Edge location to subpixel values in digital imagery

Subpixel Edge Localization Based on Adaptive Weighting of Gradients

This paper presents a subpixel edge localization method based on the adaptive weighting of gradients (AWG). The method first finds the optimal power factors to be used by the AWG through an error propagation scheme. Then, with the goal of fast implementation of the method, a process that directly relates the edge width to the optimal powers is proposed. A method that uses the squared weighting of gradients (SWG) is also proposed, which applies a power of 2 to the gradients of an edge profile to calculate the edge location with subpixel accuracy. Next, an enhanced version of the AWG that combines the SWG and AWG selectively is proposed to obtain the best localization. At present, a fitting method based on the error function (Erf) is considered to be the most accurate method among current state-of-the-art methods, but it has a very high computational cost. The experimental results show that the proposed method is computationally much less expensive and more accurate than the Erf-fitting method.

Technical Note: Impact on detective quantum efficiency of edge angle determination method by International Electrotechnical Commission methodology for cardiac x-ray image detectors

PURPOSE

Cardiac x-ray detectors are used to acquire moving images in real-time for angiography and interventional procedures. Detective quantum efficiency (DQE) is not generally measured on these dynamic detectors; the required "for processing" image data and control of x-ray settings have not been accessible. By 2016, USA hospital physicists will have the ability to measure DQE and will likely utilize the International Electrotechnical Commission (IEC) standard for measuring DQE of dynamic x-ray imaging devices. The current IEC standard requires an image of a tilted tungsten edge test object to obtain modulation transfer function (MTF) for DQE calculation. It specifies the range of edge angles to use; however, it does not specify a preferred method to determine this angle for image analysis. The study aimed to answer the question "will my choice in method impact my results?" Four different established edge angle determination methods were compared to investigate the impact on DQE.

METHODS

Following the IEC standard, edge and flat field images were acquired on a cardiac flat-panel detector to calculate MTF and noise power spectrum, respectively, to determine DQE. Accuracy of the methods in determining the correct angle was ascertained using a simulated edge image with known angulations. Precision of the methods was ascertained using variability of MTF and DQE, calculated via bootstrapping.

RESULTS

Three methods provided near equal angles and the same MTF while the fourth, with an angular difference of 6%, had a MTF lower by 3% at 1.5 mm(-1) spatial frequency and 8% at 2.5 mm(-1); corresponding DQE differences were 6% at 1.5 mm(-1) and 17% at 2.5 mm(-1); differences were greater than standard deviations in the measurements.

CONCLUSIONS

DQE measurements may vary by a significant amount, depending on the method used to determine the edge angle when following the IEC standard methodology for a cardiac x-ray detector. The most accurate and precise methods are recommended for absolute assessments and reproducible measurements, respectively.

Utilizing confocal microscopy to measure refractive index of articular cartilage

This study proposes a method for measuring the refractive index of articular cartilage within a thin and small specimen slice. The cartilage specimen, with a thickness of about 50 μm, was put next to a thin film of immersion oil of similar thickness. Both the articular cartilage and immersion oil were scanned along the depth direction using a confocal microscope. The refractive index mismatch between the cartilage and the immersion oil induced a slight axial deformation in the confocal images of the cartilage specimen that was accurately measured by a subpixel edge-detection-based technique. A theoretical model was built to quantify the focal shift of confocal microscopy caused by the refractive index mismatch. With the quantitative deformations of cartilage images and the quantified function of focal shift, the refractive index of articular cartilage was accurately interpolated. At 561 nm, 0.1 MPa and 20 °C, the overall refractive index of the six cartilage plugs was 1.3975 ± 0.0156. The overall coefficient of variation of all cartilage specimens was 0.68%, which indicated the high repeatability of our method. The verification experiments using distilled water showed a minimal relative error of 0.02%.

Optical evaluation of ink prints made with heat-treated alder and birch

Japanese woodblock printmaking is a traditional printing method practiced for centuries. The modern challenge to this fine art is the constantly decreasing amount of available wood, wild cherry tree, which has been traditionally used as a printing block material. The increasing amount of interest focuses on finding alternative wood types, which would compare successfully with the desired quality of the wild cherry tree. Our initial research has shown that heat-treated alder and birch trees could both be considered as possible alternatives for block material. In this paper we introduce the optical characterization (CIELAB color and gloss) of black ink prints made on two different handmade papers with printing blocks made of low-temperature (120°C, 140°C) heat-treated alder and birch. Results show lowered ink transfer from wood when the heat treatment temperature rises, more transferred ink from alder, and printing paper differences due to fiber content differences.

