Gray-level Interpolation Research Articles

A novel method to compensate systematic errors due to undermatched shape functions in digital image correlation

Undermatched shape functions have always been the primary source of systematic errors for non-uniform deformation measurement in digital image correlation, especially for large curvature displacement. All the other errors arising from grey-level interpolation, subset size, and speckle pattern are overwhelmed by the systematic errors due to undermatched shape functions. The effect of the first-order shape functions on polynomials is analyzed, and based on this analysis, a novel and easy to implement displacement post-processing algorithm is proposed to compensate the systematic errors. The direct digital image correlation displacement result is processed by multiple filters with the same window size as the subset, and the resulting data is employed to recover the actual displacement field. Theoretically, the proposed method is capable of recovering the original continuous displacement function of any order with no bias. The numerical results of elementary function and simulated images show that the proposed algorithm is effective in correcting the displacement systematic bias and improving the subpixel accuracy of digital image correlation. Finally, the algorithm is applied to the displacement measurement of shear band.

A solution method for image distortion correction model based on bilinear interpolation

In the process of the image generation, because the imaging system itself has differences in terms of nonlinear or cameraman perspective, the generated image will face the geometric distortion. Image distortion in general is also a kind of image degradation, which needs the geometric transform to correct each pixel position of the distorted images, so as to regain the original spatial relationships between pixels and the original grey value relation, and which is also one of important steps of image processing. From the point of view of the digital image processing, the distortion correction is actually a process of image restoration for a degraded image. In image processing, in terms of the image quality improvement and correction technology, namely the image restoration, with the wide expansion of digital image distortion correction processing applied, the processing technology of the image restoration has also become a research hotspot. In view of the image distortion issue, this paper puts forward the image distortion correction algorithm based on two-step and one-dimensional linear gray level interpolation to reduce the computation complexity of the bilinear interpolation method, and divide the distorted image into multiple quadrilaterals, and the area of the quadrilateral is associated with the distortion degree of the image in the given region, and express the region distortion of each quadrilateral with the bilinear model, thus determining parameters of bilinear model according to the position of the quadrilateral vertex in the target image and the distorted image. Experiments show that such algorithm in this paper can meet the requirements of distortion correction of most lenses, which can accurately extract the distorted edge of the image, thus making the corrected image closer to the ideal image.

3D visualisation of pore structures in cement-based materials by LSCM

The visualisation and representation of three-dimensional (3D) pore morphologies in cement-based materials are of significant interest for understanding the relationship between pore structures and durability. In this study, laser scanning confocal microscopy (LSCM) was used to observe a series of two-dimensional (2D) cross-sectional images. Thresholding was used as the image segmentation technique to group the image pixels by checking the pixel intensities against a set of thresholds. 3D models of the pore structures and the matrix were reconstructed by grey-level interpolation, which transformed the 2D cross-sectional images into 3D models. The experimental results show that the 3D complex morphologic characters of pore structures and the matrix can be accurately visualised with the image segmentation technique and grey-level interpolation.

Optimized optical setup for DIC in rock mechanics

In order to investigate the micromechanical mechan isms of argillaceous rocks under combined mechanical load and varying moisture, and observe very low strain rates of about 10 -10 s -1 , i.e. about 10 -4 per week, a specific optical setup for Digital Image Correlation (DIC) has been developed at the Sol ids Mechanics Laboratory, Ecole Polytechnique. This paper mainly presents two procedures to optimize the experimental setup and enhance the full-field strain measurement accuracy. The first one allows us to minimize the systematic DIC errors by choosing an optimal optical setup, including appropriate lens aperture and light source with sma ll wavelength, in combination with a specific grey level interpolation method (bilinear, bicubic, biquintic) in DIC algorithms. The second procedure aims at reducing the errors in duced by overall out-of-plane motions of the sample. This procedure makes use of a specifically designed optical microscope, which tracks the few tens of micrometer s out-of-plane motions of the sample all along the several months lasting test, t o compensate the magnification fluctuations which disturb the macroscopic measurements. The current optimized optical setup gives a better than 10 -5 accuracy at macro scale (3 mm gage length) and 10 -4 accuracy at microscale (about 100 µm gage length).

