Generalizing Swendsen-Wang to sampling arbitrary posterior probabilities

Many vision tasks can be formulated as graph partition problems that minimize energy functions. For such problems, the Gibbs sampler provides a general solution but is very slow, while other methods, such as Ncut and graph cuts are computationally effective but only work for specific energy forms and are not generally applicable. In this paper, we present a new inference algorithm that generalizes the Swendsen-Wang method to arbitrary probabilities defined on graph partitions. We begin by computing graph edge weights, based on local image features. Then, the algorithm iterates two steps. 1) Graph clustering: It forms connected components by cutting the edges probabilistically based on their weights. 2) Graph relabeling: It selects one connected component and flips probabilistically, the coloring of all vertices in the component simultaneously. Thus, it realizes the split, merge, and regrouping of a "chunk" of the graph, in contrast to Gibbs sampler that flips a single vertex. We prove that this algorithm simulates ergodic and reversible Markov chain jumps in the space of graph partitions and is applicable to arbitrary posterior probabilities or energy functions defined on graphs. We demonstrate the algorithm on two typical problems in computer vision--image segmentation and stereo vision. Experimentally, we show that it is 100-400 times faster in CPU time than the classical Gibbs sampler and 20-40 times faster then the DDMCMC segmentation algorithm. For stereo, we compare performance with graph cuts and belief propagation. We also show that our algorithm can automatically infer generative models and obtain satisfactory results (better than the graphic cuts or belief propagation) in the same amount of time.

Joint blind restoration and surface recovery in photometric stereo

We address the problem of simultaneous estimation of scene structure and restoration of images from blurred photometric measurements. In photometric stereo, the structure of an object is determined by using a particular reflectance model (the image irradiance equation) without considering the blurring effect. What we show is that, given arbitrarily blurred observations of a static scene captured with a stationary camera under different illuminant directions, we still can obtain the structure represented by the surface gradients and the albedo and also perform a blind image restoration. The surface gradients and the albedo are modeled as separate Markov random fields, and a suitable regularization scheme is used to estimate the different fields as well as the blur parameter. The results of the experimentations are illustrated with real as well as synthetic images.

Fast unambiguous stereo matching using reliability-based dynamic programming

An efficient unambiguous stereo matching technique is presented in this paper. Our main contribution is to introduce a new reliability measure to dynamic programming approaches in general. For stereo vision application, the reliability of a proposed match on a scanline is defined as the cost difference between the globally best disparity assignment that includes the match and the globally best assignment that does not include the match. A reliability-based dynamic programming algorithm is derived accordingly, which can selectively assign disparities to pixels when the corresponding reliabilities exceed a given threshold. The experimental results show that the new approach can produce dense (> 70 percent of the unoccluded pixels) and reliable (error rate < 0.5 percent) matches efficiently (< 0.2 sec on a 2GHz P4) for the four Middlebury stereo data sets.

Migration of Radio-Opaque Markers Injected Into Tendon Grafts: A Study Using Roentgen Stereophotogrammetric Analysis (RSA)

An increase in anterior laxity following reconstruction of the anterior cruciate ligament (ACL) can result from lengthening of the graft construct either at the sites of fixation and/or between the sites of fixation (i.e., graft substance). Roentgen stereophotogrammetric analysis (RSA), which requires that radio-opaque markers be attached to the graft, has been shown to be a useful technique in determining lengthening in these regions. Previous methods have been used for attaching radio-opaque markers to the graft, but they all have limitations particularly for single-loop grafts. Therefore, the objective of this study was to evaluate injecting markers directly into the substance of a tendon as a viable method for measuring lengthening of single-loop graft constructs by determining the maximum amount of migration after cyclic loading. Tantalum spheres of 0.8 mm diameter were used as tendon markers. Ten single-loop tendon grafts were passed through tibial tunnels drilled in calf tibias and fixed with a tibial fixation device. Two tendon markers were inserted in one tendon bundle of each graft and the grafts were cyclically loaded for 225,000 cycles from 20 N to 170 N. At specified intervals, simultaneous radiographs were obtained of the tendon markers. Marker migration was computed as the change in distance between the two tendon markers parallel to the axis of the tibial tunnel. Marker migration had a root mean square (RMS) value of less than 0.1 mm. Because the RMS value indicates the error introduced into measurements of lengthening and because this error is negligible, the method described for attaching markers to single-loop ACL grafts has the potential to be useful for determining lengthening of single-loop ACL graft constructs in in vivo studies in humans.