Measurement of shaft diameters by machine vision

A machine vision method for accurately measuring the diameters of cylindrical shafts is presented. Perspective projection and the geometrical features of cylindrical shafts are modeled in order to enable accurate measurement of shaft diameters. Some of the model parameters are determined using a shaft of known diameter. The camera model itself includes radial and tangential distortions terms. Experiments were used to measure the accuracy of the proposed method and the effect of the position of the camera relative to the shaft, as well as other factors.

Subpixel edge refinement using deformable models

We propose an approach for subpixel edge refinement based on deformable models. In our approach, the result is constrained by two kinds of information: orientation information derived from the gradient and position information. The problem is formulated in a statistical framework: the likelihood function of the observations is computed and used in a classical maximum a posteriori estimator. Two different models are proposed: a parametric model based on B-spline functions and a sampled model. Experiments on both synthetic and natural images are described that show the adequacy and effectiveness of these algorithms.

Comparison of edge analysis techniques for the determination of the MTF of digital radiographic systems

The modulation transfer function (MTF) is well established as a metric to characterize the resolution performance of a digital radiographic system. Implemented by various laboratories, the edge technique is currently the most widespread approach to measure the MTF. However, there can be differences in the results attributed to differences in the analysis technique employed. The objective of this study was to determine whether comparable results can be obtained from different algorithms processing identical images representative of those of current digital radiographic systems. Five laboratories participated in a round-robin evaluation of six different algorithms including one prescribed in the International Electrotechnical Commission (IEC) 62220-1 standard. The algorithms were applied to two synthetic and 12 real edge images from different digital radiographic systems including CR, and direct- and indirect-conversion detector systems. The results were analysed in terms of variability as well as accuracy of the resulting presampled MTFs. The results indicated that differences between the individual MTFs and the mean MTF were largely below 0.02. In the case of the two simulated edge images, all algorithms yielded similar results within 0.01 of the expected true MTF. The findings indicated that all algorithms tested in this round-robin evaluation, including the IEC-prescribed algorithm, were suitable for accurate MTF determination from edge images, provided the images are not excessively noisy. The agreement of the MTF results was judged sufficient for the measurement of the MTF necessary for the determination of the DQE.

Efficient algorithm for computation of the second-order moment of the subpixel-edge position

Subpixel-edge detection is the first stage in processing many high-level vision algorithms. However, the study of the statistical properties of such data has remained incomplete in most research. We present a method for estimating the second-order moments of the subpixel-edge position, computed by a deterministic algorithm based on three quadratic interpolations. The algorithm is tested on different types of noise (Gaussian, impulse, colored) and compared with two methods in the literature. The results show that this approach remains accurate even at high noise levels.

Shape recovery algorithms using level sets in 2-D/3-D medical imagery: a state-of-the-art review

The class of geometric deformable models, also known as level sets, has brought tremendous impact to medical imagery due to its capability of topology preservation and fast shape recovery. In an effort to facilitate a clear and full understanding of these powerful state-of-the-art applied mathematical tools, this paper is an attempt to explore these geometric methods, their implementations and integration of regularizers to improve the robustness of these topologically independent propagating curves/surfaces. This paper first presents the origination of level sets, followed by the taxonomy of level sets. We then derive the fundamental equation of curve/surface evolution and zero-level curves/surfaces. The paper then focuses on the first core class of level sets, known as "level sets without regularizers." This class presents five prototypes: gradient, edge, area-minimization, curvature-dependent and application driven. The next section is devoted to second core class of level sets, known as "level sets with regularizers." In this class, we present four kinds: clustering-based, Bayesian bidirectional classifier-based, shape-based and coupled constrained-based. An entire section is dedicated to optimization and quantification techniques for shape recovery when used in the level set framework. Finally, the paper concludes with 22 general merits and four demerits on level sets and the future of level sets in medical image segmentation. We present applications of level sets to complex shapes like the human cortex acquired via MRI for neurological image analysis.

