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- 1. Three Dimensional Cephalometrics, Morphometrics and other recent advances www.indiandentalacademy.com
- 2. Introduction ►Over the years, diagnosis and treatment planning in orthodontics and dentofacial orthopedics has relied substantially on numerous technological aids. www.indiandentalacademy.com
- 3. ►The gold standard that these aids (imaging, articulators, jaw tracking and functional analyses) attempt to achieve is the accurate replication or portrayal of the “anatomic truth”. ►The anatomic truth is the accurate three-dimensional anatomy, both static and functional, as it exists in nature. www.indiandentalacademy.com
- 4. ►The ultimate goal of the clinicians is to use these technologies, either alone or in various combinations, to delineate this anatomic truth. ►Imaging is one of the most ubiquitous tools that orthodontists use to measure and record the size and form of craniofacial structures. www.indiandentalacademy.com
- 5. ►Imaging has been traditionally used in orthodontics to record the status quo of limited anatomic structures. ►While the use of imaging in orthodontics has been relatively adequate, the fulfillment of ideal has been limited by the available technology & the quality of the database. www.indiandentalacademy.com
- 6. ►These desired goals of craniofacial imaging are closer to being achieved than ever before. ►We will be seeing in detail about the Three dimensional cephalometrics, Morphometrics & other advances in imaging which takes us a step closer to the realization of our goal. www.indiandentalacademy.com
- 7. Three Dimensional Cephalometry www.indiandentalacademy.com
- 8. ►Facial evaluation begins with a systematic, three-dimensional assessment of the frontal & profile views in three planes. ►The deformities can then be described three dimensionally in the frontal and profile views as excessive, normal, or deficient. www.indiandentalacademy.com
- 9. ►Earlier orthodontists paid little attention to the PA view ‘coz the clinical problems encountered were symmetric & appeared to be adequately recorded by the lateral view alone. ►Recently, as orthodontists have become "craniofacial orthopedists" treating more severe, often asymmetric craniofacial anomalies; the limitations of the lateral cephalogram have become obvious. www.indiandentalacademy.com
- 10. ►The Broadbent-Bolton cephalostat produces intrinsically three-dimensional information about cranial form. ►Yet in the clinical setting, this information has been used primarily two dimensions at a time in the separate study of lateral or posteroanterior cephalograms. www.indiandentalacademy.com
- 11. ►From the very first introduction of the cephalostat, Broadbent and Bolton stressed the importance of coordinating the lateral with the PA films to arrive at a distortion-free craniofacial form. ►For this purpose they described the Orientator,an exploitation of the geometry of the cephalostat to simulate stereophotogrammetry. www.indiandentalacademy.com
- 12. ►Orientator, is an acetate overlay placed over both cephalograms (LAT and PA) after they were oriented jointly along their common Frankfort horizontal plane. www.indiandentalacademy.com
- 13. History ►The earliest three dimensional measurements of the skull were made by researchers in anatomy & anthropology, primarily on dried specimens. ►The reference planes of Frankfort, His, and Camper and most of the anatomic landmarks that we currently employ were defined and measured directly prior to 1900. www.indiandentalacademy.com
- 14. ►The most widely known system for measuring the spatial relationships between the teeth and the skull in vivo was that of P.Simon, during 1920’s. ►His system, like that of his predecessor Van Loon; was essentially mechanical. It included a maxillary clutch and a frame. www.indiandentalacademy.com
- 15. ►By means of this apparatus & a wax ‘check bite’, it was possible to locate the dentition within the skull anteroposteriorly, vertically & with respect to the occlusal plane orientation. www.indiandentalacademy.com
- 16. ►Simon’s conceptions of gnathostatic measurement were essentially sound, but the technical procedures were quite demanding. ►Simon's system is important in that it focused sharply than did subsequent xray methods upon the location of structures that interest Orthodontists most— the teeth & alveolar process. www.indiandentalacademy.com
- 17. ►In the exposure of a pair of cephalograms the patient's head is not turned, but instead the cephalostat itself. The LAT and PA films would occupy positions at 90° to each other. ►By keeping the films with respect to the head, one can draw the rays connecting the x-ray source to each landmark of either film as threads in space. www.indiandentalacademy.com
- 18. ►The result is a pair of pyramidal sprays of thread, intersecting at approximately 90° throughout the interior of the space occupied in reality by the patient's head. www.indiandentalacademy.com
- 19. ►The films can be flattened into one plane by unfolding them along the "corner", with each bundle of threads (x-ray paths) flattened to the side of the other film at the appropriate distance. ►The Orientator is the diagram of the flattened threads. When superimposed over the abutted pair of films, the points in each film that correspond to any locus in the other can be visualized. www.indiandentalacademy.com
- 20. ►Broadbent & Bolton used Orientator to correct for distortion inherent in the spread of cephalometric x-ray beam. ►In 3D cephalometry we are instead truly reconstructing the location of landmarks in space. The principle of the Orientator then is identical with the ray intersection method, a photogrammetric tool. www.indiandentalacademy.com
- 21. ►For a radiographic landmark to be locatable in the space of head, it must be connected to the x-ray source in two different projections: the LAT & PA views. ►The best landmark candidates for such points are structures defined by means of the vertical coordinate, which is shared between the two views. www.indiandentalacademy.com
