Realtime surgical simulation based on Constraint particle system Hierarchical spatial hashing

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Real-time surgical simulation based
on Constraint particle system Hierarchical
spatial hashing

• Shaoting Zhang
• IGST/SJTU

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Contents
1. Introduction
2. Mathematical model
3. Collision detection
4. Experiments
5. Conclusions
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Introduction (1/3)

• With the rapid progress of virtual reality
  algorithms, computer assisted surgery system are
  continually evolving.
• The goal of surgery simulation is to provide
  means for realistic training and planning.
• The most important factor of surgery simulation
  is real time.
• Our project is sponsored by NSFC, Shanghai Renji
  Hospital and INTEL.

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Introduction (2/3)
Laparoscopic demo
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Introduction (3/3)

• System architecture

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Mathematical model(1/7)
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Mathematical model(2/7)

• Constraint based particle system set of mass
  points, connected as a tetrahedral volume mesh.
• Apply constraints to several mass points.
• Using these constraints to derive forces.
• Derived forces work to fulfill constraints.

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Mathematical model(3/7)
-v
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Mathematical model(4/7)

• Volume preservation constraint (3D).
• Pick four mass points making up a tetrahedron.
• Apply constraint that their volume should stay
  similar.
• Signed volume gets negative when tetrahedron
  inverted.

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Mathematical model(5/7)

• Elastic potential energy
• Elastic potential energy is the energy due to an
  elastic deformation of an object.
• Ks is a stiffness constraint, determines strength
  (the elastic coefficient in Mass-spring model).
• C is a soft constraint, determines amount of
  deformation (the displacement in MS model).

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Mathematical model(6/7)

• Force
• Resulting forces always work to fulfill the
  constraints.
• Forces work to minimize internal energy.
• Forces work to restore undeformed state.

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Mathematical model(7/7)

• Advantages
• Easy to plug-in new constraints.
• Behavior better tunable through unique parameters
  for distance(1D), surface(2D), volume(3D).
• Volume preservation (3D).
• Performance still high.

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Collision detection(1/5)

• Naïve CD algorithm
• for each triangle t1 in object1
• for each triangle t2 in object2
• intersect(t1, t2)
• Time complexity T(n2)

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Collision detection(2/5)

• Spatial Hashing algorithm

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Collision detection(3/5)

• Vertex v mapped into empty Hash index no
• Vertex v mapped into Hash index occupied by own
  tetrahedron t potential self collision
• If v belongs to t no
• If v does not belongs to t potential self
  collision
• Intersection test between v and t
• Vertex v mapped into Hash index occupied by
  strangers tetrahedron t potential collision
• Intersection test between v and t
• Time complexity T(n)

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Collision detection(4/5)

• Regular cell problems
• Cell-size too small mapping very slow
• Cell-size too big intersection testing very slow
• Extremely hard to find good parameters

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Collision detection(5/5)

• Hierarchical partitioning
• Compute optimal local cell size for each
  tetrahedron
• Tetrahedron occupies maximum of 8 cells

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Experiments (1/3)

• Platform

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Experiments (2/3)

• Demo

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Experiments (3/3)

• Setup
• Two objects
• 49848 tetrahedrons
• Djb2 hash function (invented by Bernstein)

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Conclusions (1/2)

• A virtual laparoscopic system
• Immersive environment
• Employ the constraint particle system
• Fast (1000HZ)
• More stable than Mass-spring
• Advance the hierarchical spatial hashing
• Real time (more than 80HZ)
• Parameters unrelated

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Conclusions (2/2)
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Thank You !
VR Group, IGST