Geodesic photogrammetry for localizing sensor positions in dense-array EEG

OBJECTIVE

An important goal for functional brain studies using EEG technology is to estimate the location of brain sources that produce the scalp-recorded signals. The accuracy of source estimates is dependent upon many variables, one of which is the accurate description of the scalp positions of the EEG sensors. The objective of the present research was to develop a photogrammatic method for sensor localization that is fast, accurate, and easy to use.

METHODS

With the novel photogrammetric method, multiple cameras were arranged in a geodesic array, and images of the sensors on the subject's head were acquired allowing for the reconstruction of the 3D sensor positions.

RESULTS

Data from the photogrammetric method were compared with data acquired with the conventional electromagnetic method. The accuracy of the photogrammatic method, quantified as RMS of the measured positions and the actual known positions, was similar (mean error = 1.27 mm) to the electromagnetic method (mean error = 1.02 mm), and both approximated the localization error of the calibration object (mean error = 0.56 mm).

CONCLUSIONS

Accurate determination of 3D sensor positions can be accomplished with minimal demands on the time of the subject and the experimenter using the photogrammetric method.

Total body centre of mass displacement estimated using ground reactions during transitory motor tasks: application to step ascent

A double integration technique is presented that estimates whole body centre of mass (CoM) displacement from signals of a single force platform, compensating for the drift and low frequency noise inherent in the signals. The technique is composed of two different integration techniques, which may also be used separately, and is applied to transitory motor tasks with known initial and final conditions such as step ascent and descent, single step, etc. First, the lowest frequencies within the force platform signals and considered not to be associated with actual movement are filtered out. Second, a regular and a time-reversed double integration are performed and weighted against each other. The technique's accuracy was assessed using computer generated force platform signals that were artificially perturbed. Experimental data were used to compare the estimated CoM displacement to that obtained from a regular double integration and from segmental analysis performed on stereophotogrammetric data. It was shown that the proposed technique's CoM displacement estimates were more repeatable and up to 50% more accurate than those of a regular double integration. Moreover, the CoM displacement estimated using a single force platform and the proposed technique was found to be not statistically different from that obtained with more demanding measurement and processing techniques such as stereophotogrammetry and segmental analysis.

Simultaneous Measurement of Three-Dimensional Joint Kinematics and Ligament Strains With Optical Methods

The objective of this study was to assess the precision and accuracy of a nonproprietary, optical three-dimensional (3D) motion analysis system for the simultaneous measurement of soft tissue strains and joint kinematics. The system consisted of two high-resolution digital cameras and software for calculating the 3D coordinates of contrast markers. System precision was assessed by examining the variation in the coordinates of static markers over time. Three-dimensional strain measurement accuracy was assessed by moving contrast markers fixed distances in the field of view and calculating the error in predicted strain. Three-dimensional accuracy for kinematic measurements was assessed by simulating the measurements that are required for recording knee kinematics. The field of view (190 mm) was chosen to allow simultaneous recording of markers for soft tissue strain measurement and knee joint kinematics. Average system precision was between ±0.004 mm and ±0.035 mm, depending on marker size and camera angle. Absolute error in strain measurement varied from a minimum of ±0.025% to a maximum of ±0.142%, depending on the angle between cameras and the direction of strain with respect to the camera axes. Kinematic accuracy for translations was between ±0.008 mm and ±0.034 mm, while rotational accuracy was ±0.082 deg to ±0.160 deg. These results demonstrate that simultaneous optical measurement of 3D soft tissue strain and 3D joint kinematics can be performed while achieving excellent accuracy for both sets of measurements.