- 22. ►Many landmarks are conventionally defined as the "top" or "bottom" points of structures: menton, condylions, superior and inferior orbital rims, and cusp tips. ►Points uppermost or lowermost in the PA ceph may not represent precisely the same points in space uppermost or lowermost in the lateral ceph. www.indiandentalacademy.com
- 23. ►The typical lateral tracing includes eight landmarks conventionally taken to lie on the midsagittal plane: S,N, ANS, supradentale, upper & lower incisal edge, menton, and pogonion. ►Of these, supradentale is visible in the PA film, as are the averaged incisal edges and menton. www.indiandentalacademy.com
- 24. ►Sella, nasion, ANS, & pogonion have little visibility, if any, in the PA film. ►With two of their coordinates supplied by the lateral film, the third may be taken to correspond to the apparent position of the midsagittal plane at the appropriate depth in the frontal film. www.indiandentalacademy.com
- 25. ►Any three-dimensional reconstruction will proceed more accurately if the bilateral landmarks on the lateral film have not been averaged. ►Instead they should be identified individually by a careful consideration of study models, dental landmarks, and auxiliary cephalometric films. www.indiandentalacademy.com
- 26. ►3D ceph landmarks x, y, & z coordinates found in the LAT and PA cephalogram using which the 3D points are reconstructed. www.indiandentalacademy.com
- 27. Registration of the films ►The theory of the cephalostat treats projections of the head in a pair of views precisely to the FH plane & separated by a 90° rotation about the vertical plane. ►But the real data is more or less divergent from the ideal. www.indiandentalacademy.com
- 28. ►Practically heads cannot be placed precisely in the FH plane, nor can the subject hold a fixed orientation while rotated 90° within the cephalostat. ►In true Bolton system, the images at 90° simultaneously by are generated almost the use of 2 x-ray systems that are themselves at 90°. Modern cephalostats have lost this crucial capability. www.indiandentalacademy.com
- 29. ►In particular, there is usually some element of rotation about the ear rods, away from the FH plane in one or both images. ►Modest amounts of such positioning error may be routinely corrected by simple computations before one proceeds to actual 3D reconstructions. www.indiandentalacademy.com
- 30. ►The films corresponding to LAT and PA projections of the same head are digitized separately. ►The digitized LAT cephalogram is rotated so that the point midway between the two porions lies on a horizontal line with the midpoint of the two orbitales . www.indiandentalacademy.com
- 31. ►The PA film is rotated so that the line between the two porions is precisely horizontal. ►This film is then subjected to a computed shear correcting for failure of the midorbitale point to lie precisely on the horizontal line between the two porions. www.indiandentalacademy.com
- 32. ►Each landmark locatable on both films is sheared by an amount corresponding to its AP separation from porion as scaled by the AP separation of midorbitale from midporion in the LAT. ►This is a satisfactory approximation to correct the procedure, a threedimensional rotation, for all angles of rotation small enough to be encountered in practice. www.indiandentalacademy.com
- 33. The ray intersection method ►After this calibration step, we may imagine that the landmark locations correspond precisely to the nominal geometry of the cephalostat. ►Each lies on one of a pair of film planes in precisely known spatial relation at 90° to each other. www.indiandentalacademy.com
- 34. ►The landmark images are at a known distance from x-ray source whose central rays are at 90° to each of the films & which intersect in space, exactly halfway between the pair of porions. ►As in Orientator, each landmark location on film is now replaced by the path in space that the x ray must have followed to arrive there: a thread connecting that digitized location to the source. www.indiandentalacademy.com
- 35. ►In this way the distortion inherent in each cephalometric projection is corrected by the combination of points from both films. ►This three-dimensional constellation of landmarks may be joined by straight lines and rotated for viewing in all directions. www.indiandentalacademy.com
- 36. Advantages ►The 3D method supports the usual biometrics of landmark locations & takes advantage of a normative data base that is suited for semiautomatic analysis of syndromic data. ►In comparison with CT, it involves low radiation dose, simpler to obtain, has an available normative data base, & is more practical for long-term serial analysis. www.indiandentalacademy.com
- 37. ►When compared with conventional cehalometrics, the 3D evaluation for one new methodology, (Acuscape & Sculptor) was more precise within approximately 1mm of the gold standard. ►The sculptor program was found to be 4 to 5 times better than the 2D approach. www.indiandentalacademy.com
- 38. Disadvantages ►The principal drawback of the method is its inability to represent curving form in three dimensions. ►One fundamental difficulty is associated with the assumption that "corresponding" landmarks in LAT and PA films actually pertain to the same three-dimensional point on the skull. www.indiandentalacademy.com
- 39. ►Some inherent flaws and errors of this scheme include tracing and digitizing errors, failure of the porions to superimpose in the lateral film, and the finite size of the x-ray source. ►It is difficult to compensate for the differences in enlargement (termed "projective displacement'') of structures which lie at different distances from the frontal and lateral film surfaces. www.indiandentalacademy.com
- 40. ►Empirical problems have prevented the routine clinical use of this Broadbent’s "biplanar" 3D method, notwithstanding its obvious conceptual brilliance. ►To overcome the problems Sheldon Baumrind and colleagues at the University of California devised another method, The Three-dimensional x-ray stereometry from paired coplanar images. www.indiandentalacademy.com
