Old Dominion University Old Dominion University

Automatic Identification of Ambiguous Automatic Identification of Ambiguous Prostate Capsule Boundary Lines Using Prostate Capsule Boundary Lines Using

Shape Information and Least Squares Shape Information and Least Squares

Curve Fitting Technique Curve Fitting Technique

Rania Hussein, Ph.D.

Rania Hussein, Ph.D.

Department of Computer Engineering Department of Computer Engineering

DigiPen Institute of Technology DigiPen Institute of Technology

Seattle, WA Seattle, WA

Frederic (Rick) D. McKenzie, Ph.D.

Frederic (Rick) D. McKenzie, Ph.D.

Department of Electrical and Computer Engineering Department of Electrical and Computer Engineering

Old Dominion University Old Dominion University

Norfolk, VA Norfolk, VA

fmckenzi@ece.odu.edu fmckenzi@ece.odu.edu

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Old Dominion University Old Dominion University

• Located near Virginia Beach

– 3 hours south of Washington, DC – Over 25,000 students

• Engineering College has over 100 Faculty

• Electrical & Computer Engineering Dept.

– 26 faculty members

– 240 undergraduate students

– 140 graduate students: 50 PhD, 90 Masters

– 2003 R&D Expenditure National Ranking of ECE at ODU according to NSF: 29

– 2004 R&D Expenditure National Ranking of ECE at ODU according to NSF: 28

• Enterprise Center, Old Dominion University

• 12 Faculty, ~55 research & admin staff

• Multidisciplinary: activities include faculty and students from all six academic colleges

• ~$7.5M in funded research in FY 2005

• Modeling & Simulation Graduate Programs

Virginia Modeling Analysis and Simulation Center

Virginia Modeling Analysis and Simulation Center

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Outline Outline

• Motivation

• Problem definition

• Background

• Approach

• Results

• Conclusion

Motivation Motivation

• Assessment of different surgical

approaches to prostatectomy using objective parameters (such as extra- capsular tissue coverage)

• Reconstruct the prostate capsule and its extra-capsular tissue from excised

specimen histology

• Capsule contour is needed and is currently drawn manually by the pathologist

• Subjective and therefore may affect the

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Problem definition Problem definition

• This research focuses on developing an algorithm that automatically identifies

this capsule contour

• Validation is performed by comparing with the hand-drawn contour of the

pathologist

Problem Definition Problem Definition

• Slices are serially cut from apex to base at precise and parallel 5mm intervals

• Sections of four microns in thickness are mounted on large glass slides

stained with Eosin and Hematoxilin

The capsule is manually marked by a pathologist as shown by the dashed line in the figure

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Background Background

• The prostate capsule is a fibromuscular band of transversely oriented collagenous fibers, and it lies between the

parenchymal contour and the periprostatic tissues

Epithelial cells

Parenchymal contour

Prostatic tissues that can be Prostatic tissues that can be

automatically classified automatically classified

• Diamond et al [19] used whole-mount

radical prostatectomy histology captured at 40x magnification (58k x 42k image size)

• Subimage sizes of 100x100 for processing

• The authors were able to correctly classify

79.3% of tissue in subregions

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Detectable Constraints Detectable Constraints

• The prostate capsule has a mean thickness of 0.5 to 2 mm [Sattar et al.]

• However, it is unrecognizable in areas

– Naturally occurring intrusion of muscle into the prostate gland at the anterior apex.

– Fusion of extraprostatic connective tissue with the prostate gland at its base.

Parenchymal Contour

Outer Contour

Capsule Contour

Limacon shape equation Limacon shape equation

• Limacon equation is r = b + a cos θ

(a) (b) (c)

Limacon curves (a) when a< b, (b) when a<b<2a, and (c) when 2a<=b.

• To take rotation into consideration, the equation

becomes r = b + a cos (θ+Φ)

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Least squares algorithm Least squares algorithm

Assuming that we have a number n of discrete data (x₁,y₁), (x₂,y₂), …(x_n,y_n) and f(x) is a function for fitting a curve.

Therefore, f(x) has the deviation (error) d from each data point, i.e. d₁ = y₁-f(x₁), d₂ = y₂-f(x₂), …, d_n = y_n-f(x_n)

Using Limacon Equation

• Select range of values for the center of the curve (cx,cy)

• Select range of values for the curve parameters (a, b)

• Select range of values for the curve rotation angle (theta)

a) Arrows point to the detected parts of the prostate capsule, (b) Arrow points to the curve representing the prostate shape located as close as possible to the capsule parts.

a b

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Merging arcs (least squares) Merging arcs (least squares)

• Once the curve is

positioned, this shape curve is combined

with the true capsule

segments

Curve Constraint Violation Curve Constraint Violation

• The generated curve can violate the

constraints

– Prostate capsule is typically located between the

parenchymal contour and the prostate

perimeter

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• Flood fill algorithm used to relocate the curve sections that violate constraints

– New points are

generated between the 2 contours

– Least square algorithm executed again for

better results

Curve Constraint Adjustment

Curve Constraint Adjustment

Experiment Results Experiment Results

• 13 specimens were used

• Tested on Pentium 4 machines with dual

processors of 3.4GHz and 1.00 GB of RAM

• Parts where capsule is

expected to exist (as figure shows) were manually

outlined.

• Tested using 3 shape

equations: Circle, Limacon, and ellipse

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Least squares testing example Least squares testing example

a) Capsule parts b) LS Generated curve c) Arcs merging

d) New points generated by flood-fill algorithm

e) Curve generated after the

2^nd run of LS f) Final curve after merging arcs from the 2^nd run

Performance evaluation Performance evaluation

• Used both the root mean square error RMSE and the percentage of error

Where

n is the number of points in the curve,

d_i is the min distance from point i in the curve to the reference curve.

Where

m is the number of points in the reference curve,

d_i is the min distance from point i in the reference curve to the curve

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Performance evaluation Performance evaluation

• Thresholds considered in our study are equal to 1%, 1.5%, and 2% of the number of pixels of the image diagonal.

Figure illustrates the size that each threshold contributes to the actual size of a prostate slice.

The squares that appear on the top left

represent the number of pixels that are equal to 1%, 1.5%, 2% of the image diagonal

respectively.

The %matching between our generated curve and the reference curve is calculated where,

%matching = 1- percentage error

Results

Results

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Results

Results

How to improve the results How to improve the results

• Use more complex shape equations with greater degree of

freedom

• A standard shape of a

prostate slice can be

defined by

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Conclusion Conclusion

• The algorithm provides better results as better shape equations are used.

• The least squares algorithm gave better results on average than a GHT algorithm.

• GHT achieved zero error within our threshold on one of the specimens, which shows that more complex

equations with greater degree of freedom is likely to give better results in the GHT.

• The combination of the two algorithms within the overall process allows a tradeoff between faster processing time and smaller errors in using more complicated and flexible prostate shapes.

Thank You!