A task-specific evaluation of three-dimensional image interpolation techniques

Recovering from missing data in population imaging - Cardiac MR image imputation via conditional generative adversarial nets

Accurate ventricular volume measurements are the primary indicators of normal/abnor- mal cardiac function and are dependent on the Cardiac Magnetic Resonance (CMR) volumes being complete. However, missing or unusable slices owing to the presence of image artefacts such as respiratory or motion ghosting, aliasing, ringing and signal loss in CMR sequences, significantly hinder accuracy of anatomical and functional cardiac quantification, and recovering from those is insufficiently addressed in population imaging. In this work, we propose a new robust approach, coined Image Imputation Generative Adversarial Network (I2-GAN), to learn key features of cardiac short axis (SAX) slices near missing information, and use them as conditional variables to infer missing slices in the query volumes. In I2-GAN, the slices are first mapped to latent vectors with position features through a regression net. The latent vector corresponding to the desired position is then projected onto the slice manifold, conditioned on intensity features through a generator net. The generator comprises residual blocks with normalisation layers that are modulated with auxiliary slice information, enabling propagation of fine details through the network. In addition, a multi-scale discriminator was implemented, along with a discriminator-based feature matching loss, to further enhance performance and encourage the synthesis of visually realistic slices. Experimental results show that our method achieves significant improvements over the state-of-the-art, in missing slice imputation for CMR, with an average SSIM of 0.872. Linear regression analysis yields good agreement between reference and imputed CMR images for all cardiac measurements, with correlation coefficients of 0.991 for left ventricular volume, 0.977 for left ventricular mass and 0.961 for right ventricular volume.

Medical Image Magnification Based on Original and Estimated Pixel Selection Models

BACKGROUND

The issue of medial image resolution enhancement is one of the most important topics for medical imaging that helps improve the performance of many post-processing aspects like classification and segmentation towards medical diagnosis.

OBJECTIVE

Our aim in this paper is to evaluate different types of pixel selection models in terms of pixel originality in medical image reconstruction problems. A previous investigation showed that selecting far original pixels has highly better performance than using near unoriginal/estimated pixels while magnifying some benchmarks in digital image processing.

MATERIAL AND METHODS

In our technical study, we apply two classical interpolators, cubic convolution (CC) and bi-linear (BL), in order to reconstruct medical images in spatial domain. In addition to the interpolators, we use some geometrical image transforms for creating the reconstruction models.

RESULTS

The results clearly demonstrate that despite the absolute preference of the original pixel selection model in the first research, we cannot see this preference in medical dataset in which the results of BL interpolator for both tested models (original and estimated pixel selection models) are approximately the same as each other and for CC interpolator, we only see a relatively better preference for the original pixel selection model.

CONCLUSION

The current research reveals the fact that selection models are not a general factor in reconstruction problems, and the structure of the basic interpolators is also a main factor which affects the final results. In other words, some interpolators in medical dataset can be affected by the selection models, while, some cannot.

Data-adapted moving least squares method for 3-D image interpolation

In this paper, we present a nonlinear three-dimensional interpolation scheme for gray-level medical images. The scheme is based on the moving least squares method but introduces a fundamental modification. For a given evaluation point, the proposed method finds the local best approximation by reproducing polynomials of a certain degree. In particular, in order to obtain a better match to the local structures of the given image, we employ locally data-adapted least squares methods that can improve the classical one. Some numerical experiments are presented to demonstrate the performance of the proposed method. Five types of data sets are used: MR brain, MR foot, MR abdomen, CT head, and CT foot. From each of the five types, we choose five volumes. The scheme is compared with some well-known linear methods and other recently developed nonlinear methods. For quantitative comparison, we follow the paradigm proposed by Grevera and Udupa (1998). (Each slice is first assumed to be unknown then interpolated by each method. The performance of each interpolation method is assessed statistically.) The PSNR results for the estimated volumes are also provided. We observe that the new method generates better results in both quantitative and visual quality comparisons.