- 41. ►The two basic and important problems faced by the biplanar method of Broadbent were: ►1.Difficulty in identifying the same landmarks in both films with confidence. and ►2. Projective displacement. www.indiandentalacademy.com
- 42. ►Since both the LAT & PA are taken at 90o to each other i.e, biplanar the same anatomic structures take up different size and shape, making it difficult to precisely identify the landmark. ►This was overcome by this coplanar method where both the films are taken more or less in the same plane making landmark identifications lot easier. www.indiandentalacademy.com
- 43. ►It is difficult to compensate for the differences in enlargement ("projective displacement'') of structures which lie at different distances from the frontal and lateral film surfaces. www.indiandentalacademy.com
- 44. ►That is to say that all the anatomic structures lying in each "para-film" plane will have the some magnification factor, no matter what their anatomic nature. ►Conversely, if two planes are at different distances from the film surface, their enlargement factors will be different, no matter what the anatomy. www.indiandentalacademy.com
- 45. ►Broadbent system is in essence a spatial and temporal composite of the two views. ►It follows that the enlargement factor for any given anatomic landmark will differ from the lateral projection to the frontal projection unless by coincidence that the structure is at same distance from both the film surfaces. www.indiandentalacademy.com
- 46. ►In order to deal with the problem of differential enlargement, a number of investigators have constructed specialized mechanical devices. ►These include the "orientator" of Broadbent, the "compensator" of Wylie and Elasser, and the "modified compensator" of Vogel. www.indiandentalacademy.com
- 47. ►This new method put forward by Baumrind to overcome these difficulties was based on an engineering tool called Photogrammetry. ►Photogrammetry -- discipline devoted to solving the problems of making 3D measurements from paired 2D images, esp. used for reconstructing terrestrial maps from photos taken from space. www.indiandentalacademy.com
- 48. ►The basic principle is the stereoscopic vision used by eye to recognize the 3D information of the object. ►When we view points at some distance from us, our eyes rotate slightly to align and focus on the points. www.indiandentalacademy.com
- 49. ►Line segments can readily be drawn from each point through the optical center of the lens of each eye. The included angle between the pair of such lines is known as the "parallactic angle'' of the point. www.indiandentalacademy.com
- 50. ►Points at different distances will have different parallactic angles. Differences in parallactic angle are interpreted by the brain as differences in distance. ►The alternative way of measuring the parallax is by using linear rather than angular measurement. The distance between two points on the connecting lines in the same plane will also depict the parallax of the point. www.indiandentalacademy.com
- 51. ►In other words viewing the points along the line with each eye focusing only on one points, the brain will perceive it to be a single point at the actual depth. ►Similarly, looking at a same point in two pictures, with each eye concentrated on one point, the brain will perceive the depth of the structure. www.indiandentalacademy.com
- 52. ►But this procedure puts extensive strain on the eyes and though with dificulty the clinician can assess the 3D info in mind, it is not possible to quantify the information and set up a database. ►To overcome this, Photogrammetry uses STEREOSCOPE for viewing the picture and then by calculating the distance between the points, i.e, parallex the depth information is quantified. www.indiandentalacademy.com
- 53. www.indiandentalacademy.com
- 54. ►Each matched pair of photographs is called a stereopair or a diapositive. ►When this technique is used for quantitative purposes, the distance between each matched (or "conjugate") pair of points is measured with a device known as a "parallax bar“. www.indiandentalacademy.com
- 55. ►The focal spot of x-ray tube is equivalent to the optical center of camera lens. In each case, the radiation travels in straight line between the object & the nodal point. ►Thus, a conventional single x-ray film is the geometric equivalent of a single conventional photograph except that the subject lies ''within" the camera instead of beyond it. www.indiandentalacademy.com
- 56. Making of the stereopairs ►The subject would be positioned in a head holder; and an exposure would be made from "camera station L1.'' ►The central ray would pass through the porion-porion axis, the focal spot to "midsagittal plane" would be maintained at 60 inches, and a length scale would be incorporated upon the film surface. www.indiandentalacademy.com
- 57. ►Immediately after exposure, the film would be removed and a new film would be shifted into the same position by some cassette-changing device. ►The second film would then be exposed from "camera station L2. ►This produces a stereopair, one of which is a standard cephalogram. This procedure produces a coplanar image. www.indiandentalacademy.com
- 58. ►The advantage of the coplanar image over the biplanar is that both x-rays are more or less similar & hence landmark identification is a lot easier & reliable. ►Though the biplanar images have the strongest mathematical correlation, its advantage is offset by the projection error and landmark identification. ►As we will be seeing the coplanar images still retain a strong correlation. www.indiandentalacademy.com
- 59. ►A – biplanar system with rays orthogonal and film in 2 planes. ►B – films placed in single plane. ►C – head is rotated by 90o. Both are not standardized films. ►D – orthogonal rays are made to be acute. www.indiandentalacademy.com
- 60. ►One of the systems dedicated for producing coplanar images for 3D stereometry with 2 cassette holders. www.indiandentalacademy.com
