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GEOMETRIC PROPERTIES OF THE 3D SPINE CURVE

GEOMETRIC PROPERTIES OF THE 3D SPINE CURVE. J.M. Sotoca 1 , M. Buendía 2 , J.M. Iñesta 3 and F.J. Ferri 4 1 Dpto. Lenguajes y Sistemas Informáticos. Universidad Jaume I. 2 Dpto. Fisiología. Universidad de Valencia. 3 Dpto. Lenguajes y Sistemas Informáticos. Universidad de Alicante.

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GEOMETRIC PROPERTIES OF THE 3D SPINE CURVE

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  1. GEOMETRIC PROPERTIES OF THE 3D SPINE CURVE J.M. Sotoca1, M. Buendía2, J.M. Iñesta3 and F.J. Ferri4 1Dpto. 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.

  2. STRUCTURED LIGHT:Range 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. • This method allows the surface reconstruction in objects without texture. • Makes it easier to solve the stereo correspondence problem. Pros: Cons: • Only valid in controlled environments. • Sensitive to light condition changes and kinds of surfaces.

  3. THE INDEXATION PROBLEM • It’s 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.

  4. BACK PLANE VALID CALIBRATED SPACE FRONT PLANE CAMERA CAMERA PROJECTOR PROJECTOR EXPERIMENTAL SETTING: Simplification by means of a front plane. IMAGE 1: IMAGE 2:

  5. Projector Oc1 d1 Oc2 Camera d2 Oc1p Oc2p R e12 P D z Front plane Rp Pp P1 P2 R2 D Back plane • Relation of deep between distances with origin in the point Oc2p. • D/d2 is connected with the angular aperture of beam of light between the front and the back planes. EXPERIMENTAL SETTINGS:Arbitrary 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.

  6. SURFACES RECONSTRUCTION:Application 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.

  7. MORPHOLOGY OF THE SPINE:Medical 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

  8. MORPHOLOGY OF THE SPINE:Scoliosis. • 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.

  9. Cervical-thoracic Thoracic Thoraco-lumbar Double major right thoracic-left lumbar Lumbar MORPHOLOGY OF THE SPINE:The Ponsetti-Friedman classification.

  10. STUDY OF THE FRONT AND SAGITTAL PLANES:Thoracic 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.

  11. STUDY OF THE FRONT AND SAGITTAL PLANES:Thoracic 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.

  12. STUDY OF THE SPINE CURVE IN 3D:Curvature and torsion. • C(u) : [pi, pi+1] 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:

  13. STUDY OF THE SPINE CURVE IN 3D:The 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.

  14. 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 imagewas 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.

  15. y  ..............  x z Left: A representation of the curvature and the torsion . Right: The Frenet frame of normal spine curve. STUDY OF THE SPINE CURVE IN 3D:A normal spine curve.

  16. 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.

  17. 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.

  18. 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.

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