Three-dimensional scene flow

Just as optical flow is the two-dimensional motion of points in an image, scene flow is the three-dimensional motion of points in the world. The fundamental difficulty with optical flow is that only the normal flow can be computed directly from the image measurements, without some form of smoothing or regularization. In this paper, we begin by showing that the same fundamental limitation applies to scene flow; however, many cameras are used to image the scene. There are then two choices when computing scene flow: 1) perform the regularization in the images or 2) perform the regularization on the surface of the object in the scene. In this paper, we choose to compute scene flow using regularization in the images. We describe three algorithms, the first two for computing scene flow from optical flows and the third for constraining scene tructure from the inconsistencies in multiple optical flows.

Correcting interperspective aliasing in autostereoscopic displays

An image presented on an autostereoscopic system should not contain discontinuities between adjacent views. A viewer should experience a continuous scene when moving from one view to the next. If corresponding points in two perspectives do not spatially abut, a viewer will experience jumps in the scene. This is known as interperspective aliasing. Interperspective aliasing is caused by object features far away from the stereoscopic screen being too small, which results in visual artifacts. By modeling a 3D point as a defocused image point, we can adapt Fourier analysis to devise a depth-dependent filter kernel that allows filtering of a stereoscopic 3D image. For synthetic 3D data, we use a simpler approach, which is to smear the data by a distance proportional to its depth.

A quasi-dense approach to surface reconstruction from uncalibrated images

This paper proposes a quasi-dense approach to 3D surface model acquisition from uncalibrated images. First, correspondence information and geometry are computed based on new quasi-dense point features that are resampled subpixel points from a disparity map. The quasi-dense approach gives more robust and accurate geometry estimations than the standard sparse approach. The robustness is measured as the success rate of full automatic geometry estimation with all involved parameters fixed. The accuracy is measured by a fast gauge-free uncertainty estimation algorithm. The quasi-dense approach also works for more largely separated images than the sparse approach, therefore, it requires fewer images for modeling. More importantly, the quasidense approach delivers a high density of reconstructed 3D points on which a surface representation can be reconstructed. This fills the gap of insufficiency of the sparse approach for surface reconstruction, essential for modeling and visualization applications. Second, surface reconstruction methods from the given quasi-dense geometry are also developed. The algorithm optimizes new unified functionals integrating both 3D quasi-dense points and 2D image information, including silhouettes. Combining both 3D data and 2D images is more robust than the existing methods using only 2D information or only 3D data. An efficient bounded regularization method is proposed to implement the surface evolution by level-set methods. Its properties are discussed and proven for some cases. As a whole, a complete automatic and practical system of 3D modeling from raw images captured by hand-held cameras to surface representation is proposed. Extensive experiments demonstrate the superior performance of the quasi-dense approach with respect to the standard sparse approach in robustness, accuracy, and applicability.

Accuracy and precision of radiostereometric analysis in the measurement of three-dimensional micromotion in a fracture model of the distal radius

The purpose of the current study was to verify the feasibility of radiostereometric analysis (RSA) in monitoring three-dimensional fracture micromotion in fractures of the distal radius. The experimental set-up consisted of a simulated model of an extra-articular Colles' fracture, including metallic beads inserted into the bone on either side of the fracture site. The model was rigidly fixed to high precision micrometer stages allowing controlled translation in three axes and rotation about the longitudinal and transverse axes. The whole construct was placed inside a RSA calibration cage with two perpendicular radiographic film cassettes. Accuracy was calculated as the 95% prediction intervals from the regression analyses between the micromotion measured by RSA and actual displacements measured by micrometers. Precision was determined as the standard deviation of five repeated measurements of a 200 microm displacement or a 0.5 degrees rotation along a specific axis. Translations from 25 microm to 5mm were measured with an accuracy of +/-6 microm and translations of 200 microm were measured with a precision of 2-6 microm. Rotations ranging from 1/6 degrees to 2 degrees were measured with an accuracy of +/-0.073 degrees and rotations of 1/2 degrees were measured with a precision of 0.025 degrees -0.096 degrees . The number of markers and their configuration had greater impact on the accuracy and precision of rotation than on those of translation. Aside from the unknown rate of clinical marker loosening, the current results favor the use of at least four markers in each bone fragment in distal radius fractures. These results suggest a strong rationale for the use of RSA as an objective tool for comparing different treatment modalities and novel bone graft substitutes aimed at stabilization of fractures of the distal radius.