- 61. ►The following parameters must be known if 3D maps are to be made from pairs of two-dimensional images: ►1. The principal point of both the films. ►2. The distance between the two stations ( L1 and L2 called base B). ►3. The perpendicular distance from the film to the source. www.indiandentalacademy.com
- 62. ►1.Principal point -- The location on the film of the point of contact of central ray from x-ray. The principal point of L1 is needed to define the origin of coordinate system. L2 is needed to define X axis. ►2.The perpendicular distance from each exposure station to the film plane is designated "H" (for height) & should, in simple case, be equal for both x-rays. www.indiandentalacademy.com
- 63. ►Knowing these values, by using simple mathematical calculations the three coordinates for the points are measured, and using these coordinates a 3D wire diagram is reconstituted. ►The origin of the coordinates can be controlled, and the reconstituted figure can be standardized, for future comparison and evaluation. www.indiandentalacademy.com
- 64. Advantages ►More precise than the Broadbent and Bolton system. ►Errors from patient movement can be corrected by using reference landmarks, whose definite relation we know. ►The projective displacement is not there. ►Can take use of the available normative database. www.indiandentalacademy.com
- 65. Disadvantages ►Again cannot represent curving forms. ►Needs a dedicated special x-ray apparatus with precise calibration. ►Needs complex patient positioning arrays to avoid errors. ►Without calibration the reliability degrades rapidly. www.indiandentalacademy.com
- 66. Morphometrics www.indiandentalacademy.com
- 67. Introduction ►Analysis of size and shape for diagnosis, evaluation, comparison, and future reference forms an integral part of orthodontic diagnosis. ►The methods currently available to evaluate craniofacial from include Anthropometry, Photogrammetry, Cephalometry, Computed tomography, magnetic resonance imaging, etc. www.indiandentalacademy.com
- 68. ►Invariably cephalometry continues to be the most versatile technique for investigation of the craniofacial skeleton because of its validity and practicability. ►Despite the inherent distortion and differential magnification, in comparison with newer imaging techniques the cephalogram produces a high diagnostic yield at a low physiological cost www.indiandentalacademy.com
- 69. ►There are 2 distinct groups of analytical methods used in cephalometry: ►Landmark based techniques and ►Boundary outline methods. ►Landmark-based techniques are dependent on cephalometric landmarks. ►Boundary outline techniques survey only the perimeter of the structure. www.indiandentalacademy.com
- 70. ► The use of algebraic measurements in traditional ceph analyses is known as conventional ceph analysis (CCA). ► It is a landmark based technique. ► Linear distance measurements between two landmarks. ► Angles, ► Areas & ratios are the parameters used by CCA. www.indiandentalacademy.com
- 71. Limitations of CCA ►Relies on the use of a reference structure for orientation and superimposition: that is assumed to be biologically constant but in reality not so. ►Measurements calculate the magnitude of vectors between landmarks, ignoring their direction. ►www.indiandentalacademy.com measured, not the shape. Only size is
- 72. ►To overcome all these, newer methods of cephalometric analysis were developed in place of CCA. Morphometrics is one such. ►Morphometrics = morph + metrikos (Gr). form + measurement. Morphometrics = Measurement of form. ►In reality it consists of procedures which facilatate mapping of visual information into a mathematical representation. www.indiandentalacademy.com
- 73. ►Morphometrics is measurement of form. What is form? ►Form, fundamentally is the displacement of space by area or volume due to an object that is subject to scale difference. ►Simply stated, Form = Size + Shape + Structure. www.indiandentalacademy.com
- 74. Types of morphometrics ►Morphometrics in representation of form, mapping of visual information into a numerical representation, viable for statistical analysis. The different types are: ►1. ►2. ►3. ►4. Multivariate Morphometrics. Co-ordinate Morphometrics. Boundary Morphometrics. Structure Morphometrics. www.indiandentalacademy.com
- 75. Multivariate Morphometrics ►This type of morphometrics is applied to datasets composed of distances, angles and ratios. ►Multivariate Morphometrics (MM) is defined as the use of quantitative methods to discover the structure of interrelationships of multiple measurements. www.indiandentalacademy.com
- 76. ►MM evolved to meet the need for procedures aimed at measuring the degree of similarity within and between two or more forms using multiple measurements. ►It is based on the concept that simultaneous utilization of numerous variables provides more information than a large number of individual variables being assessed seperately. www.indiandentalacademy.com
- 77. ►Usually MM are based on measurement system composed of distances, angles and ratios, the Conventional Metric Approach (CMA). ►MM (CMA) does not quantify the form boundary or textural considerations. ►Used as an adjunct to Co-ordinate Morphometrics. www.indiandentalacademy.com
- 78. ►This method is extremely useful for gaining insights about : ►1. How variables are structured? ►2. How the groups are related? www.indiandentalacademy.com
- 79. Some applications include : ►1. Establishing the similarity between different forms. ►2. Measuring the variation that is present using set of uncorrelated variables. ►3. Investigating the structure of measurements used to describe form. ►4. Identifying the components of size and shape. www.indiandentalacademy.com
- 80. Four commonly used methods for dealing with form difference between groups are: ►1. ►2. ►3. ►4. Discriminant functions. Mahalanobis D2 statistic. Canonical variate analysis. Cluster analysis. www.indiandentalacademy.com