Curvature interpolation method for image zooming

We introduce a novel image zooming algorithm, called the curvature interpolation method (CIM), which is partial-differential-equation (PDE)-based and easy to implement. In order to minimize artifacts arising in image interpolation such as image blur and the checkerboard effect, the CIM first evaluates the curvature of the low-resolution image. After interpolating the curvature to the high-resolution image domain, the CIM constructs the high-resolution image by solving a linearized curvature equation, incorporating the interpolated curvature as an explicit driving force. It has been numerically verified that the new zooming method can produce clear images of sharp edges which are already denoised and superior to those obtained from linear methods and PDE-based methods of no curvature information. Various results are given to prove effectiveness and reliability of the new method.

Respiratory acoustic thoracic imaging (RATHI): assessing intrasubject variability

Respiratory acoustic thoracic imaging (RATHI) permits analysing lung sounds (LS) temporal and spatial distribution, however, a deep understanding of RATHI repeatability associated with the pulmonary function is necessary. As a consequence, in the current work intrasubject variability of RATHI is evaluated at different airflows. For generating RATHIs, LS were acquired at the posterior thoracic surface. The associated image was computed at the inspiratory phases by interpolation through a Hermite function. The acoustic information of eleven subjects was considered at airflows of 1.0, 1.5 and 2.0 L/s. Several RATHIs were generated for each subject according to the number of acquired inspiratory phases. Quadratic mutual information based on Cauchy-Schwartz inequality (I(CS)) was used to evaluate the degree of similitude between intrasubject RATHIs. The results indicated that, for the same subject, I(CS) averaged 0.893, 0.897, and 0.902, for airflows of 1.0, 1.5, and 2 L/s, respectively. In addition, when the airflow was increased, increments in intensity values and in the dispersion of the spatial distribution reflected in RATHI were observed. In conclusion, since the intrasubject variability of RATHI was low for airflows between 1.0 and 2.0 L/s, the pattern of sound distribution during airflow variations is repeatable but differences in sound intensity should be considered.

Comparison of scene-based interpolation methods applied to CT abdominal images

Three-dimensional (3-D) interpolation from 2-D image slices is widely used to aid the display, analysis and other biomedical image processing. We investigate the performance of 5 scene-based interpolation methods: linear, cubic spline, modified cubic spline and sine-based functions (Dirichlet apodization and Hanning apodization). We test our methods on four sets of computed tomography (CT) abdominal images, which have more organs in them compared to other biomedical images. Results show that, contrary to the 1-D or 2-D cases, linear interpolation acts as well as, even slightly better than all the other methods in the sense of signal to noise ratio in most cases, while the computational load of linear interpolation is only about half of the other methods. The reason for the relative high performance of linear interpolation is probably the large distance between consecutive images, which indicates low inter-slice correlation.

Respiratory acoustic thoracic imaging (RATHI): Assessing deterministic interpolation techniques

As respiratory sounds contain mechanical and clinical pulmonary information, technical efforts have been devoted during the past decades to analysing, processing and visualising them. The aim of this work was to evaluate deterministic interpolating functions to generate surface respiratory acoustic thoracic images (RATHIs), based on multiple acoustic sensors. Lung sounds were acquired from healthy subjects through a 5 x 5 microphone array on the anterior and posterior thoracic surfaces. The performance of five interpolating functions, including the linear, cubic spline, Hermite, Lagrange and nearest neighbour method, were evaluated to produce images of lung sound intensity during both breathing phases, at low (approximately 0.5ls(-1)) and high (approximately 1.0ls(-1)) airflows. Performance indexes included the normalised residual variance nrv (i.e. inaccuracy), the prediction covariance cv (i.e. precision), the residual covariance rcv (i.e. bias) and the maximum squared residual error semax (i.e. tolerance). Among the tested interpolating functions and in all experimental conditions, the Hermite function (nrv=0.146 +/- 0.059, cv= 0.925 +/- 0.030, rcv = -0.073 +/- 0.068, semax = 0.005 +/- 0.004) globally provided the indexes closest to the optimum, whereas the nearest neighbour (nrv=0.339 +/- 0.023, cv = 0.870 +/- 0.033, rcv= 0.298 +/- 0.032, semax = 0.007 +/- 0.005) and the Lagrange methods (nrv = 0.287 +/- 0.148, cv = 0.880 +/- 0.039, rcv = -0.524 +/- 0.135, semax = 0.007 +/- 0.0001) presented the poorest statistical measurements. It is concluded that, although deterministic interpolation functions indicate different performances among tested techniques, the Hermite interpolation function presents a more confident deterministic interpolation for depicting surface-type RATHI.