Adaptively merging large-scale range data with reflectance properties

In this paper, we tackle the problem of geometric and photometric modeling of large intricately shaped objects. Typical target objects we consider are cultural heritage objects. When constructing models of such objects, we are faced with several important issues that have not been addressed in the past-issues that mainly arise due to the large amount of data that has to be handled. We propose two novel approaches to efficiently handle such large amounts of data: A highly adaptive algorithm for merging range images and an adaptive nearest-neighbor search to be used with the algorithm. We construct an integrated mesh model of the target object in adaptive resolution, taking into account the geometric and/or photometric attributes associated with the range images. We use surface curvature for the geometric attributes and (laser) reflectance values for the photometric attributes. This adaptive merging framework leads to a significant reduction in the necessary amount of computational resources. Furthermore, the resulting adaptive mesh models can be of great use for applications such as texture mapping, as we will briefly demonstrate. Additionally, we propose an additional test for the k-d tree nearest-neighbor search algorithm. Our approach successfully omits back-tracking, which is controlled adaptively depending on the distance to the nearest neighbor. Since the main consumption of computational cost lies in the nearest-neighbor search, the proposed algorithm leads to a significant speed-up of the whole merging process. In this paper, we present the theories and algorithms of our approaches with pseudo code and apply them to several real objects, including large-scale cultural assets.

Quantification of soft tissue artefact in motion analysis by combining 3D fluoroscopy and stereophotogrammetry: a study on two subjects

BACKGROUND

Soft tissue artefact is the most invalidating source of error in human motion analysis using optoelectronic stereophotogrammetry. It is caused by the erroneous assumption that markers attached to the skin surface are rigidly connected to the underlying bones. The quantification of this artefact in three dimensions and the knowledge of how it propagates to relevant joint angles is necessary for the interpretation of gait analysis data.

METHODS

Two subjects, treated by total knee replacement, underwent data acquisition simultaneously with fluoroscopy and stereophotogrammetry during stair climbing, step up/down, sit-to-stand/stand-to-sit, and extension against gravity. The reference 3D kinematics of the femur and tibia was reconstructed from fluoroscopy-based tracking of the relevant prosthesis components. Soft tissue artefact was quantified as the motion of a grid of retro-reflecting makers attached to the thigh and shank with respect to the underlying bones, tracked by optoelectronic stereophotogrammetry. The propagation of soft tissue artefact to knee rotations was also calculated.

FINDINGS

The standard deviation of skin marker trajectory in the corresponding prosthesis-embedded anatomical frame was found up to 31 mm for the thigh and up to 21 mm for the shank. The ab/adduction and internal/external rotation angles were the most affected by soft tissue artefact propagation, with root mean square errors up to 192% and 117% of the corresponding range, respectively.

INTERPRETATIONS

In both the analysed subjects the proximal thigh showed the largest soft tissue artefact. This is subject- and task-specific. However, larger artefact does not necessarily produce larger propagated error on knee rotations. Propagated errors were extremely critical on ab/adduction and internal/external rotation. These large errors can nullify the usefulness of these variables in the clinical interpretation of gait analysis.

Aortic stentgraft movement detection using digital roentgen stereophotogrammetric analysis on plane film radiographs -- initial results of a phantom study

PURPOSE

To evaluate the feasibility of aortic stentgraft micromovement detection using digital roentgen stereophotogrammetric analysis on plane film radiographs.

MATERIAL AND METHODS

An aortic stentgraft used for demonstration purposes was marked with 10 tantalum markers of 0.8 mm in diameter. The stentgraft was placed on a Plexiglas phantom with 5 tantalum markers of 1 mm in diameter simulating a fixed segment needed for mathematical analysis. In a subsequent step, the stentgraft was placed onto an orthopaedic spine model to simulate in vivo conditions.in a next step. Two radiographs taken simultaneously from different angles were used for simulating different stentgraft movement, e. g. translation, angulation, aortic pulsation and migration in the spine model. Movement of the stentgraft markers was analysed using a commercially available digital RSA setup (UmRSA(R) 4.1, RSA Biomedical, Umea, Sweden).