- 81. Discriminant functions ►This assist in placement of unknown specimens in to known groups. ►This is done by increasing the discrimination between groups based on a set of commonly held measurements. www.indiandentalacademy.com
- 82. ►Discrimination is achieved by finding a transformation in form which maximizes between group differences while minimizing within group variation. ►Group identity and membership within the group must be known in advance otherwise cluster analysis is indicated. www.indiandentalacademy.com
- 83. ►The discriminants were computed to maximize the between group variance relative to the within group variance. ►The discriminant function for the specimen is the sum of all linear distance of how far apart, each multiplied by a weighing co-efficient. ►Each discriminant function score is orthogonal with respect to all others. www.indiandentalacademy.com
- 84. Mahalanobis D statistic 2 ►The distance between groups is measure and squared . ►This squared distance between groups is termed the “generalized distance” or “D2 statistic of Mahalanobis". ►It describes the relatedness or similarity between forms based on multiple uncorrelated measurements. www.indiandentalacademy.com
- 85. Canonical variate analysis ►The form of an subject to be assessed is taken, rotated through an axis so that within group variation is minimized. ►The image is rescaled, transformed and deformed until within group variation is made circular. www.indiandentalacademy.com
- 86. ►The image or the form is rotated again through an axis this time such that between group variations is maximized. ►Both the rotated & rescaled axis is called the “Canonical Axis” for that image. ►These axes are orthogonal to each other. They are in fact the representation for the image or the group. www.indiandentalacademy.com
- 87. Cluster analysis ►This method deals with the identification of group structures. ►That is given a collection of objects are there recognizable subgroups? ►More than one clustering method has to be used to get a reliable result. www.indiandentalacademy.com
- 88. There are two methods to find the difference within groups: ►1. Factor analysis. ►2. Principal component analysis. (PCA). www.indiandentalacademy.com
- 89. ►Both of these deals with differences and interrelationships within the variables themselves. ►These give an idea about the structure of the underlying variables and how they vary with each other. ►Identify which of those uncorrelated variables are in turn the primary determinants of form and reduce the statistical load. www.indiandentalacademy.com
- 90. Procrustes superimposition ►It is a variant of the landmark based morphometric method, and a superimposition method. ►Procrustes a robber in Greek mythology, belived his iron bed to be unique and as a standard of length. ►His victims if small were stretched, those taller were chopped off their legs to fit the size of the bed. www.indiandentalacademy.com
- 91. ►His “one size fits all” concept was utilized in the superimposition method. ►Each form is represented by a series of landmark co-ordinates forming a figure known as configuration. ►Each configuration is scaled first to the same size. www.indiandentalacademy.com
- 92. ►The Procrustes superimposition algorithms translate the configurations to superimpose the centroids and rotate the configurations to minimize the differences. ►This is essentially the position of ‘bestfit’. After the superimposition, the mean configuration called the consensus is computed. www.indiandentalacademy.com
- 93. ►For each land mark the Procrustes residual is calculated as the diff between the location of landmarks in each form, and its position in the consensus. ►These can be plotted to display the shape variance. ►Procrustes superimposition has been used for evaluation of normal and syndromic craniofacial growth. www.indiandentalacademy.com
- 94. Co-ordinate morphometrics ►Based solely on the data points composed of 2D or 3D co-ordinates, usually in the Cartesian system. ►It ignores the boundary of the form. ►Most of these are based on D’Arcy Thompson’s Transformation grids. www.indiandentalacademy.com
- 95. This includes the following methods: ►1. Conventional Metric Approach (CMA) including the Conventional Ceph Analysis. ►2. Biorthogonal Grids (BOG). ►3. Finite Element Method (FEM). ►4. Thin Plate Spline Analysis (TPS). ►5. Euclidean Distance Matrix Analysis www.indiandentalacademy.com (EDMA).
- 96. Conventional Metric Approach ►Based on distances, angles and ratios. ►Homologus points should be taken for plotting. ► CMA and its CCA both are incomplete mapping, not describing the shape or shape changes. www.indiandentalacademy.com
- 97. Biorthogonal grids ►The BOG is developed by Bookstein. ►This also uses the homologus point representation. ►The foundation of the BOG method is comparison between two 2D forms. ►One form is designated as the base form and the other as one which reflects the shape changes from the base form. www.indiandentalacademy.com
- 98. ►The shape changes are viewed as deformations from the basic form. ►The base form is constructed with landmarks of our interest, whose shape change we are going to study. ►The base form is usually a triangle, though any polygon can be used. www.indiandentalacademy.com
- 99. ►The triangle is constructed and a circle is drawn inside the triangle touching the boundary. ►Once this triangle transforms in to another triangle, the circle gets transformed in to an ellipse. Base triangle www.indiandentalacademy.com Deformed triangle
- 100. ►The major and minor axes of the ellipse and the corresponding diameters of the circle are the representations of shape changes. ►They represent the “principal dilatations” or estimates of maximum stretch or shrinkage due to the deformation. www.indiandentalacademy.com
- 101. ►The cross denoting the centre of the ellipse with its major and minor axes represents a tensor for that shape change. ►The ratio of major axis to minor axis is considered as the estimator of shape change. www.indiandentalacademy.com
