Multiresolution Pyramid Research Articles

Robust Multiscale Deformable Registration of 3D Ultrasound Images

In this paper, we embed the minimization scheme of an automatic 3D non-rigid registration method in a multiscale framework. The initial model formulation was expressed as a robust multiresolution and multigrid minimization scheme. At the finest level of the multiresolution pyramid, we introduce a focusing strategy from coarse-to-fine scales which leads to an improvement in the accuracy of the registration process. A focusing strategy has been tested for a linear and a non-linear scale-space. Results on real 3D ultrasound images are discussed.

Multi-resolution segmentation of soil moisture imagery by watershed pyramids with region merging

A new image segmentation method is presented for application to remotely sensed imagery. The method incorporates the advantages of previous watershed segmentation techniques while greatly improving the two main disadvantages of such techniques: computational efficiency and control over region scale. Computational efficiency is attained through the use of a multi-resolution image pyramid, and control over region scale is accomplished through a variational region merging algorithm. We apply the segmentation method to remotely sensed estimates of surface soil moisture. Experimental results of computational efficiency and comparison with other segmentation methods are presented.

A pyramid-based front-end processor for dynamic vision applications

Real-time vision tasks such as autonomous driving require prodigious computing power yet practical vision systems need to be compact and low cost. I suggest that such systems can be partitioned into two computing stages, for and interpretation, respectively, and that each of these stages can be implemented as a single integrated circuit or a small number of such circuits. The two stages differ in data representation and computing architecture: The front-end stage operates on sampled image data and its computations are performed on a processor optimized for signal level processing. The high-level stage operates on abstract and symbolic image data and its computations ate performed on a general-purpose microprocessor. In this paper I describe a segmented pipeline architecture for front-end processing and a chip level processor implementation. This vision front-end processor is designed to support early vision functions, such as feature enhancement and motion and stereo analysis, for a broad range of dynamic vision applications. The approach makes systematic use of a multiresolution pyramid framework to achieve high computational efficiency, robustness, and precision.

Multiresolution Design of Aperture Operators

The design of an aperture operator is based on adequately constraining the spatial domain and the graylevel range in order to diminish the space of operators and, consequently, the estimation error. The design of a resolution constrained operator is based on adequately combining information from two or more different resolutions and has the same motivation, that is, diminish the space of operators to facilitate design. This paper joins these approaches and studies multiresolution design of aperture operators for grayscale images. Spatial resolution constraint, range resolution constraint and the combination of both constraints are characterized, and the error increase by using the constrained filter in place of the optimal unconstrained one is analyzed. Pyramidal multiresolution design involves applying the resolution constraint approach hierarchically, from the higher to the lower resolution space. These approaches are also characterized and their error increase analyzed. The system that has been implemented to design pyramidal multiresolution operators is described and has its complexity (memory and runtime) analyzed. Several simulations and two applications for deblurring are shown and compared to optimal linear filters. The results confirm the usefulness of the approach.

ANALYSIS OF SYMMETRIC MULTIWAVELETS AND ITS APPLICATION FOR IMAGE COMPRESSION

Multiwavelets are the new addition to the body of wavelet theory. It is also based on the idea of multiresolution analysis (MRA). An MRA is usually generated by one scaling function. However, such wavelets cannot possess the properties of compact support, linear phase, and orthogonality simultaneously. Realized as matrix-valued filterbanks leading to wavelet bases, multiwavelets can offer these three properties simultaneously which are strongly desired in many applications, such as a fast multiresolution pyramid decomposition algorithm of image with the 2 ґ 2 matrix. To succeed using the EZW algorithms, we wish there still are some of the relationships between ancestors and their offspring. But the relationship is not very clear after the conventional iteration of multiwavelet decomposition which is similar to the scalar wavelet decomposition, and the encoding effect and efficiency are not very good. Therefore, this paper presents full new decomposition and quantization methods adapt to the symmetric property of multiwavelets. Extensive experimental results demonstrate that our techniques exhibit performance equal or superior to the conventional decomposition methods.