RESULTS

Our study shows the feasibility of measuring aortic stentgraft movement and changes in stentgraft shape in the submillimeter range using digital roentgen stereophotogrammetric analysis. Translation along the 3 cardinal axes, change in stentgraft shape, simulation of aortic pulsation and simulation of in vivo conditions could be described precisely.

CONCLUSION

Aortic stentgraft movement detection using digital roentgen stereophotogrammetric analysis on plane film radiographs is a very promising, precise method.

New automated iris image acquisition method

I propose a new iris image acquisition method based on wide- and narrow-view iris cameras. The narrow-view camera has the functionalities of automatic zooming, focusing, panning, and tilting based on the two-dimensional and three-dimensional eye positions detected from the wide- and narrow-view stereo cameras. By using the wide- and narrow-view iris cameras, I compute the user's gaze position, which is used for aligning the X-Y position of the user's eye, and I use the visible-light illuminator for fake-eye detection.

Face localization and authentication using color and depth images

This paper presents a complete face authentication system integrating both two-dimensional (color or intensity) and three-dimensional (3-D) range data, based on a low-cost 3-D sensor, capable of real-time acquisition of 3-D and color images. Novel algorithms are proposed that exploit depth information to achieve robust face detection and localization under conditions of background clutter, occlusion, face pose alteration, and harsh illumination. The well-known embedded hidden Markov model technique for face authentication is applied to depth maps and color images. To cope with pose and illumination variations, the enrichment of face databases with synthetically generated views is proposed. The performance of the proposed authentication scheme is tested thoroughly on two distinct face databases of significant size. Experimental results demonstrate significant gains resulting from the combined use of depth and color or intensity information.

A novel method for in vivo knee prosthesis wear measurement

Wear remains an important cause of failure in knee replacement. Of the current methods of early performance assessment or prediction, simulators have been un-physiological, single X-ray film analyses remain limited by accuracy and retrieval and survival methods have a prohibitive time scale. An accurate method is needed to allow a timely assessment of polyethylene component wear in vivo, when a new design is introduced, in order to predict likely outcome. We present a new method for measuring wear in vivo that we believe will allow this prediction of long-term wear. X-ray film pairs were taken of implanted prosthetic metal components. When the X-ray system was calibrated, projections of the appropriate Computer Aided Design (CAD) model could be matched to the shapes on the scanned X-ray films to find component positions. Interpenetration of the metal femoral component into the polyethylene component could then be established and represents our estimate of "wear". This method was used to measure in vivo prosthesis wear to an accuracy of 0.11 mm.

Using geometric constraints through parallelepipeds for calibration and 3D modeling

This paper concerns the incorporation of geometric information in camera calibration and 3D modeling. Using geometric constraints enables more stable results and allows us to perform tasks with fewer images. Our approach is motivated and developed within a framework of semi-automatic 3D modeling, where the user defines geometric primitives and constraints between them. It is based on the observation that constraints, such as coplanarity, parallelism, or orthogonality, are often embedded intuitively in parallelepipeds. Moreover, parallelepipeds are easy to delineate by a user and are well adapted to model the main structure of, e.g., architectural scenes. In this paper, first a duality that exists between the shape parameters of a parallelepiped and the intrinsic parameters of a camera is described. Then, a factorization-based algorithm exploiting this relation is developed. Using images of parallelepipeds, it allows us to simultaneously calibrate cameras, recover shapes of parallelepipeds, and estimate the relative pose of all entities. Besides geometric constraints expressed via parallelepipeds, our approach simultaneously takes into account the usual self-calibration constraints on cameras. The proposed algorithm is completed by a study of the singular cases of the calibration method. A complete method for the reconstruction of scene primitives that are not modeled by parallelepipeds is also briefly described. The proposed methods are validated by various experiments with real and simulated data, for single-view as well as multiview cases.

