Jos B. T. M. Roerdink

The watershed transform: definitions, algorithms and parallelization strategies

The watershed transform is the method of choice for image segmentation in the field of mathematical morphology. We present a critical review of several definitions of the watershed transform and the associated sequential algorithms, and discuss various issues which often cause confusion in the literature. The need to distinguish between definition, algorithm specification and algorithm implementation is pointed out. Various examples are given which illustrate differences between watershed transforms based on different definitions and/or implementations. The second part of the paper surveys approaches for parallel implementation of sequential watershed algorithms.

Denoising functional MR images: a comparison of wavelet denoising and Gaussian smoothing

We present a general wavelet-based denoising scheme for functional magnetic resonance imaging (fMRI) data and compare it to Gaussian smoothing, the traditional denoising method used in fMRI analysis. One-dimensional WaveLab thresholding routines were adapted to two-dimensional (2-D) images, and applied to 2-D wavelet coefficients. To test the effect of these methods on the signal-to-noise ratio (SNR), we compared the SNR of 2-D fMRI images before and after denoising, using both Gaussian smoothing and wavelet-based methods. We simulated a fMRI series with a time signal in an active spot, and tested the methods on noisy copies of it. The denoising methods were evaluated in two ways: by the average temporal SNR inside the original activated spot, and by the shape of the spot detected by thresholding the temporal SNR maps. Denoising methods that introduce much smoothness are better suited for low SNRs, but for images of reasonable quality they are not preferable, because they introduce heavy deformations. Wavelet-based denoising methods that introduce less smoothing preserve the sharpness of the images and retain the original shapes of active regions. We also performed statistical parametric mapping on the denoised simulated time series, as well as on a real fMRI data set. False discovery rate control was used to correct for multiple comparisons. The results show that the methods that produce smooth images introduce more false positives. The less smoothing wavelet-based methods, although generating more false negatives, produce a smaller total number of errors than Gaussian smoothing or wavelet-based methods with a large smoothing effect.

Connected Shape-Size Pattern Spectra for Rotation and Scale-Invariant Classification of Gray-Scale Images

In this paper, we describe a multiscale and multishape morphological method for pattern-based analysis and classification of gray-scale images using connected operators. Compared with existing methods, which use structuring elements, our method has three advantages. First, in our method, the time needed for computing pattern spectra does not depend on the number of scales or shapes used, i.e., the computation time is independent of the dimensions of the pattern spectrum. Second, size and strict shape attributes can be computed, which we use for the construction of joint 2D shape-size pattern spectra. Third, our method is significantly less sensitive to noise and is rotation-invariant. Although rotation invariance can also be approximated by methods using structuring elements at different angles, this tends to be computationally intensive. The classification performance of these methods is discussed using four image sets: Brodatz, COIL-20, COIL-100, and diatoms. The new method obtains better or equal classification performance to the best competitor with a 5 to 9-fold speed gain

A General Algorithm for Computing Distance Transforms in Linear Time

A new general algorithm for computing distance transforms of digital images is presented. The algorithm consists of two phases. Both phases consist of two scans, a forward and a backward scan. The first phase scans the image column-wise, while the second phase scans the image row-wise. Since the computation per row (column) is independent of the computation of other rows (columns), the algorithm can be easily parallelized on shared memory computers. The algorithm can be used for the computation of the exact Euclidean, Manhattan (L 1 norm), and chessboard distance (L ∞ norm) transforms.

Changes in cortical grey matter density associated with long-standing retinal visual field defects

Retinal lesions caused by eye diseases such as glaucoma and age-related macular degeneration can, over time, eliminate stimulation of parts of the visual cortex. This could lead to degeneration of inactive cortical neuronal tissue, but this has not been established in humans. Here, we used magnetic resonance imaging to assess the effects of prolonged sensory deprivation in human visual cortex. High-resolution anatomical magnetic resonance images were obtained in subjects with foveal (age-related macular degeneration) and peripheral (glaucoma) retinal lesions as well as age-matched controls. Comparison of grey matter between patient and control groups revealed density reductions in the approximate retinal lesion projection zones in visual cortex. This indicates that long-term cortical deprivation, due to retinal lesions acquired later in life, is associated with retinotopic-specific neuronal degeneration of visual cortex. Such degeneration could interfere with therapeutic strategies such as the future application of artificial retinal implants to overcome lesion-induced visual impairment.

