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Volumetric information about the patient’s anatomy is quite valuable for medical diagnosis. Computed tomography (CT) is the
common imaging modality for 3D visualization of bone tissue but rising costs in health care system demand for new approaches.
A promising one is to use a 3D model being deformable under the constraint of statistical plausibility. The model is adapted
to the patient’s anatomy by extracting the specific bone features from several conventional radiographs (2D–3D registration).
These have to be acquired under different angles thus providing the features’ 3D position by means of which the model is deformed.
The resulting bone representation may then be used for medical diagnosis instead of using CT data. Present work validates
accuracy of the resulting bone shape and thus of the diagnosis relying thereon. Results are starting point for further implementations
and modifications in order to reduce remaining errors.

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... The PDM used in the second co-institution (BrainLAB AG), which we named as BrainLAB-PDM, was constructed from a training database consisted of 23 CT scans, as described in Gollmer (2006), where one dataset was taken as the master shape, and all other datasets were aligned with the master shape. The differences between MEM-PDM and BrainLAB-PDM are: (a) the BrainLAB-PDM contains much larger anatomical structures than the MEM-PDM, (b) part of the intramedullary canal is also modeled in BrainLAB-PDM but not in MEM-PDM, and (c) the surface representations of BrainLAB-PDM are much nosier than those of MEM-PDM. ...

... A plastic bone together with its CT scan was used for the first and the second studies, which were performed in the second coinstitution (Gollmer, 2006). The surface model segmented from the CT scan of the plastic bone was used as the ground truth to evaluate the overall reconstruction performance. ...

Constructing a 3D bone surface model from a limited number of calibrated 2D X-ray images (e.g. 2) and a 3D point distribution model is a challenging task, especially, when we would like to construct a patient-specific surface model of a bone with pathology. One of the key steps for such a 2D/3D reconstruction is to establish correspondences between the 2D images and the 3D model. This paper presents a 2D/3D correspondence building method based on a non-rigid 2D point matching process, which iteratively uses a symmetric injective nearest-neighbor mapping operator and 2D thin-plate splines based deformations to find a fraction of best matched 2D point pairs between features extracted from the X-ray images and those extracted from the 3D model. The estimated point pairs are then used to set up a set of 3D point pairs such that we turn a 2D/3D reconstruction problem to a 3D/3D one, whose solutions are well studied. Incorporating this 2D/3D correspondence building method, a 2D/3D reconstruction scheme combining a statistical instantiation with a regularized shape deformation has been developed. Comprehensive experiments on clinical datasets and on images of cadaveric femurs with both non-pathologic and pathologic cases are designed and conducted to evaluate the performance of the 2D/3D correspondence building method as well as that of the 2D/3D reconstruction scheme. Quantitative and qualitative evaluation results are given, which demonstrate the validity of the present method and scheme.

Reconstruction of patient-specific 3D bone surface from 2D calibrated fluoroscopic images and a point distribution model is
discussed. We present a 2D/3D reconstruction scheme combining statistical extrapolation and regularized shape deformation
with an iterative image-to-model correspondence establishing algorithm, and show its application to reconstruct the surface
of proximal femur. The image-to-model correspondence is established using a non-rigid 2D point matching process, which iteratively
uses a symmetric injective nearest-neighbor mapping operator and 2D thin-plate splines based deformation to find a fraction
of best matched 2D point pairs between features detected from the fluoroscopic images and those extracted from the 3D model.
The obtained 2D point pairs are then used to set up a set of 3D point pairs such that we turn a 2D/3D reconstruction problem
to a 3D/3D one. We designed and conducted experiments on 11 cadaveric femurs to validate the present reconstruction scheme.
An average mean reconstruction error of 1.2 mm was found when two fluoroscopic images were used for each bone. It decreased
to 1.0 mm when three fluoroscopic images were used.
Keywordspoint distribution model-surface reconstruction-2D/3D correspondence-extrapolation-deformation-thin-plate splines