Spacetime stereo: a unifying framework for depth from triangulation

Depth from triangulation has traditionally been investigated in a number of independent threads of research, with methods such as stereo, laser scanning, and coded structured light considered separately. In this paper, we propose a common framework called spacetime stereo that unifies and generalizes many of these previous methods. To show the practical utility of the framework, we develop two new algorithms for depth estimation: depth from unstructured illumination change and depth estimation in dynamic scenes. Based on our analysis, we show that methods derived from the spacetime stereo framework can be used to recover depth in situations in which existing methods perform poorly.

Stability of the Birmingham hip resurfacing arthroplasty at two years

The Birmingham hip resurfacing metal-on-metal arthroplasty was introduced in 1997 and has shown promising short- to mid-term results. We used radiostereophotogrammetric analysis (RSA) to study the stability of 20 resurfacing arthroplasties over a follow-up period of 24 months.

Radiological examinations for RSA were performed immediately after surgery and at two, six, 12 and 24 months after operation. Precision and detection of migration thresholds (non-zero movement) were calculated.

All the results corresponded well to those found in similar experimental arrangements with standard hip prostheses. Migration of the cup and vertical and mediolateral migration of the head were calculated. The values were low at two years compared with those of earlier studies of cemented femoral components in conventional total hip replacements indicating that there was no evidence of excessive early migration or loosening of the components.

Photogrammetry and Conventional Impressions for Recording Implant Positions: A Comparative Laboratory Study

BACKGROUND

The development of digitized techniques for manufacturing implant frameworks has made possible alternative "impression" techniques for recording implant positions.

PURPOSE

The objective of the present study was to test the precision and accuracy of a three-dimensional photogrammetric technique to record implant positions in vitro and to compare casts made with this technique with conventional casts fabricated with two conventional impression techniques.

MATERIALS AND METHODS

Twenty casts were fabricated from 10 polyether (Impregum, ESPE Dental AG, Seefeld, Germany) impressions and 10 plaster (Kühns Abdrucksgips, Ernst Hirnischs GmbH, Goslar, Germany) impressions of one master model. The casts were measured in a coordinate measuring machine (Zeiss Prismo VAST, Oberkochen, Germany) and compared with the master model. Six separate three-dimensional photographs of the master model were taken with a special camera. After the photographs were measured with an analytic plotter, results were analyzed and compared to the coordinates of the original model and casts.

RESULTS

A systematic pattern of distortion in the x-axis was found for the two impression techniques. Expansion of the implant arch at the terminal implants (p < .01) averaged 22 microm and 94 microm on photographs and plaster casts, respectively. Polyether casts contracted an average of 52 microm when compared with the master (p < .01). In absolute figures, photogrammetry and the polyether technique reproduced the x-axis and three-dimensional parameters more accurately than the plaster technique did when cylinder center point distortion was compared (p < .05 to p < .001). However, angular cylinder distortion in absolute figures was greater with the photographic technique than with either of the impression techniques (p < .05-p < .001).

CONCLUSION

Photogrammetry is a valid option for recording implant positions and has a precision comparable to that of conventional impression techniques. At present, however, it is limited to framework fabrication techniques that are based on digital platforms.

Bewertung von Präzision und Genauigkeit der digitalen Oberflächenphotogrammetrie mit dem DSP 400 System / Assessment of Precision and Accuracy of Digital Surface Photogrammetry with the DSP 400 System

The objective of the present study was to evaluate the precision and accuracy of facial anthropometric measurements obtained through digital 3-D surface photogrammetry with the DSP 400 system in comparison to traditional 2-D photogrammetry. Fifty plaster casts of cleft infants were imaged and 21 standard anthropometric measurements were obtained. For precision assessment the measurements were performed twice in a subsample. Accuracy was determined by comparison of direct measurements and indirect 2-D and 3-D image measurements. Precision of digital surface photogrammetry was almost as good as direct anthropometry and clearly better than 2-D photogrammetry. Measurements derived from 3-D images showed better congruence to direct measurements than from 2-D photos. Digital surface photogrammetry with the DSP 400 system is sufficiently precise and accurate for craniofacial anthropometric examinations.