GEOMETRIC PROPERTIES OF THE 3D SPINE CURVE

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GEOMETRIC PROPERTIES OF THE 3D SPINE CURVE

• J.M. Sotoca1, M. Buendía2, J.M. Iñesta3 and F.J.
  Ferri4
• 1 Dpto. Lenguajes y Sistemas Informáticos.
  Universidad Jaume I.
• 2 Dpto. Fisiología. Universidad de Valencia.
• 3 Dpto. Lenguajes y Sistemas Informáticos.
  Universidad de Alicante.
• 4 Dpto. Informática. Universidad de Valencia.

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STRUCTURED LIGHTRange retrieval method
alternative to stereo imaging.

• A light source with a known pattern is utilised
  instead of a camera.
• A set of landmarks are created on the objects
  by the light pattern.
• The 3D positions of those landmarks are
  computed.

Pros

• This method allows the surface reconstruction in
  objects without texture.
• Makes it easier to solve the stereo
  correspondence problem.

Cons

• Only valid in controlled environments.
• Sensitive to light condition changes and kinds of
  surfaces.

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THE INDEXATION PROBLEM

• Its the problem in structured light dual to the
  correspondence problem in stereovision.
• It represents the labelling of the landmarks
  artificially created by the pattern when it is
  projected over the scene.
• Once solved, the range data can be retrieved.
• Different approaches to help the solution colour
  codes, binary patterns, constraints.
• We have introduced a mark in the pattern that
  sets a reference for landmark indexation.

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EXPERIMENTAL SETTING Simplification by means of
a front plane.
IMAGE 1
IMAGE 2
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EXPERIMENTAL SETTINGSArbitrary direction of the
optical axis.
This way z is computed as a function only of
distances between pixels, the distance between
both calibration planes, D and the distance of
the camera d2.
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SURFACES RECONSTRUCTIONApplication over back
humans.

• Elements of the reconstruction

• Back grid image.

• Front grid image.

• Object image with landmarks.

• Object grid image.

• Phases of the reconstruction

• Mask region.

• Skeletonized and the node-seeking algorithms.

• Indexation of images.

• Topography map.

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MORPHOLOGY OF THE SPINEMedical problem.

• Serious deformities in the human spine are
  present in the 0.3 of the population.
• Study of the thoracic and lumbar regions,
  analysing these pathologies that suppose bigger
  deformity
• Scoliosis, kyphosis and lordosis.
• The detection is thought a clinic visualization
  of the cosmetic deformity. Frequent x-ray
  examinations are necessary.
• The habitual prognosis is realised measuring the
  Cobb angle and the projection of the vertebral
  pedicles.

45?
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MORPHOLOGY OF THE SPINEScoliosis.

• Characteristics
• A lateral bend of the spine.
• Rotation of the vertebrae bodies.
• Prominence of the ribs and the disfiguring hump.
• The deterioration of the spine occurs quickly, so
  a prevention of the illness is necessary.
• Nomenclature of Ponsetti and Friedman
• Cervical-thoracic.
• Thoracic.
• Thoraco-lumbar.
• Double major.
• Lumbar.

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MORPHOLOGY OF THE SPINEThe Ponsetti-Friedman
classification.
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STUDY OF THE FRONT AND SAGITTAL PLANESThoracic
scoliosis. The Cobb angle is 45.0? in the
thoracic region.

• Projection of the spine curve for front X-ray
  image over back surface.
• The lateral asymmetry in the front plane is 41.7?
  in the thoracic region and 19.4? in the lumbar
  region.
• The kyphosis angle is 53.9? and the lordosis
  angle is 47.5?.

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STUDY OF THE FRONT AND SAGITTAL PLANESThoracic
scoliosis. The Cobb angle is 45.0? in the
thoracic region.

• Projection of the spine curve obtain with
  landmarks over the back surface.
• The lateral asymmetry in the front plane is 47.7?
  in the thoracic region and 32.1? in the lumbar
  region.
• The kyphosis angle is 50.4? and the lordosis
  angle is 51.9?.

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STUDY OF THE SPINE CURVE IN 3DCurvature and
torsion.

• C(u) pi, pi1 ??3 is a parameterisation of
  the spine curve by mean of a polynomial fitting.
• Px and Pz are the coefficients of the polynomial
  using a threshold in the corresponding
  correlation index, and nx y nz are the degrees of
  the polynomial,
• The curvature ? and the torsion ? can be
  calculated from an arbitrary parametric curve
  through the following expressions

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STUDY OF THE SPINE CURVE IN 3DThe frenet frame.

• For each point of the curve, a natural local
  reference system called Frenet frame can be
  defined by the following expressions
• where t is the tangent vector of the curve,
  b is the binormal vector and n is the normal
  vector.
• If we consider ? and ? as the angle variations of
  the vectors t and b, respectively, can arrive to
  the following relations for the curvature and the
  torsion
• where s is the arc length of the curve.
  Thus, ? and ? are the angular velocities of t and
  b.
• The curvature gives information about the changes
  in the orientation of the curve and torsion
  provides information about its rotation.

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EXPERIMENTS AND RESULTS.

• A sample of 76 patients (42 female and 36 male).
• A group of 12 patients, aged from 11 and 18
  years, had an idiopathic scoliosis process.
• The Ponsetti-Friedman classification 4
  thoracic, 2 thoraco-lumbar, 1 lumbar and 5 double
  major curves.
• The correlation index obtained between the
  lateral asymmetry in the spine curve obtain with
  landmarks and the Cobb angle obtain by means of
  front X-ray image was r 0.89.
• The values for the kyphosis and lordosis angles
  for a group of 30 normal subjects were 44.5?11.8
  and 34.1?10.0 degrees for male and 46.1?11.6 and
  39.1?12.6 degrees for female.

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STUDY OF THE SPINE CURVE IN 3DA normal spine
curve.
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STUDY OF THE SPINE CURVE IN 3D.
Front plane
Sagittal plane
Thoracic scoliosis. The Cobb angle is 45.0? in
the thoracic region. Left A representation of
the curvature and the torsion. Right The Frenet
frame of Front and Sagittal planes.
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STUDY OF THE SPINE CURVE IN 3D.
Left A patient with a double major scoliosis
with thoracic Cobb angle of 30? and lumbar Cobb
angle of 30?. Right A patient with a
thoraco-lumbar scoliosis with thoracic Cobb angle
of 24? and lumbar Cobb angle of 12?.
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CONCLUDING REMARKS.

• A reconstruction of the back human surface has
  been developed using a structured light sheme.
• We compare the spine curve obtain with landmarks
  over the back surface with the projection of the
  spine curve in front X-ray image and have
  obtained a good correlations.
• We get a description of different types of
  deformities in the spine as a function of the
  curvature and torsion. Also, the Frenet frame is
  represented along the spine curve.