- 102. ►The BOG is used by Bookstein for studying shape changes in craniofacial anomalies. ►When BOG is used for biological subjects it is called “Tensor Biometrics”. ►The disadvantage is that it measures shape change rather than the shape as such. ►Like CMA it cannot represent curves. www.indiandentalacademy.com
- 103. Finite Elements Method ►This is similar to BOG if not identical. ►It is also based on homologus landmarks and is invariant with respect to the coordinate system. ►Very similar to BOG, but that many triangles (Finite Elements) are constructed. www.indiandentalacademy.com
- 104. ►The average shape change of all the triangles is computed for the shape change for the whole form. ►The principal dilatations in BOG are called as “strain measures” here. ►The triangles are the basic forms used in 2D FEM. www.indiandentalacademy.com
- 105. ►The triangles are replaced by hexahedrons in 3D FEM. ►Each cube is represented by 8 homologus points in the Cartesian system. ►The cubes are non-homogenous unlike triangles and hence represent spatially varying tensor fields. www.indiandentalacademy.com
- 106. FEM on Face www.indiandentalacademy.com FEM on Tooth
- 107. FEM based Ceph analysis ►Discretization of the craniofacial complex in to finite elements based on the normal biometric landmarks. www.indiandentalacademy.com
- 108. FEM depicting size and shape changes using colour coding for easy comprehension www.indiandentalacademy.com
- 109. Thin Plate Spline Analysis ►TPS analyze shape change using theory of surface spline interpolations. ►The TPS function colloquially known as “bending energy” is visualized as an infinetely thin metal sheet draped over a set of landmarks, extending infinitely in all directions. www.indiandentalacademy.com
- 110. ►The configurations of two forms are matched exactly to minimize the bending energy. ►If two forms are identical bending energy is zero. ►The magnitude and location of bending energy can be identified depending upon the size and position of the deformation of the plate. www.indiandentalacademy.com
- 111. ►The thin plate where shape changes, i.e, “bending energy” is depicted by the colour gradient. www.indiandentalacademy.com
- 112. ►In affine transformations the parallel lines in the plate remain parallel. ►The bending energy of the affine transformation is zero and only the tilting of the plate may occur. ►In non-affine transformations the there will be local deformations, these are represented as “partial warps”. www.indiandentalacademy.com
- 113. ►Shape changes can be statistically analyzed using multivariate statistical techniques, based on partial warp scores. ►TPS has been applied to three dimensions for studying changes in cranial base. www.indiandentalacademy.com
- 114. Euclidean distance matrix analysis ►This was developed by Lele at the John Hopkins. ►Utilizes 3D Cartesian co-ordinates of the homologus points to identify local areas of shape change. www.indiandentalacademy.com
- 115. ►Initially a ‘mean form’ from distances of all possible landmarks is computed. ►These distances are the EDM representations which is averaged to yield a mean matrix for the sample. ►Calculation of a distance difference matrix using ratio of similarity between forms on pair wise distances is calculated. www.indiandentalacademy.com
- 116. ►This distance difference matrix is then sorted to identify the areas of maximum and minimum change. ►These EDMA does not distinguish between size and shape individually. ►The results obtained are similar to FEM. www.indiandentalacademy.com
- 117. Boundary morphometrics ►These techniques takes boundary outlines, and not points. ►Very useful in assessing shape where landmarks are scarce. ►Indispensable if boundary outline is the primary area of interest. www.indiandentalacademy.com
- 118. The advantages of boundary outline methods are that: ►Recreation of the boundary precisely is possible. ►It is an information preserving method. ►A combination of boundary outline form can incorporate homologus points also. www.indiandentalacademy.com
- 119. There are six boundary outline methods: ►1. ►2. ►3. ►4. ►5. Median Axis Function. Fourier Descriptors. Eigen Shape Analysis. Fourier Transforms. Wavelets. www.indiandentalacademy.com
- 120. Median Axis Function ►It is also called as symmetric axis or line skeleton. ►MAF is defined as the locus of points which lie in the interior of the form, exactly equidistant from the border of the outline. www.indiandentalacademy.com
- 121. ►It is a method of collapsing of a 2D outline in to a curve or a line. ►Consists of embedding a series of overlapping circles or discs that touch the outline such that they are tangential to the borders of the outline. ►The centers of those circles now define those two points and when we join the centers we get a stick figure. www.indiandentalacademy.com
- 122. Stick figure of a mandible using MAA www.indiandentalacademy.com
- 123. ►The circle usually touches two points in the periphery. ►If it touches three points it encloses a bifurcation. ►The circles contains two variants (determinants) : ►The structure of the median axis (stick figure). ►Radius of the circle i.e, width of MAF at the tangent points. www.indiandentalacademy.com
- 124. ►Circles are used in a 2D structure, where as it can converted to spheres and used in 3D measurements. ►MAF is not unique, it is possible for classes of similar shapes to have an identical medial axis. ►The radius function must be computed regularly to have an individual representation. www.indiandentalacademy.com
- 125. Conventional Fourier Descriptors ►The approach of Fourier analysis can be viewed as a transformation of data from one domain to another. ►In biology it refers to the transformation from spatial domain to the frequency domain. www.indiandentalacademy.com
- 126. ►This is also termed as decomposition of the spatial configuration (Boundary) in to frequency components (amplitude & phase relationships). ►This procedure of decomposition is called “Fourier analysis” or “Harmonic analysis”. ►The inverse process of recreation of an image from data is called “Harmonic synthesis”. www.indiandentalacademy.com
