Mark D. Benedict, PhDUES, Inc.

MBenedict@UES.com

Generating Realistic Damage Models for Composite Materials using the Python Programming

Language

μCT Scan Based ModelingGoal: Micro/Meso scale high fidelity models of as-processed composite materialsGeneration of simulation input from μCT scans requires segmentation Optimal Segmentation in a low contrast environment is challengingContrast enhancement techniques tend to introduce many artifacts

Registered Volumetric ImageStacks of microCT Images Geometric and Materials Property Description for Simulation High Fidelity Models

Integration of Image Segments into a 3D Geometric Description

Independent Mesh Method (IMM) used to model same specimen.

Simulation geometry generated from a priori knowledge of specimen geometry.

Processing or “sanding” was performed on the assumed geometry to improve results by compensating for inability to properly describe the specimen geometry.

Lesson Learned: it would be desirable to generate the simulation geometry from actual sample including processing it has experienced

Image Segmentation Using Available Commercial Packages

Goal: Separate fiber tows from matrix from inclusions, voids, etc.

Overlap in intensity makes thresholding of limited utility

Limited contrast due to similar densities of composite components

Scan artifacts at high gradient regions (voids, inclusions)

Texture is a salient feature of these images

Threshold BasedOver Segmentation

Typical rawCT image

“Ringing”Artifact

Inclusion

Orthogonal scan of same dataset

Inclusion

Custom Image Segmentation

What to do when you dont know what to do?: Read many papers

Literature review, particularly from the CV community offered promise.

Broad range of algorithms - What is the best implementation for exploration?

E. Sharon et al. IEEE Computer Society Conference on Computer Vision and Pattern Recognition, 2001

Z. Lin et al. Visualisation 2000, Pan-Sydney Workshop on Visual Information Processing,December, 2000.

Conferences in Research and Practice in InformationTechnology, Vol. 2. P. Eades and J. Jin, Eds

Why Python?

Batteries Included (Numpy,ndimage,Mayavi,pysparse)Rapid Implementation of pseudocodeInteractive coding.

Method 1: Unseeded Region Growth

Versatile, minimal parameter, segmentation technique.

Morphological: Boundary growth

Limited intensity range can cause problems with assigning pixels to a given region. Anisotropic filters should be considered to convey texture information

Potential scan order/growth order dependance of result.

Extension to multi-spectral data and Volumetric data is straightforward but limited by scaling performance of algorithm.

Unallocated Border Pixels

Identified Regions

z is next pixel to add to a region

Difference Measure

Acceptance Criterion

Unseeded Region Growth Segmentation Results

Excellent discretization of intensity range as seen in histogram

Regions in the interior of matrix are still over segmented

Boundaries are partitioned as Regions of their own due to local mixing of statistics from the two adjacent regions!

Method II: Pulse Coupled Neural Network

Algorithm inspired by experimental observation of image segmentation process with a mammalian visual cortex

One to One correspondence between image pixels and neurons, neurons only connected to nearest neighbors

Activation of a neuron (pixel) makes it more likely that its neighbors will also activate...creating a Pulse of activation

Typically each time dependent group of activations, or pulse, correlates well with a segment in the image

Iterative, Dense Matrix Algebra=Efficient implementations

Popular method, many variants

Easily extended to Volumetric Data

Feeding Input

Linking Input

Activation Value

Activation Function

Threshold Value

M

W

X

Si,j

1

VF

VL

exp(-!F)

Fi,j

exp(-!L)

Feeding

Linkingβ

Ui,j

Threshold

Heaviside(Ui,j)

Surrounding Neurons

Yi,j

VTexp(-!T)

Ti,j

ModulationReceptive Fields Pulse Generator

One Iteration of PCNN algorithm

Pulse Coupled Neural Network Segmentation Results

PCNN provides a reduced histogram that can be Usefully thresholded.

Excellent pre-filter

Region Growth-PCNN results are very similar to the URG results. Faster algorithm however

Noticeable problems with boundaries thickness in RG-PCNN

No ability to separate tows

RG-PCNN Results

PCNN Results

Method III: Segmentation by Weighted Aggregation

Segmentation as Graph Partitioning and Coarsening

Use multi-scale measures of intensity, texture, shape, and boundary integrity

Algebraic Multigrid Solver

Linear Time complexity

Can be extended to Volumetric Data?

Standard AMG “pyramid”

Graph

Segment

State vector

Saliency Function

Termination Criteria

Segmentation by Weighted Aggregation Results

Excellent segmentation of matrix from tows and glue.

Boundary class still present. Further investigation warranted.

Morphologic opening operations might yield sufficiently smooth classification.

Results need to be applied to Volumetric data.

Conclusion:

Use Texture Information in Weighted Aggregation to segment tows from one anotherMove Segmentation routines into Volumetric analysisPython Takeaway:

“Batteries Included’ such as numpy, ndimage, pysparse greatly accelerate implementationCombo Develop/Deploy

References:URG:Visualisation 2000, Pan-Sydney Workshop on Visual Information Processing,December, 2000. Conferences in Research and Practice in InformationTechnology, Vol. 2. P. Eades and J. Jin, Eds

PCNN:Z Wang et. al. ”Review of pulse-coupled neural networks” Image and Vision Computing, Vol 28 pp.5-13 (2009)

Segmentation by Weighted Aggregation:E Sharon, A Brandt, and R Basri,”Segmentation and boundary detection using multiscale intensity measurements” IEEE Computer Society Conference on Computer Vision and Pattern Recognition Vol 1(2001)

IMM:Endel V. Iarve, David H. Mollenhauer, Eric G. Zhou,Timothy Breitzman, and Thomas J. Whitney, ”Independent mesh method-based prediction of local and volume average fields in textile composites” Composites Part A, Vol 40, Issue 12, pp.1880-1890 (2009)

Peridynamics:S. Silling et, al.,”Peridynamic states and constitutive modeling”J Elasticity, Vol 88, No.2, pp.151-184 (2007):

The author would like to thank David Mollenhauer (AFRL/RXBC) and John Maguire (AFRL/RXM) for their support, guidance, and input.

All work performed at AFRL/RXBN, WPAFB, Dayton, Ohio under contract CR&D III TO 86, FA8650-07-D-5800