A non-self-intersecting adaptive deformable surface for complex boundary extraction from volumetric images

This paper proposes a non-self-intersecting multiscale deformable surface model with an adaptive remeshing capability. The model is specifically designed to extract the three-dimensional boundaries of topologically simple but geometrically complex anatomical structures, especially those with deep concavities such as the brain, from volumetric medical images. The model successfully addresses three significant problems of conventional deformable models when dealing with such structures-sensitivity to model initialization, difficulties in dealing with severe object concavities, and model self-intersection. The first problem is addressed using a multiscale scheme, which extracts the boundaries of objects in a coarse-to-fine fashion by applying a multiscale deformable surface model to a multiresolution volume image pyramid. The second problem is addressed with adaptive remeshing, which progressively resamples the triangulated deformable surface model both globally and locally, matching its resolution to the levels of the volume image pyramid. Finally, the third problem is solved by including a non-self-intersection force among the customary internal and external forces in a physics-based model formulation. Our deformable surface model is more efficient, much less sensitive to initialization and spurious image features, more proficient in extracting boundary concavities, and not susceptible to self-intersections compared to most other models of its type. This paper presents results of applying our new deformable surface model to the extraction of a spherical surface with concavities from a computer-generated volume image and a brain cortical surface from a real MR volume image.

Multiresolution Analysis for Optimal Binary Filters

The performance of a designed digital filter is measured by the sum of the errors of the optimal filter and the estimation error. Viewing an image at a high resolution results in optimal filters having smaller errors than at lower resolutions; however, higher resolutions bring increased estimation error. Hence, choosing an appropriate resolution for filter design is important. The present paper provides expressions for both the error of the optimal filter and the design error for estimating optimal filters in a pyramidal multiresolution framework. The analysis is facilitated by a general characterization of suitable sequences of resolution-constraint mappings. The error expressions are generated from resolution to resolution in a telescoping manner. To take advantage of data at all resolutions, one can use a hybrid multiresolution design to arrive at a multiresolution filter. A sequence of filters is designed using data at increasing resolutions, each filter serves as a prior filter for the next, and the last filter is taken as the designed filter. The value of the multiresolution filter at a given observation is based on the highest resolution at which conditioning by the observation is considered significant.

Robust multiresolution alignment of MRI brain volumes.

An algorithm for the automatic alignment of MRI volumes of the human brain was developed, based on techniques adopted from the computer vision literature for image motion estimation. Most image registration techniques rely on the assumption that corresponding voxels in the two volumes have equal intensity, which is not true for MRI volumes acquired with different coils and/or pulse sequences. Intensity normalization and contrast equalization were used to minimize the differences between the intensities of the two volumes. However, these preprocessing steps do not correct perfectly for the image differences when using different coils and/or pulse sequences. Hence, the alignment algorithm relies on robust estimation, which automatically ignores voxels where the intensities are sufficiently different in the two volumes. A multiresolution pyramid implementation enables the algorithm to estimate large displacements. The resulting algorithm is used routinely to align MRI volumes acquired using different protocols (3D SPGR and 2D fast spin echo) and different coils (surface and head) to subvoxel accuracy (better than 1 mm).

Optimization of mutual information for multiresolution image registration

We propose a new method for the intermodal registration of images using a criterion known as mutual information. Our main contribution is an optimizer that we specifically designed for this criterion. We show that this new optimizer is well adapted to a multiresolution approach because it typically converges in fewer criterion evaluations than other optimizers. We have built a multiresolution image pyramid, along with an interpolation process, an optimizer, and the criterion itself, around the unifying concept of spline-processing. This ensures coherence in the way we model data and yields good performance. We have tested our approach in a variety of experimental conditions and report excellent results. We claim an accuracy of about a hundredth of a pixel under ideal conditions. We are also robust since the accuracy is still about a tenth of a pixel under very noisy conditions. In addition, a blind evaluation of our results compares very favorably to the work of several other researchers.