A morphological algorithm for improving radio-frequency interference detection

A technique is described that is used to improve the detection of radio-frequency interference in astronomical radio observatories. It is applied on a two-dimensional interference mask after regular detection in the time-frequency domain with existing techniques. The scale-invariant rank (SIR) operator is defined, which is a one-dimensional mathematical morphology technique that can be used to find adjacent intervals in the time or frequency domain that are likely to be affected by RFI. The technique might also be applicable in other areas in which morphological scale-invariant behaviour is desired, such as source detection. A new algorithm is described, that is shown to perform quite well, has linear time complexity and is fast enough to be applied in modern high resolution observatories. It is used in the default pipeline of the LOFAR observatory.

CPM: a deformable model for shape recovery and segmentation based on charged particles

A novel, physically motivated deformable model for shape recovery and segmentation is presented. The model, referred to as the charged-particle model (CPM), is inspired by classical electrodynamics and is based on a simulation of charged particles moving in an electrostatic field. The charges are attracted towards the contours of the objects of interest by an electrostatic field, whose sources are computed based on the gradient-magnitude image. The electric field plays the same role as the potential forces in the snake model, while internal interactions are modeled by repulsive Coulomb forces. We demonstrate the flexibility and potential of the model in a wide variety of settings: shape recovery using manual initialization, automatic segmentation, and skeleton computation. We perform a comparative analysis of the proposed model with the active contour model and show that specific problems of the latter are surmounted by our model. The model is easily extendable to 3D and copes well with noisy images.

Depth-Dependent Halos: Illustrative Rendering of Dense Line Data

We present a technique for the illustrative rendering of 3D line data at interactive frame rates. We create depth-dependent halos around lines to emphasize tight line bundles while less structured lines are de-emphasized. Moreover, the depth-dependent halos combined with depth cueing via line width attenuation increase depth perception, extending techniques from sparse line rendering to the illustrative visualization of dense line data. We demonstrate how the technique can be used, in particular, for illustrating DTI fiber tracts but also show examples from gas and fluid flow simulations and mathematics as well as describe how the technique extends to point data. We report on an informal evaluation of the illustrative DTI fiber tract visualizations with domain experts in neurosurgery and tractography who commented positively about the results and suggested a number of directions for future work.

Accelerating Wavelet Lifting on Graphics Hardware Using CUDA

The Discrete Wavelet Transform (DWT) has a wide range of applications from signal processing to video and image compression. We show that this transform, by means of the lifting scheme, can be performed in a memory and computation-efficient way on modern, programmable GPUs, which can be regarded as massively parallel coprocessors through NVidias CUDA compute paradigm. The three main hardware architectures for the 2D DWT (row-column, line-based, block-based) are shown to be unsuitable for a CUDA implementation. Our CUDA-specific design can be regarded as a hybrid method between the row-column and block-based methods. We achieve considerable speedups compared to an optimized CPU implementation and earlier non-CUDA-based GPU DWT methods, both for 2D images and 3D volume data. Additionally, memory usage can be reduced significantly compared to previous GPU DWT methods. The method is scalable and the fastest GPU implementation among the methods considered. A performance analysis shows that the results of our CUDA-specific design are in close agreement with our theoretical complexity analysis.

Euclidean Skeletons of Digital Image and Volume Data in Linear Time by the Integer Medial Axis Transform

A general algorithm for computing Euclidean skeletons of 2D and 3D data sets in linear time is presented. These skeletons are defined in terms of a new concept, called the integer medial axis (IMA) transform. We prove a number of fundamental properties of the IMA skeleton, and compare these with properties of the CMD (centers of maximal disks) skeleton. Several pruning methods for IMA skeletons are introduced (constant, linear and square-root pruning) and their properties studied. The algorithm for computing the IMA skeleton is based upon the feature transform, using a modification of a linear-time algorithm for Euclidean distance transforms. The skeletonization algorithm has a time complexity which is linear in the number of input points, and can be easily parallelized. We present experimental results for several data sets, looking at skeleton quality, memory usage and computation time, both for 2D images and 3D volumes.