Level Sets Framework Refactoring

Arnaud Gelas, Kishore Mosaliganti, Nicolas Rannou, Lydie Souhait,

Sean MegasonBoston

02/03/2011

Outline

• Goals• Principles• Status

o Traitso Fast Marching

Image / Mesh Stopping Criterion Constrained Topology Shortest Path Computation Isotropic / Anisotropic

o Level Sets / GPU • Plan• Requirements

Goal: Generic Level Set Framework

• Multi-level set support• simultaneous evolution of level sets

• Multi-channel support• Vector or tensor data segmentation

• Level set representation• Mesh-based (unstructured), image, or parametric

• Terms used in the PDE• Add/delete terms in the update equation

• Topological constraints

• Stopping criterion• RMS, Iterations, target points 

STATUSDiscrete Level Set

Traits

• TInputDomain

• TNode

• TOutputDomain

• TSuperclass

Traits - Base Class

template< class TInputDomain,class TNode,class TOutputDomain,class TSuperclass >

class LevelSetTraits{public:

typedef [...]class NodePair :

public std::pair< NodeType, OutputPixelType >  [...]   

};

Traits - Image Specialization

template<unsigned int VDimension,class TInputPixel,typename TOutputPixel >

class ImageLevelSetTraits :public LevelSetTraits<      Image< TInputPixel, VDimension >,      Index< VDimension >,      Image< TOutputPixel, VDimension >,      ImageToImageFilter<         Image< TInputPixel, VDimension >,        Image< TOutputPixel, VDimension > >

    >

Traits - Mesh Specialization

template< unsigned int VDimension,typename TInputPixel,class TInputMeshTraits,typename TOutputPixel,class TOutputMeshTraits >

class MeshLevelSetTraits : public LevelSetTraits<      Mesh< TInputPixel, VDimension, TInputMeshTraits >,

typename TInputMeshTraits::PointIdentifier,      Mesh< TOutputPixel, VDimension, TOutputMeshTraits >,      MeshToMeshFilter<          Mesh< TInputPixel, VDimension, TInputMeshTraits >,        Mesh< TOutputPixel, VDimension, TOutputMeshTraits > >

Fast Marching

• Code available at the following address:      https://github.com/arnaudgelas/itkFastMarching

• Numbers:o 36 testso Tested

Fedora 13, 14 (64 bits) Ubuntu 10.10 (64 bits) Mac OS-X 10.5, 10.6

o Coverage: 80.49%

Stopping Criterion - Base Class

class StoppingCriterionBase : public Object{public:

virtual bool IsStatisfied() const = 0;virtual const std::string GetDescription() const = 0;

};

Stopping Criterion - Examples

• Threshold on the current valueo Equivalent to the current implementation of

itk::FastMarchingImageFilter<>

• Reached Target Nodes (One, Some, All), with possible overshoot offseto Equivalent to the current implementation of

itk::FastMarchingUpWindGradientImageFilter<>

Constrained Topology

[Tustisson'10 - Insight Journal 778] Escher's Ants as Metaphor: Topological Marching for the Well-Composed, Genus Zero Crowd

Minimal Path Extraction

[Mueller'08 - Insight Journal 213] Fast Marching Minimal Path Extraction in ITK

Isotropic / Anisotropic

Isotropic

• Can be solved using current implementation

Anisotropic

• Several possible schemes

• which one the best?

• make it easy to implement any of these methods

Requirements

    Possible performance improvement         UpdateNeighbors() calls 2 * ImageDimension

UpdateValue()     Thread Pool ?

Fast Marching - Process ?

• Integration Process?

o Should we struggle for its integration (backward compatibility) ?

o Should we struggle a second time when integrating new level sets framework?

Fast Marching - Process ?

• update software guide?

o When ?

o How ?

o Any constraint?

FUTURE WORK

Plan• Git repository• Discrete Representations

o Domain Traitso Iteratorso Dense

Term container Propagation Advection Curvature Chan & Vese energy

Multithread Reinitialization Stopping Criterion

Plan• Discrete Representations

• Sparse – Constrained Topology – Multithread

• Real time algorithm [Shi]

• Parametric Representations • Splines• RBF

Discrete Level Sets - simplified view(a) while( ! m_StoppingCriterion->IsSatisfied() )(b)     {(c)     for each level set ls_i in the level set container(d)         {(e)         for each nodes n_j in the domain of ls_i(f)              {(g)             for each term t_k in the term container(h)                {(i)                 Compute Term Value t_k( n_j, ls_i )(j)                 Compute Term Contribution for time step computation(k)                }(l)              Evaluate the updated level set function ( delta( ls_i( n_j) ) )(m)            }(n)         }(o)      Compute time step from CFL Condition (p)      for each level set ls_i in the level set container (q)        {(r)         Update the level set function ls_i(s)        Reinitialize to signed distance function (if requested by user)(t)         }(u)     }

GPU Involvement - 1

(a) while( !m_StoppingCriterion->IsSatisfied() )(b)     {(c)     for each level set ls_i in the level set container(d)         {(e)         for each nodes in the domain of ls_i(f)              {(g)             for each term t_k in the term container(h)                {•              Compute Term Value t_k( n_j, ls_i )

 GPU implementation during pixel updates at (i): (i) Pixel neighborhood in image and level set is copied to GPU memory (ii) Terms are evaluated in the GPU function (iii)Each term will have a CPU and GPU implementation (iv)A term factory will call the GPU implementation (v) Advantages:

• Minimal changes in the current proposed design • Drawbacks:

• very bad according to performance

GPU Involvement -2

(a) while ( !m_StoppingCriterion->IsSatisfied() )(b)     {(c)     for each level set ls_i in the level set container(d)         {(e)         for each nodes in the domain of ls_i(f)              {(g)             for each term t_k in the term container(h)                {•                Compute Term Value t_k( n_j, ls_i )

• Entire while loop iteration (a) in GPU • Everything is copied inside the GPU memory• Advantages:

• Fastest solution in terms of performance 

• Downside:• memory limitation of the GPU (<2 Gb) • Code duplication: CPU and GPU • Note: Copy b/w memory 4Gb/s

GPU Involvement -3

In the last scenario, the code nesting is different:   (a) while( !m_StoppingCriterion->IsSatisfied() )(b)     {(c)     for each level set ls_i in the level set container(d)         {(e)         for each term in the term container(f)              {(g)             for each nodes in the domain of ls_i(h)                  {(i)                   Evaluate the updated level set function                      [ ... ]

In this one the GPU Implementation will occur for the most nested for loop (g) • Keep copying the level set and image in each iteration in the GPU • Second most optimal implementation for GPU • No code duplication

Questions and Comments ?