The effect of interpolation methods in surface definition: an experimental study

A state-of-the-art review of automated extraction of rock mass discontinuity characteristics using three-dimensional surface models

Mathematical formulation of unsmooth surfaces such as the physical earth poses several difficulties. To achieve an accurate formulation, each and every point of the surface must be defined, which is practically impossible. Therefore, in modelling such surfaces there is a need for an adequate number and distribution of reference points as well as an appropriate interpolation method. Working on computerised three-dimensional (3D) models, users can dynamically make various analyses on the surface, one of which is the volume calculation. The accuracy of the volume calculation depends on the appropriateness of the interpolation method used in creating 3D models. The present study, which aims to investigate the accuracy of the calculated volumes of objects with irregular structures, uses an artificial object with irregular form whose volume can be indirectly calculated. Using different interpolation methods on this artificial object through photogrammetrically measured reference points, 3D surface models were formed and volumes were calculated. A comparison between the measured and calculated volume figures revealed that the Inverse Distance Weighting (INDW), Nearest Neighbour (NENE) and Triangulation with Linear (TLIN) interpolation methods yielded more accurate results than the other methods. In order to investigate the volumetric accuracy, the same procedure was applied to a regular geometrically-shaped conical frustum and a pyramidal frustum with different numbers of faces, whose reference points on the surface were reproduced in accordance with mathematical rules. The volume of the pyramidal frustum which was obtained using different interpolation methods was then compared to that of the pyramidal frustum which was mathematically calculated and that of the conical frustum which was taken as the reference surface. The comparison demonstrated that the Data Metrics (DMET), INDW and Minimum Curvature (MCRV) interpolation methods yielded better results in terms of volumetric accuracy. Keywords: Interpolation methods, DTM, landform volume, volumetric accuracy.

The subject of the investigation reported in this paper is the visualization of three-dimensional (3D) surface models in a 3D mapping survey using terrestrial laser scanning (TLS). The Cangkuang Temple nearby Garut City was chosen as the object. The laser technology instruments used were a Topcon GLS-1000 (Geodetic Laser Scanner) and a Topcon IS (Image Station). Twelve points at the same position in each 3D surface model were selected. The coordinate system of the IS was then transformed into the coordinate system of the GLS-1000 using a 3D similarity transformation model. The 3D distances were calculated for each model. Differences in distance were considered as errors in the x, y, and z direction. The standard deviation of the distance differences was ±0.301 m. Some of the distance differences did not fall within the range of tolerances (about 15%). The 3D surface model visualization of the Cangkuang Temple that was created from the GLS-1000 data was more precise than the one created from the IS data. In the future, such 3D surface model visualizations could be used for documentation, preservation and reconstruction of heritage buildings.

3D data model is an indispensable component to any 3D GIS, and forms the basis of 3D spatial analysis and representation. At present, plenty of representative 3D data models are proposed. However, existing models neglect the display result and the consumption of storage space. Based on the analysis of existing 3D GIS data model, a 3D surface model is proposed for fast visualization in this paper, which is composed of node, segment and triangle. The data structure and formal representation of the proposed 3D surface model is developed to organize and store data of 3D model. Finally, an experiment is made to compare this 3D surface model with other 3D data model, and the result demonstrates that the 3D surface model proposed in this paper is superior to the existing data model in terms of data volume, moreover, it can acquire fast visualization speed.

The use of volume data and digital three-dimensional (3D) surface models in biology has increased quickly and steadily. Various methods are available to acquire 3D data, among them episcopic imaging techniques. Based on the episcopic microscopy with on-block staining protocol of Weninger et al. (Anat Embryol 197:341–348, 1998), we describe a simple and versatile setup for episcopic microtomy. It is composed of a consumer DSLR digital camera combined with standard histology equipment. The workflow of block surface staining and imaging, image processing, stack alignment, surface generation (including a custom Amira® macro), and 3D model editing is described in detail. For our sample specimen (Alytes obstetricans; Amphibia: Anura) we obtained images with a pixel size of 5.67 × 5.67 µm2. The generated image stacks allowed distinguishing different tissues and were well-suited for creating a 3D surface model. We analyzed the alignment quality achieved by various selections of specimen and fiducial marker spots. The fiducial spots had a significant positive effect on the alignment quality with the best alignment having a maximum mean alignment error of about 44.7 µm. We further tested the APS-C camera with combinations of macro lens, extension tube or teleconverter. The macro lens and extension tube yielded the smallest pixel size of 2.53 × 2.53 µm2. Considering data quality and resolution, and depending on object sizes and research goals, DSLR captured episcopic microtomy can be an alternative to other techniques, such as traditional histological sectioning or micro-computed tomography.

Hiding a text message, audio data, 2D image or 3D model into some another image or model is called Wa- termarking. This paper presents a new idea to watermark a 3D surface model into another 3D surface model based on wavelets, Multi-Resolution Representation (MRR) and ANFIS: Adaptive Neuro Fuzzy Inference System. ANFIS model is trained by using a hybrid method which will then produce a weight factor as ANFIS output. Depending upon the ANFIS output, system selects different locations in horizontal sub-band of the 3D model coefficient to insert the watermark into the model. The watermark is extracted from the watermarked model by using non-blind method. The system is trained and tested against various 3D models. Results show that the system is robust for similarity transformations, noise attacks, smoothing attacks, and cropping attacks.