Ball stud inspection system using machine vision

In this paper, a vision-based inspection system that measures the dimensions of a ball stud is designed and implemented. The system acquires silhouetted images by backlighting and extracts the outlines of the nearly dichotomized images in subpixel accuracy. The sets of boundary data are modeled with reasonable geometric primitives and the parameters of the models are estimated in a manner that minimizes error. Jig-fixtures and servo systems for the inspection are also contrived. The system rotates an inspected object to recognize the objects in space not on a plane. The system moves the object vertically so that it may take several pictures of different parts of the object, resulting in improvement of measuring resolution. The performance of the system is evaluated by measurement of the dimensions of a standard ball, a standard cylinder, and a ball stud.

Precise measurement of cat patellofemoral joint surface geometry with multistation digital photogrammetry

Three-dimensional joint models are important tools for investigating mechanisms related to normal and pathological joints. Often these models necessitate accurate three-dimensional joint surface geometric data so that reliable model results can be obtained; however, in models based on small joints, this is often problematic due to limitations of the present techniques. These limitations include insufficient measurement precision the requirement of contact for the measurement process, and lack of entire joint description. This study presents a new non-contact method for precise determination of entire joint surfaces using multistation digital photogrammetry (MDPG) and is demonstrated by determining the cartilage and subchondral bone surfaces of the cat patellofemoral (PF) joint. The digital camera-lens setup was precisely calibrated using 16 photographs arranged to achieve highly convergent geometry to estimate interior and distortion parameters of the camera-lens setup. Subsequently, six photographs of each joint surface were then acquired for surface measurement. The digital images were directly imported to a computer and newly introduced semi-automatic computer algorithms were used to precisely determine the image coordinates. Finally, a rigorous mathematical procedure named the bundle adjustment was used to determine the three-dimensional coordinates of the joint surfaces and to estimate the precision of the coordinates. These estimations were validated by comparing the MDPG measurements of a cylinder and plane to an analytical model. The joint surfaces were successfully measured using the MDPG method with mean precision estimates in the least favorable coordinate direction being 10.3 microns for subchondral bone and 17.9 microns for cartilage. The difference in measurement precision for bone and cartilage primarily reflects differences in the translucent properties of the surfaces.

Boundary detection using simulation of particle motion in a vector image field

This paper introduces a novel approach in image processing based on a vector image model. A major advantage of the model is that it allows vector operations to be performed on an image. An example of a vector operation is the computation of mechanical moments for detecting inhomogeneities in an object or equivalently edges in an image. A new edge operator derived from a vector image model yields an edge vector field analogous to the Hamiltonian gradient field of the image. The distinct feature of the edge vector field is that edge vectors form current loops encompassing the objects. This feature is exploited to develop a new boundary extraction algorithm based on particle motion in a force field. The edge vector field forces a particle to move along the edges while an orthogonal normalized Laplacian gradient vector field guarantees that the particle will not drift away from the edges. The object boundary can be obtained from the convergent path of the particle trajectory. Using a fine stepping factor, the extracted boundary can achieve subpixel accuracy. The proposed algorithm has major advantages over the conventional edge-detection, edge-thinning, and edge-linking techniques in that it effectively utilizes both direction and magnitude of edges. The algorithm is simple, robust and performs very well even on high curvature objects.

Color image processing by using binary quaternion-moment-preserving thresholding technique

This paper presents a new moment-preserving thresholding technique, called the binary quaternion-moment-preserving (BQMP) thresholding, for color image data. Based on representing color data by the quaternions, the statistical parameters of color data can be expressed through the definition of quaternion moments. Analytical formulas of the BQMP thresholding can thus be determined by using the algebra of the quaternions. The computation time for the BQMP thresholding is of order of the data size. By using the BQMP thresholding, quaternion-moment-based operators are designed for the application of color image processing, such as color image compression, multiclass clustering of color data, and subpixel color edge detection. The experimental results show that the proposed operator for color image compression can have output picture quality acceptable to human eyes. In addition, the proposed edge operator can detect the color edge at the subpixel level. Therefore, the proposed BQMP thresholding can be used as a tool for color image processing.