This paper describes a computational approach to edge detection. The success of the approach depends on the definition of a comprehensive set of goals for the computation of edge points. These goals must be precise enough to delimit the desired behavior of the detector while making minimal assumptions about the form of the solution. We define detection and localization criteria for a class of edges, and present mathematical forms for these criteria as functionals on the operator impulse response. A third criterion is then added to ensure that the detector has only one response to a single edge. We use the criteria in numerical optimization to derive detectors for several common image features, including step edges. On specializing the analysis to step edges, we find that there is a natural uncertainty principle between detection and localization performance, which are the two main goals. With this principle we derive a single operator shape which is optimal at any scale. The optimal detector has a simple approximate implementation in which edges are marked at maxima in gradient magnitude of a Gaussian-smoothed image. We extend this simple detector using operators of several widths to cope with different signal-to-noise ratios in the image. We present a general method, called feature synthesis, for the fine-to-coarse integration of information from operators at different scales. Finally we show that step edge detector performance improves considerably as the operator point spread function is extended along the edge.

Häufig liegt einer computergestützten Operationsplanung lediglich ein Satz von wenigen 2D-Röntgenbildern zugrunde. Dennoch
ist es ein Anliegen, auf Basis solcher Daten Rückschlüsse auf die dreidimensionale Anatomie des Patienten zu ziehen. In dieser
Arbeit wird ein Verfahren vorgestellt, das mithilfe eines statistischen 3D-Formmodells (SFM) des Beckens die geometrisch sowie
toplogisch komplexe 3D-Form aus wenigen Röntgenbildern rekonstruiert. Dies geschieht durch eine Optimierung, welche den Abstand
der Silhouette des Modells in den Projektionsebenen zur Silhouette des Objekts in den Röntgenbildern minimiert. Das Verfahren
wird an 23 synthetisch erzeugten Datensätzen validiert.

Constructing anatomical shape from extremely sparse information is a challenging task. A priori information is often required to handle this otherwise ill-posed problem. In the present paper, we try to solve the problem
in an accurate and robust way. At the heart of our approach lies the combination of a three-stage anatomical shape reconstruction
technique and a dense surface point distribution model (DS-PDM). The DS-PDM is constructed from an already-aligned sparse
training shape set using Loop subdivision. Its application facilitates the setup of point correspondences for all three stages
of surface reconstruction due to its dense description. The proposed approach is especially useful for accurate and stable
surface reconstruction from sparse information when only a small number of a priori training shapes are available. It adapts gradually to use more information derived from the a priori model when larger number of training data are available. The proposed approach has been successfully validated in a preliminary
study on anatomical shape reconstruction of two femoral heads using only dozens of sparse points, yielding promising results.

We present a new algorithm, called marching cubes, that creates triangle models of constant density surfaces from 3D medical data. Using a divide-and-conquer approach to generate inter-slice connectivity, we create a case table that defines triangle topology. The algorithm processes the 3D medical data in scan-line order and calculates triangle vertices using linear interpolation. We find the gradient of the original data, normalize it, and use it as a basis for shading the models. The detail in images produced from the generated surface models is the result of maintaining the inter-slice connectivity, surface data, and gradient information present in the original 3D data. Results from computed tomography (CT), magnetic resonance (MR), and single-photon emission computed tomography (SPECT) illustrate the quality and functionality of marching cubes. We also discuss improvements that decrease processing time and add solid modeling capabilities.

We describe a method for automatically building statistical shape models from a training set of example boundaries/surfaces. These models show considerable promise as a basis for segmenting and interpreting images. One of the drawbacks of the approach is, however, the need to establish a set of dense correspondences between all members of a set of training shapes. Often this is achieved by locating a set of "landmarks" manually on each training image, which is time consuming and subjective in two dimensions and almost impossible in three dimensions. We describe how shape models can be built automatically by posing the correspondence problem as one of finding the parameterization for each shape in the training set. We select the set of parameterizations that build the "best" model. We define "best" as that which minimizes the description length of the training set, arguing that this leads to models with good compactness, specificity and generalization ability. We show how a set of shape parameterizations can be represented and manipulated in order to build a minimum description length model. Results are given for several different training sets of two-dimensional boundaries, showing that the proposed method constructs better models than other approaches including manual landmarking-the current gold standard. We also show that the method can be extended straightforwardly to three dimensions.

