimage by 2.

Compare withoriginal image

To prevent thresholdi g noise, use:MAX( noise threshold, (dilated image)/2)

... ..... ... ....... 2 1_. .. .. ... .

5.4

BIT PLANE VECTOR CORRELATION

Vector morpholooy. A type of erosion.

In the usual erosion a t,

structurino element is -. -

defined and the AND -f "operation is applied to !-.the image bitplane;

or, very loosely, I'0 S = AND I

In vector morphology, the image is several bitplanes of features, say two features F1 and F2.The structuring element also has multiple states.

F si F F21E E-jS2;

Image Structuring element

I S = (AND FI) AND (AND F2)5) 5Z

An example of character recognition is given in alater section.

73

IMAGE PROCESSING

STATE - OF - THE - ART

TECHNOLOGY

MUST USE PARALLEL PROCESSORS

MIMD - COARSE GRAINEDSIMD - FINE GRAINED

MIMD

HYPERCUBE

COMPLEX MICROPROCESSORSYSTEMS

MIMD

PIPELINE

MEMORYHH

I SJMDHYPERCUBE

agIII- IIIIti iimigtiei -

FINE GRAINED PROCESSORS

SIMD

MESH CONNECTED

FINE GRAINED PROCESSORS

I CSIMD

LINEAR ARRAY

AIS - 5000

1 .4

TYPICAL PROGRAM FLOW

IMAGESOBEL-X ._1MAG.

IMMAGE

FEATURE

FINDING

SOBEL-YDIR.

NENEIGHBORHOOD E 8

PIXEL REGISTERS 8 S

MEMOY 8 SE 8 NEIGHOROO~0DDAAT

C NROL I 8INL CCUTRNFR/ 8 PA XSTG

COMMANDp LOGICSTATUS

SIGAL

eIghoroo Prcsin2tgeBok iga

ENIRNMNTL ESARH NSITTEOFMIHIAP.O BX 818AN AROR MI4807861 (13994120 TLE 44091OWI

U' 0w

o 0

Utu

003

0 0

Za zIt T

mL w

CL~ <w < < C

0,0

C -Kj

0,

SCHEIMATIC DIAGRAM OF ONE PROCESSOR ELEMENT

CcM

CMCMomniSin ounIpi

C2 CY7 3C C0 - Cr

. MaxVideo Image Processors

THE

44MaxVideoFAMILY

DIGIMAX VFIR

Performs AID and D/A conversion on RS-170 (60Hz) Linear pixel processor performs 3 x 3 two dimen-

and CCIR 50Hzi standard video signals in real time. sional convolution or 10 x 1 FIR filter on 512 x 512Eight camera inputs are software selectable. 32 image in one frame time. 100 million, 20-bit preci-banks or input/output Look-Up Tables. Three output sion multiply accumulates per second. Full 20-bitD'A channels, and graphics overlay hardware are precision at end of adder tree.

p,-.%,ided.

FRAMESTORE SNAP

Three complete 8-bit 512 x 512 stores on a singie Real time non-linear Systolic Neighborhood Areaboard. Can be utilized as three independent 8-bit Processor. Performs 180 million 8-bit comparisonsbutters or as one 16- or 24-bit deep framestore. (10 million neighborhoods) per second;, mathemati-Extensive multiplexing tor user flexibility. cal morphology: erosion and dilation algorithm

implementation.

MAX-SP PROTOMAXI II ._

Signal Processor performs full frame single point Wire wrap prototyping module for developingFIR filtering in one frame time. Multi-image merging, MaxVideo compatible designs. PROTOMAX in-

differencing multiplier, minimum/maximum oper- cludes interface circuitry and connectors to bothations, ALU clipper unit, barrel shifter and LUTs. MAXbus and P1 connector of VMEbu,.

THE

MaxVideoFAMILY

MAX-XFS MAX-GRAPH

Transposing framestore %%hich contains two com- Stand-alone VME graphics controller supportingplete frames ot ideo storage. Each frame can be simultaneous displa, or 256 colors. Has uniqueread andor %ritten in row or column order to capability of overlaying graphics with real timeachieve real time 90 degree image transposition. It digital video signals. Implements primitive opera-is useful for realizing separated horizontal and tions for a variety of geometric draw and fill com-vertical pipelines, mands.

INTERPOLATOR MAX-SIGMA

Performs sub-pixel, multirate sampling in real time. Variable aperture iup to 64 by 256) moving a\,erageIt can perform tirst order transformation in one convolution module. Performs hipass, low pass anddimension. Its 8-point aperture and sinc interpola- band pass filters.tion algorithm vield an extremely precise 16-bitresult in conjunction with ADDGEN-1.

ADDGEN-1 FEATUREMAX

Address generator module which works in conjunc- Performs histogram and feature list extraction intion with the INTERPOLATOR module. It creates the real time. Featur, st extraction stores the x, yaddressing necessary to allow INTERPOLATOR to coordinates ot up to 16K spatial grey level specificperform first order transformations to 32-bits of events.spatial resolution. Sub-pixel rnultirate samplingmodule.

MaxVideo Image Processors

THE

JA MaxVideoFAMILY

EUCLID MAX-SCAN

High speed general DSP module. Supported by an Analog and digital acquisition module. Completelyexten,,ve preprogrammed "C" callable library and a programmable acquisition rates from DC to 20complete complement of development tools includ. MHz. Extensive and flexible synchronous optionsing an ANSI standard "C" compiler. Concurrent allow interface to numerous devices.data movement and processing and MAXbuscompatibility lead a long list of standard features.

ROI-STORE VFIR-MK i

A true advancement on dataimaging storage. Rang- Second generation Video Finite Impulse Responseing in capacities trom 512K bytes to 2 megabytes Filter. Implements a b4-point arbitrary coefficientana operating on user defined regions of interest, convolution/correlat on on a 10 MHz stream. 640Hardware supported pan, scroll and zoom features million multiplv-accumulates per second allows torallo,, tor greater programming tlexibility real-time 8 x 8 or 04 x I operations.MAX-MUX MAX-BOX

oil

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suitable for ruggedized use.

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MATHEMATICAL MORPHOLOGY APPLIED TO MULTI-SCALE

IMAGE REPRESENTATION AND SHAPE DESCRIPTION*

by

Petros Maragos

Division of Applied Sciences

Harvard University

Cambridge, MA 02138

*Talk given at the Workshop on Mathematical Morphology, Toni Bevill Center,

Huntsville, Alabama, July 25-26, 1988.

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Intelligent Systems Laboratory

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