The use of 3D models for progressive transmission and broadcasting applications is an interesting challenge due to the nature and complexity of such content. In this paper, a new image format for the representation of 3D progressive model is proposed. The powerful spectral analysis is combined with the state of art Geometry Image(GI) to encode static 3D models into spectral geometry images(SGI) for robust 3D shape representation. Based on the 3D model's surface characteristics, SGI separated the geometrical image into low and high frequency layers to achieve effective Level of Details(LOD) modeling. For SGI, the connectivity data of the model is implicitly encoded in the image, thus removing the need for additional channel bits allocated for its protection during transmission. We demonstrated that by coupling SGI together with an efficient channel allocation scheme, an image based method for 3D representation suitable for adoption in conventional broadcasting standard is proposed. The proposed framework is effective in ensuring the smooth degradation of progressive 3D models across varying channel bandwidths and packet loss conditions.

The bolus is used to cover tumors in the shallow skin of cancer patients for a desired dose distribution in the high-energy radiotherapy. This research develops methods to improve the accuracy of bolus shaping by unfolding the human surface model for refolding. A surface segmentation method is proposed to separate a non-developable surface into a few pieces based on a clustering method to increase flattenability. In the segmentation process, a 3D surface model is embedded into a spectral space using a Laplacian matrix to combine the surface segmentation saliency and geometric characteristics. A smooth common boundary is designed based on clustering results to simplify the shape of each part. The 3D surface model is unfolded into 2D patches by the coordinate transformation and optimized using a mass-spring model. Case studies are conducted to verify the effectiveness of the proposed method in the bolus shaping.

A new surface modeling is proposed to supply interpolation and continuity via expanded Bezier basis and laser scanning. This 3D model is generated via virtual points and Pascal triangle to improve accuracy, sped, and memory size of traditional models.

This paper presents a methodology for generating semi-automated 3D models of urban area from multiple high- resolution satellite images. Adoption of Rational Function Models (RFM's) during recent years as a replacement for satellite's rigorous sensor model by many commercial imagery providers makes 3D information extraction fast and reliable for most of end-users. This paper presents an application of RFM in generating 3D terrain models, i.e. bear-ground models void of any vegetation and man-made objects, as well as 3D surface modeling (surface models with man-made objects). A fast one- dimensional terrain-dependent object-based search technique for identifying correspondences in multiple images followed by a refined 2D search to obtain an optimal correspondence match is introduced. Corresponding objects are then used in conjunction with the RFM to generate 3D model of the area. Example of correspondence matching and a 3D model generated for a selected area of Yokohama, Japan using QuickBird stereo images is presented.

Predictive geometrical model of the upper extremity of human fibula

Proceedings of the 2011 joint ACM workshop on Human gesture and behavior understanding

As assyriologists have to handle tremendous amounts of important documents of ancient history written in cuneiform script, like the epic of Gilgamesh, we are developing an efficent system to support their daily tasks. Previous projects demonstrated the application of holography and early close-range 3D scanners for this task. Based on experiences from our previous projects in archaeology, we are focusing on processing the vast amounts of data of high resolution 3D models from todays close-range 3D scanners like the Breuckmann smartSCAN-3D-HE. The presented method exploits the high-resolution of the 3D models to extract the impressed characters as well as other features like fingerprints. Previous work typically used rendering techniques from computer graphics to visualize the characters, which then had to be processed manually. More recent approaches use methods from differential geometry for detection and extraction of coarse contour lines. These methods are computationally fast, and well-established for industrial application, but cannot cover the variations of human handwriting in form of the – wedge shaped – cuneiform script. To overcome the variations in size of the wedges, we choose a multiscale approach using integrating geometry. A transformation invariant function is achieved by calculating the volumes of multiple concentric spheres intersecting the volume below the 3D model's surface at each point. Due to this multiscale approach, this function is represented by the so-called feature vector. By classifying these feature vectors using auto-correlation, our system – called GigaMesh – can automatically extract characters, requiring only one parameter: the approximated line (wedge) width in mm. Results are shown for cuneiform tablets from the collections of the Assyriologie Heidelberg as well as from the Uruk-Warka Sammlung. Finally an outlook regarding character (en)coding and integration into related projects like the Cuneiform Digital Library Initiative (CDLI) is given.

Three-dimensional distribution of articular cartilage thickness in the elderly cadaveric acetabulum: a new method using three-dimensional digitizer and CT

Ultrasonography has gained increased utility to diagnose pelvic fractures in horses; however, internal pelvic contours can be difficult to appreciate from external palpable landmarks. We developed three-dimensional (3D) simulations of the pelvic ultrasonographic examination to assist with translation of pelvic contours into two-dimensional (2D) images. Contiguous 1mm transverse computed tomography (CT) images were acquired through an equine femur and hemipelvis using a single slice helical scanner. 3D surface models were created using a DICOM reader and imported into a 3D modeling and animation program. The bone models were combined with a purchased 3D horse model and the skin made translucent to visualize pelvic surface contours. 3D models of ultrasound transducers were made from reference photos, and a thin sector shape was created to depict the ultrasound beam. Ultrasonographic examinations were simulated by moving transducers on the skin surface and rectally to produce images of pelvic structures. Camera angles were manipulated to best illustrate the transducer-beam-bone interface. Fractures were created in multiple configurations. Animations were exported as QuickTime movie files for use in presentations coupled with corresponding ultrasound videoclips. 3D models provide a link between ultrasonographic technique and image generation by depicting the interaction of the transducer, ultrasound beam, and structure of interest. The horse model was important to facilitate understanding of the location of pelvic structures relative to the skin surface. While CT acquisition time was brief, manipulation within the 3D software program was time intensive. Results were worthwhile from an instructional standpoint based on user feedback.