Reconstruction of patient-specific 3D bone surface from 2D calibrated fluoroscopic images and a point distribution model is discussed. We present a 2D/3D reconstruction scheme combining statistical extrapolation and regularized shape deformation with an iterative image-to-model correspondence establishing algorithm, and show its application to reconstruct the surface of proximal femur. The image-to-model correspondence is established using a non-rigid 2D point matching process, which iteratively uses a symmetric injective nearest-neighbor mapping operator and 2D thin-plate splines based deformation to find a fraction of best matched 2D point pairs between features detected from the fluoroscopic images and those extracted from the 3D model. The obtained 2D point pairs are then used to set up a set of 3D point pairs such that we turn a 2D/3D reconstruction problem to a 3D/3D one. We designed and conducted experiments on 11 cadaveric femurs to validate the present reconstruction scheme. An average mean reconstruction error of 1.2 mm was found when two fluoroscopic images were used for each bone. It decreased to 1.0 mm when three fluoroscopic images were used.

The authors describe a general-purpose, representation-independent method for the accurate and computationally efficient registration of 3-D shapes including free-form curves and surfaces. The method handles the full six degrees of freedom and is based on the iterative closest point (ICP) algorithm, which requires only a procedure to find the closest point on a geometric entity to a given point. The ICP algorithm always converges monotonically to the nearest local minimum of a mean-square distance metric, and the rate of convergence is rapid during the first few iterations. Therefore, given an adequate set of initial rotations and translations for a particular class of objects with a certain level of `shape complexity', one can globally minimize the mean-square distance metric over all six degrees of freedom by testing each initial registration. One important application of this method is to register sensed data from unfixtured rigid objects with an ideal geometric model, prior to shape inspection. Experimental results show the capabilities of the registration algorithm on point sets, curves, and surfaces

The decomposition of deformations by principal warps is demonstrated. The method is extended to deal with curving edges between landmarks. This formulation is related to other applications of splines current in computer vision. How they might aid in the extraction of features for analysis, comparison, and diagnosis of biological and medical images is indicated.

Model-based vision is firmly established as a robust approach to recognizing and locating known rigid objects in the presence of noise, clutter, and occlusion. It is more problematic to apply model-based methods to images of objects whose appearance can vary, though a number of approaches based on the use of flexible templates have been proposed. The problem with existing methods is that they sacrifice model specificity in order to accommodate variability, thereby compromising robustness during image interpretation. We argue that a model should only be able to deform in ways characteristic of the class of objects it represents. We describe a method for building models by learning patterns of variability from a training set of correctly annotated images. These models can be used for image search in an iterative refinement algorithm analogous to that employed by Active Contour Models (Snakes). The key difference is that our Active Shape Models can only deform to fit the data in ways consistent with the training set. We show several practical examples where we have built such models and used them to locate partially occluded objects in noisy, cluttered images.

