Level Sets Framework
Refactoring
Arnaud Gelas, Kishore Mosaliganti,
Nicolas Rannou, Lydie Souhait,
Sean Megason
Boston
02/03/2011
Outline
• Goals
• Principles
• Status
o Traits
o 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
Discrete Level Set
STATUS
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 tests
o 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 value
o Equivalent to the current implementation of
itk::FastMarchingImageFilter<>
• Reached Target Nodes (One, Some, All),
with possible overshoot offset
o 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
o
o
Domain Traits
Iterators
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)
{
(i)
Compute Term Value t_k( n_j, ls_i )
GPU implementation during pixel updates at (i):
• Pixel neighborhood in image and level set is copied to GPU memory
• Terms are evaluated in the GPU function
• Each term will have a CPU and GPU implementation
• A term factory will call the GPU implementation
• 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)
{
(i)
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 ?