Derivation of optimal filters for the detection of coronary arteries

In this paper optimal filters for the detection of coronary arteries with a diameter range of 0.5-6.0 mm in digital X-ray images are derived using a computational approach. This approach is based on the two requirements for optimal detection. First, the filter should maximize the number of detected true edges and minimize the number of detected false edges. Second, if an edge has been detected, its position should be as close as possible to the true edge position in the image. Since the grey value profile in a digital X-ray image associated with an arterial vessel is asymmetric, the theory on edge detection derived by Canny has been expanded with two additional boundary constraints to make it suitable for the derivation of filters for asymmetric edges. It is demonstrated that it is possible to derive optimal filters for coronary segments. The localization error, defined by the square root of the sum of the squared systematic and random errors in the assessment of the arterial diameter, depends on the size of the coronary artery and the amount of noise in the image. In this paper, an evaluation study is described to assess the relationship between localization error and the amount of noise upon the vessel profile. For that purpose, an analytical description of the vessel profile in an angiographic image was derived. For the larger arteries the relation between noise and localization error was found to be linear and no systematic over- or underestimations were observed, even if the noise level was very high. However, it can be shown that the smallest diameter that can be measured depends on the amount of noise present in the data. Even for images that contain only a low amount of noise, arterial diameters below 0.7 mm cannot be measured accurately. If the noise in the image increases, the lowest measurable arterial diameter value also increases. Also the random error increases rapidly for vessel diameters below 1.2 mm, but with a limited amount of noise and a diameter value above 0.7 mm the random error is still acceptable [0.15 mm (21%) for 0.7-mm vessels, 0.06 mm (6%) for 1-mm vessels].

Validation of displacement measurements obtained from ultrasonic images during indentation testing

Biomechanical features of soft tissue are commonly investigated by indentation, a procedure where a blunt probe is advanced and the ensuing deformation of the tissue surface recorded. If it were possible to visualize subsurface anatomy during the indentation process, biomechanical investigation of internal tissue features might be feasible. The purpose of this experiment was to determine the accuracy of ultrasonically-derived measures of displacement obtained during indentation testing of an ultrasonic phantom. Using a 5-MHz sector transducer mounted to an automated indentation device, ultrasonic estimates of distance between a stationary target surface and the moving ultrasonic transducer were obtained and validated to a criterion. Depending on the method used to locate the target surface on the resulting B-mode image, the mean displacement error ranged from 14.37% to 22.05%. Use of this protocol for human tissue assessment, in vivo or otherwise, may be appropriate if the displacements of interest are greater than the error of the procedure.

Detection of composite edges

The paper presents a new parametric model-based approach to high-precision composite edge detection using orthogonal Zernike moment-based operators. It deals with two types of composite edges: (a) generalized step and (b) pulse/staircase edges. A 2-D generalized step edge is modeled in terms of five parameters: two gradients on two sides of the edge, the distance from the center of the candidate pixel, the orientation of the edge and the step size at the location of the edge. A 2-D pulse/staircase edge is modeled in terms of two steps located at two positions within the mask, and the edge orientation. A pulse edge is formed if the steps are of opposite polarities whereas a staircase edge results from two steps having the same polarity. Two complex and two real Zernike moment-based masks are designed to determine parameters of both the 2-D edge models. For a given edge model, estimated parameter values at a point are used to detect the presence or absence of that type of edge. Extensive noise analysis is performed to demonstrate the robustness of the proposed operators. Experimental results with intensity and range images are included to demonstrate the efficacy of the proposed edge detection technique as well as to compare its performance with the geometric moment-based step edge detection technique and Canny's (1986) edge detector.

Model-based frequency response characterization of a digital-image analysis system for epifluorescence microscopy

We describe a model-based method for estimating the spatial frequency response of a digital-imaging system (e.g., a CCD camera) that is modeled as a linear, shift-invariant image acquisition subsystem that is cascaded with a linear, shift-variant sampling subsystem. The method characterizes the twodimensional frequency response of the image acquisition subsystem to beyond the Nyquist frequency by accounting explicitly for insufficient sampling and the sample-scene phase. Results for simulated systems and a real CCD-based epifluorescence microscopy system are presented to demonstrate the accuracy of the method.

A robust filtering algorithm for subpixel reconstruction of chain coded line drawings

A robust algorithm is presented for smoothing and achieving subpixel accuracy in the reconstruction of chain coded line drawings. The algorithm does not remove sharp corners and does not need a priori knowledge of curvature statistics. A fast on-line implementation can be achieved using a table look-up. A simplified algorithm can be used for reconstructing digitized polygons.