This paper presents a new algorithm for reconstruction of 3D shapes using a few x-ray views and a statistical model. In many
applications of surgery such as orthopedics, it is desirable to define a surgical planning on 3-D images and then to execute
the plan using standard registration techniques and image-guided surgery systems. But the cost, time and x-ray dose associated
with standard pre-operative Computed Tomography makes it difficult to use this methodology for rather standard interventions.
Instead, we propose to use a few x-ray images generated from a C-Arm and to build the 3-D shape of the patient bones or organs
intra-operatively, by deforming a statistical 3-D model to the contours segmented on the x-ray views. In this paper, we concentrate
on the application of our method to bone reconstruction. The algorithm starts from segmented contours of the bone on the x-ray
images and an initial estimate of the pose of the 3-D model in the common coordinate system of the set of x-ray projections.
The statistical model is made of a few principal modes that are sufficient to represent the normal anatomy. Those modes are
built by using a generalization of the Cootes and Taylor method to 3-D surface models, previously published in MICCAI’98 by
the authors. Fitting the model to the contours is achieved by using a generalization of the Iterative Closest Point Algorithm
to nonrigid 3D/2D registration. For pathological shapes, the statistical model is not valid and subsequent local refinement
is necessary. First results are presented for a 3-D statistical model of the distal part of the femur.

This paper describes a general purpose, representation independent
method for the accurate and computationally efficient registration of
3-D shapes including free-form curves and surfaces. The method handles
the full six-degrees of freedom and is based on the iterative closest
point (ICP) algorithm, which requires only a procedure to find the
closest point on a geometric entity to a given point. The ICP algorithm
always converges monotonically to the nearest local minimum of a
mean-square distance metric, and experience shows that the rate of
convergence is rapid during the first few iterations. Therefore, given
an adequate set of initial rotations and translations for a particular
class of objects with a certain level of 'shape complexity', one can
globally minimize the mean-square distance metric over all six degrees
of freedom by testing each initial registration. For examples, a given
'model' shape and a sensed 'data' shape that represents a major portion
of the model shape can be registered in minutes by testing one initial
translation and a relatively small set of rotations to allow for the
given level of model complexity. One important application of this
method is to register sensed data from unfixtured rigid objects with an
ideal geometric model prior to shape inspection. The described method is
also useful for deciding fundamental issues such as the congruence
(shape equivalence) of different geometric representations as well as
for estimating the motion between point sets where the correspondences
are not known. Experimental results show the capabilities of the
registration algorithm on point sets, curves, and surfaces.

We propose a new 3D/2D registration method for vertebrae of the scoliotic spine, using two conventional radiographic views (postero-anterior and lateral), and a priori global knowledge of the geometric structure of each vertebra. This geometric knowledge is efficiently captured by a statistical deformable template integrating a set of admissible deformations, expressed by the first modes of variation in Karhunen-Loeve expansion, of the pathological deformations observed on a representative scoliotic vertebra population. The proposed registration method consists of fitting the projections of this deformable template with the preliminary segmented contours of the corresponding vertebra on the two radiographic views. The 3D/2D registration problem is stated as the minimization of a cost function for each vertebra and solved with a gradient descent technique. Registration of the spine is then done vertebra by vertebra. The proposed method efficiently provides accurate 3D reconstruction of each scoliotic vertebra and, consequently, it also provides accurate knowledge of the 3D structure of the whole scoliotic spine. This registration method has been successfully tested on several biplanar radiographic images and validated on 57 scoliotic vertebrae. The validation results reported in this paper demonstrate that the proposed statistical scheme performs better than other conventional 3D reconstruction methods.

The decomposition of deformations by principal warps is
demonstrated. The method is extended to deal with curving edges between
landmarks. This formulation is related to other applications of splines
current in computer vision. How they might aid in the extraction of
features for analysis, comparison, and diagnosis of biological and
medical images in indicated

We present a new set of algorithms for line-art rendering of smooth surfaces. We introduce an efficient, deterministic algorithm for finding silhouettes based on geometric duality, and an algorithm for segmenting the silhouette curves into smooth parts with constant visibility. These methods can be used to find all silhouettes in real time in software. We present an automatic method for generating hatch marks in order to convey surface shape. We demonstrate these algorithms with a drawing style inspired by A Topological Picturebook by G. Francis.

Bookstein: Principal Warps: Thin-Plate Splines and the Decomposition of Deformations

Ebrahimi: MESH: Measuring Error between Surfaces using the Hausdorff Distance

- N Aspert
- D Santa-Cruz
- N. Aspert