Morphology-based three-dimensional interpolation

In many medical applications, the number of available two-dimensional (2-D) images is always insufficient. Therefore, the three-dimensional (3-D) reconstruction must be accomplished by appropriate interpolation methods to fill gaps between available image slices. In this paper, we propose a morphology-based algorithm to interpolate the missing data. The proposed algorithm consists of several steps. First, the object or hole contours are extracted using conventional image-processing techniques. Second, the object or hole matching issue is evaluated. Prior to interpolation, the centroids of the objects are aligned. Next, we employ a dilation operator to transform digital images into distance maps and we correct the distance maps if required. Finally, we utilize an erosion operator to accomplish the interpolation. Furthermore, if multiple objects or holes are interpolated, we blend them together to complete the algorithm. We experimentally evaluate the proposed method against various synthesized cases reported in the literature. Experimental results show that the proposed method is able to handle general object interpolation effectively.

Survey: interpolation methods in medical image processing

Image interpolation techniques often are required in medical imaging for image generation (e.g., discrete back projection for inverse Radon transform) and processing such as compression or resampling. Since the ideal interpolation function spatially is unlimited, several interpolation kernels of finite size have been introduced. This paper compares 1) truncated and windowed sinc; 2) nearest neighbor; 3) linear; 4) quadratic; 5) cubic B-spline; 6) cubic; g) Lagrange; and 7) Gaussian interpolation and approximation techniques with kernel sizes from 1 x 1 up to 8 x 8. The comparison is done by: 1) spatial and Fourier analyses; 2) computational complexity as well as runtime evaluations; and 3) qualitative and quantitative interpolation error determinations for particular interpolation tasks which were taken from common situations in medical image processing. For local and Fourier analyses, a standardized notation is introduced and fundamental properties of interpolators are derived. Successful methods should be direct current (DC)-constant and interpolators rather than DC-inconstant or approximators. Each method's parameters are tuned with respect to those properties. This results in three novel kernels, which are introduced in this paper and proven to be within the best choices for medical image interpolation: the 6 x 6 Blackman-Harris windowed sinc interpolator, and the C2-continuous cubic kernels with N = 6 and N = 8 supporting points. For quantitative error evaluations, a set of 50 direct digital X rays was used. They have been selected arbitrarily from clinical routine. In general, large kernel sizes were found to be superior to small interpolation masks. Except for truncated sinc interpolators, all kernels with N = 6 or larger sizes perform significantly better than N = 2 or N = 3 point methods (p << 0.005). However, the differences within the group of large-sized kernels were not significant. Summarizing the results, the cubic 6 x 6 interpolator with continuous second derivatives, as defined in (24), can be recommended for most common interpolation tasks. It appears to be the fastest six-point kernel to implement computationally. It provides eminent local and Fourier properties, is easy to implement, and has only small errors. The same characteristics apply to B-spline interpolation, but the 6 x 6 cubic avoids the intrinsic border effects produced by the B-spline technique. However, the goal of this study was not to determine an overall best method, but to present a comprehensive catalogue of methods in a uniform terminology, to define general properties and requirements of local techniques, and to enable the reader to select that method which is optimal for his specific application in medical imaging.

Subunity coordinate translation with Fourier transform to achieve efficient and quality three-dimensional medical image interpolation

A new approach to the interpolation of three-dimensional (3D) medical images is presented. Instead of going through the conventional interpolation scheme where the continuous function is first reconstructed from the discrete data set and then resampled, the interpolation is achieved with a subunity coordinate translation technique. The original image is first transformed into the spatial-frequency domain. The phase of the transform is then modified with n-1 linear phase terms in the axial direction to achieve n-1 subunity coordinate translations with a distance 1/n, where n is an interpolation ratio, following the phase shift theorem of Fourier transformation. All the translated images after inverse Fourier transformation are then interspersed in turn into the original image. Since windowing plays an important role in the process, different window functions have been studied and a proper recommendation is provided. The interpolation quality produced with the present method is as good as that with the sampling (sinc) function, while the efficiency, thanks to the fast Fourier transformation, is very much improved. The approach has been validated with both computed tomography (CT) and magnetic resonance (MR) images. The interpolations of 3D CT and MR images are demonstrated.