Assessment of Digital Image Correlation Measurement Errors: Methodology and Results

Optical full-field measurement methods such as Digital Image Correlation (DIC) are increasingly used in the field of experimental mechanics, but they still suffer from a lack of information about their metrological performances. To assess the performance of DIC techniques and give some practical rules for users, a collaborative work has been carried out by the Workgroup “Metrology” of the French CNRS research network 2519 “MCIMS (Mesures de Champs et Identification en Mécanique des Solides / Full-field measurement and identification in solid mechanics, http://www.ifma.fr/lami/gdr2519 )”. A methodology is proposed to assess the metrological performances of the image processing algorithms that constitute their main component, the knowledge of which being required for a global assessment of the whole measurement system. The study is based on displacement error assessment from synthetic speckle images. Series of synthetic reference and deformed images with random patterns have been generated, assuming a sinusoidal displacement field with various frequencies and amplitudes. Displacements are evaluated by several DIC packages based on various formulations and used in the French community. Evaluated displacements are compared with the exact imposed values and errors are statistically analyzed. Results show general trends rather independent of the implementations but strongly correlated with the assumptions of the underlying algorithms. Various error regimes are identified, for which the dependence of the uncertainty with the parameters of the algorithms, such as subset size, gray level interpolation or shape functions, is discussed.

Three‐dimensional image registration of MR proximal femur images for the analysis of trabecular bone parameters

This study investigated the feasibility of automatic image registration of MR high-spatial resolution proximal femur trabecular bone images as well as the effects of gray-level interpolation and volume of interest (VOI) misalignment on MR-derived trabecular bone structure parameters. For six subjects in a short-term study, a baseline scan and a follow-up scan of the proximal femur were acquired on the same day. For ten subjects in a long-term study, a follow-up scan of the proximal femur was acquired 1 year after the baseline. An automatic image registration technique, based on mutual information, utilized a baseline and a follow-up scan to compute transform parameters that aligned the two images. In the short-term study, these parameters were subsequently used to transform the follow-up image with three different gray-level interpolators. Nearest-neighbor interpolation and B-spline approximation did not significantly alter bone parameters, while linear interpolation significantly modified bone parameters (p<0.01). Improvement in image alignment due to the automatic registration for the long-term and short-term study was determined by inspecting difference images and 3D renderings. This work demonstrates the first application of automatic registration, without prior segmentation, of high-spatial resolution trabecular bone MR images of the proximal femur. Additionally, inherent heterogeneity in trabecular bone structure and imprecise positioning of the VOI along the slice (anterior-posterior) direction resulted in significant changes in bone parameters (p<0.01). Results suggest that automatic mutual information registration using B-spline approximation or nearest neighbor gray-level interpolation to transform the final image ensures VOI alignment between baseline and follow-up images and does not compromise the integrity of MR-derived trabecular bone parameters used in this study.

OS11-1-6 Displacement Measurement in the Whole View Field by Image Correlation : Consideration of Gray Level Interpolation and Correction

OS11-1-6 Displacement Measurement in the Whole View Field by Image Correlation : Consideration of Gray Level Interpolation and Correction

Polygon interpolation for serial cross sections

In this paper, a new technique for contour interpolation between slices is presented. We assumed that contour interpolation is equivalent to the interpolation of a polygon that approximates the object shape. The location of each polygon vertex is characterized by a set of parameters. Polygon interpolation can be performed on these parameters. These interpolated parameters are then used to reconstruct the vertices of the new polygon. Finally, the contour is approximated from this polygon using a cubic spline interpolation. This new technique takes into account the shape, the translation, the size, and the orientation of the object's contours. A comparison with regular shape-based interpolation is made on several object contours. The preliminary results show that this new method yields a better contour and is computationally more efficient than shape-based interpolation. This technique can be applied to gray-level images too. The interpolation result of an MR image does not show artifact of intermediate substance commonly seen in a typical linear gray-level interpolation.

Simultaneous observation of phase-stepped photoelastic fringes using a pixelated microretarder array

An instantaneous phase stepping and subsequent phase analysis method, using a charge-coupled device (CCD) camera with a pixelated form-birefringent microretarder array, is proposed for 2-D birefringence distribution measurement. A birefringent sample placed behind a polarizer and a quarter-wave plate is analyzed by the proposed method. Light emerging from the sample is recorded using a CCD camera that has a pixelated microretarder array on the CCD plane. This microretarder array has four different principal directions. That is, an image obtained by the CCD camera contains four data corresponding to four different optical axes of the retarder. The four images separated from the image recorded by the CCD camera are reconstructed using gray-level interpolation. Then, the distributions of the Stokes parameters that represent the state of polarization are calculated from the four images. The birefringence parameters, that is, the angle of the principal axis and the phase retardation, are then obtained from these Stokes parameters. This method is applicable to real-time inspection of optical elements as well as the study of the mechanics of time-dependent materials, because multiple exposures are unnecessary for sufficient data acquisition in the completion of data analysis.