- 127. ►Two types of FD approaches have been widely used, both convert the data to polar co-ordinates prior to analysis. ►One is based on measurements from a center within the form, preferably a centroid. ►The other uses angular functions based on points located on the outline. www.indiandentalacademy.com
- 128. ►How many harmonics are needed to achieve a satisfactory fit of the FD as an expected function to the boundary outline (observed form). ►The residual of fit is calculated and is used for comparison between FD’s. ►Elliptical Fourier Functions have now superseded the conventional FD’s. www.indiandentalacademy.com
- 129. Eigen Shape Analysis ►The use of ESA facilitates the reduction of the morphological shape space to a comparatively few dimensions that contain most of the differences in shape. ►So it is claimed to have reduced the minimum number of factors necessary for recognizing subtle shape differences. www.indiandentalacademy.com
- 130. ►This utilizes Fourier functions using tangent functions. ►So basically uses angular measurements when compared to Conventional FD’s which utilizes the sine and the cos data. ►There is no need for centroid, and is basically a single valued function. www.indiandentalacademy.com
- 131. Elliptical Fourier Functions ►EFF is also a type of pattern recognition. ► The EFF technique was developed originally for military aircraft identification and like conventional Fourier functions is a curve-fitting procedure. www.indiandentalacademy.com
- 132. ►The basic principle involves embedding a set of closely spaced observed measurements on an object’s boundary into a mathematical function. ►EFF is a parametric solution to shape description, deriving a pair of equations as functions of a third variable www.indiandentalacademy.com
- 133. ►The first harmonic represents an ellipse, with higher harmonics detecting increasingly localized shape differences. ►The accuracy of the procedure can be determined by calculating a residual value-the difference between the observed data & the predicted values derived from the EFF. www.indiandentalacademy.com
- 134. ►EFF is very loyal in representing the shape and shape differences. ►It is one of the most commonly used boundary representation method. ►Though currently it is used only for the 2D data, it has been developed for use in 3 d forms also. www.indiandentalacademy.com
- 135. Fourier Transformations ►These are the recent developments of the Conventional Fourier descriptions. ►There are 2 types of Fourier transformations 1. Discrete Fourier transform (DFT). 2. Continuous Fourier transform (CFT). www.indiandentalacademy.com
- 136. ►FT’s are bit complicated in their calculations, but software has developed to compute them automatically. ►They have the ability to reproduce even minor details of shape changes. ►To reduce the computer computation times, newer tech like Fast Fourier Transform (FFT) & Short Time Fourier transform (STFT) are developed. www.indiandentalacademy.com
- 137. Wavelets ►These are similar to the FT’s. ►Unlike the FT’s which are continuous representations over the period -∞ to +∞, wavelets are limited duration. ►Similarly they are of two types ►1. Continuous wavelet transform (CWT). ►2. Discrete wavelet transform (DWT). www.indiandentalacademy.com
- 138. ►Though both FT’s and the wavelets are the currently developed geometric morphometric methods which are highly versatile, their regular use in biologic morphometrics is yet to be realized. ►Both can represent many functions and characteristics of the object, rather than like the primitive methods. www.indiandentalacademy.com
- 139. Structural Morphometrics ►These are techniques that numerically describe the characterizing of the surface or the internal structure of the form. ►Structure is also that, which is inside the boundary outline. www.indiandentalacademy.com
- 140. ►It can be both internal or external structure of the object. ►It can be either surface texture or roughness, or the internal structures like the bony trabaculae, or the chemical structures the crystal lattices. www.indiandentalacademy.com
- 141. There are three approaches: ►1. Fourier Transforms. ►2. Wavelets. ►3. Optical Data analysis/ Coherent Optical Processing. They are also yet to influence the field of biologic morphometrics. www.indiandentalacademy.com
- 142. Recent Advances www.indiandentalacademy.com
- 143. ►Change is the only thing that does not change. ►Yes there are many recent advances in the field of Orthodontics and especially in the area of Craniofacial Imaging. ►Few of them have really a great potential to be developed especially for Craniofacial imaging. www.indiandentalacademy.com
- 144. Digital Imaging ►The interest in digital imaging has resulted due to a number of different reasons. ►In terms of necessity, utilization of digital imaging provides the ability for the computer to manipulate data to allow complex introduced techniques may reduce patient radiation exposure. www.indiandentalacademy.com
- 145. ►The elimination of hard-copy X-ray film may decrease storage needs and enable teleradiology, or the transmittance, of images over the phone and internet. ►The digital process is a collection of information of binary form, resulting in the construction of a computerized image. www.indiandentalacademy.com
- 146. ►In most types of digital radiography, electromagnetic energy (X-radiations) is converted to an electrical charge by an X-ray sensor. ►These sensors include charge-coupled devices (CCDs), amorphous silicon and amorphous selenium chips are arranged in an array when used in large X-ray applications. www.indiandentalacademy.com
- 147. ►Another method of converting the X-ray into an electrical charge for digital use is the storage based phosphor plate. ►These plates are thin, wireless, flexible plates similar to intensifying screens. ►The re-usable phosphor plates store the energy from X-ray beam, and are then “read” by a laser scanner which detects the intensity & location of the stored energy. www.indiandentalacademy.com