Instantaneous phase-stepping interferometry using polarization imaging with a micro-retarder array

An instantaneous phase-stepping and subsequent phase analysis method, using a CCD camera with a form-birefringent micro-retarder array, is proposed for interferometry. An optical setup of a polarization interferometry using a Twyman-Green interferometer with two polarizers is constructed to analyze the distribution of out-of-plane displacement. Light emerging from the interferometer is recorded using a CCD camera that has micro-retarder array on the CCD plane. This micro-retarder array has four different principal directions. That is, an image obtained by the CCD camera contains four types of data corresponding to four different optical axes of the retarder. The four images separated from the image recorded by the CCD camera are reconstructed using gray-level interpolation. Then, the distributions of the Stokes parameters that represent the state of polarization are calculated from the four images. The phase distribution of the interference fringe pattern produced by the Twyman-Green interferometer is then obtained from these Stokes parameters. This method is applicable to time-dependent phenomena because multiple exposures are unnecessary for sufficient data acquisition in the completion of phase analysis.

DIRECTIONAL COHERENCE INTERPOLATION FOR THREE-DIMENSIONAL GRAY-LEVEL IMAGES

A novel three-dimensional gray-level interpolation method called the Directional Coherence Interpolation (DCI) is presented in the paper. The principal advantage of the proposed approach is that it leads to significantly higher visual quality in 3D rendering when compared with traditional image interpolation methods. The basis of DCI is a form of directional image-space coherence. DCI interpolates the missing image data along the maximum coherence directions (MCD), which are estimated from the local image intensity yet constrained by a generic smoothness term. In order to further improve both the algorithm efficiency and robustness, we also propose to apply a pyramidal search strategy for MCD estimation. This coarse-to-fine scheme requires less computation time by starting with the reduced amount of data and propagating searching results to finer resolutions. DCI can incorporate image shape and structure information without the prior requirement of explicit representation of object boundary/surface. Extensive experiments were performed on both synthetic and real medical images to evaluate the proposed approaches. The experimental results show that the proposed methods are able to handle general object interpolation, while achieving both accuracy and efficiency in interpolation compared with the existing techniques.

3D long bone reconstruction based on level sets

In medical imaging a three-dimensional (3D) object must often be reconstructed from serial cross-sections to aid in the comprehension of the object's structure as well as to facilitate its automatic manipulation and analysis. The most popular interpolation scheme for a sequence of image slices is the shape-based method, where object information extracted from a given 3D volume image is used in guiding the interpolation process. The paper presents a level set reformulation of the well-known shape-based method as well as a new automatic level set method, which offers better performance. In particular, we focus on X-ray examinations of long bones, which also requires us to deal with the problem of an optimal slice positioning. To this aim, a 2D version of the proposed algorithm will be used to localize a subset of slices from the entire volume image. A number of experiments were performed on computed tomographic real images to evaluate the proposed approach. The experimental results show a substantial improvement of visual effects (qualitative evaluation) using the proposed method in comparison to both the conventional gray-level interpolation scheme and the shape-based method. Compared with the shape-based interpolation scheme the proposed method has much lower computational cost.

Fast rectifying airborne infrared scanning image based on GPS and INS

Airborne infrared scanning image is often distorted due to the change of the airplane’s attitude and position. Therefore, some ground control points (GCPs) must be used to rectify the raw infrared image by traditional approach. A new method is tested in this paper to rectify scanning image fast based on global positioning system (GPS) and inertial navigation system (INS). First, the positions of some pixels within the same scanning line are calculated, and then these pixels are used as GCPs to rectify the whole scanning line. The gray level interpolation and strips mosaic are also discussed in this paper. The data of flight tests processed shows this method is feasible.

三次元声道内の音圧分布に基づく声道長の推定

The purpose of this study was to estimate the vocal-tract length based on the distribution of sound pressure in the three-dimensional vocal tract during production of the vowels /a/ and /i/. The distribution of sound pressure was estimated in the three-dimensional vocal tract using the Finite Element Method (FEM).The three-dimensional shapes of a vocal tract and a dental crown were measured using Magnetic Resonance Imaging (MRI). A male subject was asked to produce the vowels /a/ and /i/ while wearing a dental crown plate that contained a contrast medium for MRI processing. Three-dimensional MR images of the vocal tract for each sound were obtained while the subject’s tongue was kept still.The vocal tract shapes were obtained from profiles of their sagittal sections. First, sagittal MR images (4-mm interval) were estimated from coronal MR images using grey-level interpolation. Second, air-tissue boundaries of the sagittal sections were obtained from each MR image using a threshold operation in which the threshold value is the average of grey levels at the air-tissue border points. Adjacent air-tissue boundaries are connected by spline interpolation, since the vocal tract shapes are constructed by a cascade connection of the air-tissue boundaries.The three-dimensional vocal tract shapes during vowel production were divided with a tetrahedral element (/a/: 11, 179 elements, 3, 185 nodes; /i/: 12, 763 elements, 3, 558 nodes). At the glottis, the whole area of the cross-section was driven, and at the radiational surface, the radiational impedance was assumed to be that of a circular piston in a rigid sphere. The boundary condition of the wall was defined as the wall impedance.The distribution of sound pressure shows that a sound wave propagates in the vocal tract as a non-plane wave in the high-frequency region.In this study, the vocal tract model with cascading circular tubes was called the VT model. The vocal tract transfer characteristics for both the VT model and the three-dimensional FEM model were determined. A comparison of the VT model and FEM model showed that they share almost the same characteristics in the low-frequency region, but express a difference at high frequencies.The vocal-tract length was estimated based on the distribution of sound pressure in the three-dimensional vocal tract. As a result, in the case of /a/, the vocal-tract length is 188 mm for a driving frequency of 1000 Hz, and 226 mm for a driving frequency of 3000 Hz. In the case of /i/, the vocal-tract length is 163 mm for a driving frequency of 1000 Hz, and 173 mm for a driving frequency of 3000 Hz. These results suggest that the vocal-tract is long in the high-frequency region.

Shape-based grey-level image interpolation

The three-dimensional (3D) object data obtained from a CT scanner usually have unequal sampling frequencies in the x-, y- and z-directions. Generally, the 3D data are first interpolated between slices to obtain isotropic resolution, reconstructed, then operated on using object extraction and display algorithms. The traditional grey-level interpolation introduces a layer of intermediate substance and is not suitable for objects that are very different from the opposite background. The shape-based interpolation method transfers a pixel location to a parameter related to the object shape and the interpolation is performed on that parameter. This process is able to achieve a better interpolation but its application is limited to binary images only. In this paper, we present an improved shape-based interpolation method for grey-level images. The new method uses a polygon to approximate the object shape and performs the interpolation using polygon vertices as references. The binary images representing the shape of the object were first generated via image segmentation on the source images. The target object binary image was then created using regular shape-based interpolation. The polygon enclosing the object for each slice can be generated from the shape of that slice. We determined the relative location in the source slices of each pixel inside the target polygon using the vertices of a polygon as the reference. The target slice grey-level was interpolated from the corresponding source image pixels. The image quality of this interpolation method is better and the mean squared difference is smaller than with traditional grey-level interpolation.

Accurate measurement of three-dimensional shapes of a vocal tract and a dental crown using magnetic resonance imaging: Japanese fricative consonants

Three-dimensional MR images of the vocal tract of three adult males were obtained during steady-state production of the Japanese fricatives /s/, /sh/, and /shu/. MR images of dental crowns containing a small amount of water were obtained using a dental crown plate which was shaped so as to attach tightly to the subject’s dental crown by thermoforming which contained a contrast medium for MR imaging. A computer algorithm based on gray level interpolation and threshold operation for air–tissue boundary tracing of arbitrary sections of the vocal tract taken from axial and coronal MR images were proposed. Images of arbitrary sections of the vocal tract were reconstructed from 3-D MR images using gray level interpolation based on the sampling theorem. Gray level thresholds were computed from the gray levels at points on the air–tissue border. The boundary tracing error of the dental crowns from the 3-D MR images was less than 5.7%. The 3-D shape and area function of the vocal tract during production of the Japanese fricatives /s/, /sh/, and /shu/ were obtained.

Interferometric spacing measurements of the Bernoulli head/disk interface

Head-to-disk spacing in a flexible disk drive (Bernoulli technology) is measured interferometrically using monochromatic light in conjunction with a grey level interpolation scheme. Measurements in the center region of a Bernoulli head indicate that the minimum head-disk separation is less than 50 nm, suggesting that the asperity contacts occur in the area of the closest approach. The spacing distribution of a typical Bernoulli head is reported, as well as a parameter study of spacing as a function of rotational speed. >