- 148. ►Once the X-ray energy has converted to an electrical charge, a computer with a frame-grabber circuit board (digitizer) sample the photosensor value (voltage) and converts (digitizer) them into a picture element array (pixels). ►Since the information is in digital form, it can be integrated together with other digital information such as intraoral & extraoral photographs & tomographs to form composite profile. www.indiandentalacademy.com
- 149. Teleradiology ►Early 1982 marked the initial meeting of the First International Conference and Workshop on Picture Archiving and Communications Systems (PACS) for Medical Applications. ►This electronic transport of the images will continue to meet challenges as new technology surface www.indiandentalacademy.com
- 150. 3D CT ►The CT images can be manipulated to undergo a three-dimensional reconstruction of the image. ►The final image can be fed through a computer aided design system and either viewed on a computer screen or processed into plastic via milling machines or laser stereolithography. www.indiandentalacademy.com
- 151. ►The technique is sophisticated enough to be able to extract an element out of the image, such as the mandible, and view it in isolation from other structures. www.indiandentalacademy.com
- 152. Microcomputed Tomography ►MicroCT is principally the same as CT except that the reconstructed cross sections are confined to a much smaller area. ►The future of microCT lies in being able to sample data over a much smaller volume than full body volume, thereby significantly reducing the radiation exposure to the patient. www.indiandentalacademy.com
- 153. ►This technique can now measure bone connectivity in all three dimensions and even record anisotropy, both of which are not possible even with histology. ►This method has been used clinically to evaluate osteoblastic/osteoclastic alveolar remodeling as well as bone dehiscences and root resorption. www.indiandentalacademy.com
- 154. Tuned-aperture Computer Tomography ►TACT system is able to convert multiple two-dimensional images created from multiple arbitrary projection source positions into a three-dimensional image. ►The future of TACT will lie in its ability to assist in the evaluation of alveolar bone & detection of root resorption. www.indiandentalacademy.com
- 155. MR Spectroscopy ►MRI works by obtaining a resonance signal from the hydrogen nucleus, and therefore is essentially an imaging of water in the tissue. ►MR spectroscopy works in a similar manner, but allows the imaging of any molecule or compound in the tissue. www.indiandentalacademy.com
- 156. ►MR spectroscopy is useful for the study of skeletal muscle physiology. ►This approach has been applied for the study of phosphate metabolism in muscles of children with bruxism. ►They have applications to a better understanding of changes in muscle functions. www.indiandentalacademy.com
- 157. Structured Light ►Structured light scanning enables the topology of the face to be digitized simply, and without ionizing radiation. ►The result is a three-dimensional “shell” of the patient’s face, viewable on a computer monitor. www.indiandentalacademy.com
- 158. ►The eventual goal of this technique is to merge the facial “shell” and underlying Xray data from other sources to complete the 3D structure for diagnosis, treatment planning and assessment. ►3D facial analyses are now a possibility, and 3D superimposition revealing treatment effect & outcome will soon be a reality. www.indiandentalacademy.com
- 159. Cone Beam Computerized Tomography ►It is a type of CT that is more or less similar to the DPT in function. ►This has tremendous potential to be used in orthodontics, and is expected to replace all other imaging modalities in the near future. www.indiandentalacademy.com
- 160. ►In contrast to the CT it uses a low energy fixed anode tube with a cone shaped Xray beam. ►The image sensors used are solid state image sensor or an amorphous silicon plate. www.indiandentalacademy.com
- 161. ►CBCT uses 1 rotation sweep of the patient similar to the DPT. Image data can be collected for a complete maxillofacial volume or limited areas. ►The accuracy is very high coz the projection is orthogonal and the rays are parallel with each other. The object is also very near to the sensor producing a 1 to 1 measurements. www.indiandentalacademy.com
- 162. Picture of a CBCT image www.indiandentalacademy.com
- 163. Discussion ►What is an ideal imaging? The underlying principle of ideal imaging is the determination of anatomic truth in terms of accurate portrayal of spatial orientation, size, form, and relationship of desired structures of features. www.indiandentalacademy.com
- 164. The ideal imaging modality is the one which maximizes the desired information and minimizes the physiological risk and economical cost to the patient. www.indiandentalacademy.com
- 165. www.indiandentalacademy.com c o n c l u s i o n
- 166. ►Despite the inherent distortion & differential magnification, in comparison with newer imaging techniques, the cephalogram produces a high diagnostic yield at a low physiological cost, the ideal with the techniques available now. www.indiandentalacademy.com
- 167. ►The newer techniques has to be simplified for the practicing orthodontist to emerge as an alternative to cephalmetrics. ►For the every day clinician cephalogram will continue to be the imaging tool, where newer methods are useful for research and study of ethnographical data. www.indiandentalacademy.com
- 168. References ►Morphometrics for the life sciences ----- lestrel. ►AJO_DO OCT 1983 – 3D Ceph. OCT 1988 – 3D Ceph. MAY 2004 – morphometrics. SEPT 2004 – 3D imaging. DEC 1981 – Photogrammetry. ►AO 1999 NO 6 – review of imaging. 1994 NO 5 – FEM based Ceph Analysis. ►EJO 2003 25 – size and shape measurements. www.indiandentalacademy.com
- 169. www.indiandentalacademy.com Leader in continuing dental education www.indiandentalacademy.com

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