A new flexible bi-orthogonal filter design for multiresolution filterbanks with application to image compression

We propose a new fast method with great potential for multiresolution pyramid decomposition of signals and images. The method allows unusual flexibility in choosing a filter for any task involving the multiresolution analysis and synthesis. Using our method, one can choose any low-pass filter for the multiresolution filtering. This method enabled us to choose the best filters for set partitioning in hierarchical trees (SPIHT) image compression for the corresponding support sizes. The compression results for our seven tap filters are better than those of the 9/7 wavelet filters and approximately the same as those of the 10/18 filters, while at the same time our seven tap filters are faster than 10/18 filters.

Variable‐Resolution Displays for Visual Communication and Simulation

AbstractThe spatial resolution of the human visual system decreases as a function of angular distance from the direction of gaze. This fact can be exploited in various applications to increase image compression, to increase image processing speed, and to decrease access time for image data. This paper describes a multiresolution pyramid method for creating variable resolution displays in real time using general purpose computers. The location of the high resolution region(s) can be dynamically controlled by the user with a pointing device (e.g., a mouse or an eye tracker) or by an algorithm. Our method has a number of advantages: high computational speed and efficiency, smooth artifact‐free variable resolution, and compatibility with other image processing software/ hardware. Applications to video communications (MPEG) and graphic simulation are described.

Video coding with a variable block-sizing technique in the wavelet transform domain

In this paper, we present an efficient video coding technique based on a variable block-sizing (VBS) technique and the wavelet transform. Quadtrees are used for VBS segmentation on the wavelet-transformed frame which is decomposed into pyramid multiresolution subbands. Feature areas are extracted during the growth of the quadtree on each subband. Motion estimation/compensation and vector quantization are performed on only the extracted feature areas in the subband. Since the VBS technique is very effective in lowering overall coding rates, the proposed coder is designed for very low bit-rate video coding. Simulation results are presented at 14.4 kbits/s for videoconferencing sequences. To evaluate the performance of the proposed coder, comparisons are made with results obtained by the H.263 standard.

Motion estimation using a complex-valued wavelet transform

This paper describes a new motion estimation algorithm that is potentially useful for both computer vision and video compression applications. It is hierarchical in structure, using a separable two-dimensional (2-D) discrete wavelet transform (DWT) on each frame to efficiently construct a multiresolution pyramid of subimages. The DWT is based on a complex-valued pair of four-tap FIR filters with Gabor-like characteristics. The resulting complex DWT (CDWT) effectively implements an analysis by an ensemble of Gabor-like filters with a variety of orientations and scales. The phase difference between the subband coefficients of each frame at a given subpel bears a predictable relation to a local translation in the region of the reference frame subtended by that subpel. That relation is used to estimate the displacement field at the coarsest scale of the multiresolution pyramid. Each estimate is accompanied by a directional confidence measure in the form of the parameters of a quadratic matching surface. The initial estimate field is progressively refined by a coarse-to fine strategy in which finer scale information is appropriately incorporated at each stage. The accuracy, efficiency, and robustness of the new algorithm are demonstrated in comparison testing against hierarchical implementations of intensity gradient-based and fractional-precision block matching motion estimators.

High Performance Hierarchical Block-based Motion Estimation for Real-Time Video Coding

The paper addresses the problem of block-based motion estimation (BBME) for video sequence coding, and a hierarchical strategy that sharply reduces the computation is proposed.Estimation is performed by computing a coarse motion field calculated at the highest level of a multiresolution pyramid, and successively refining it. The preliminary estimation is performed by a full-search fixed-size block matching, whose computational load is low due to the reduced scale.At the successive levels, the initial field is updated by both increasing the spatial density and refining the vectors. In the areas where the approximation is satisfactory, the spatial sampling is left unchanged and only the vectors are updated; in the other areas, a higher number of vectors are used.A novel strategy to perform vector propagation and adaptive correction jointly has been implemented, which allows both an efficient level-to-level update of the motion field and an effective recovery from wrong estimations.The advantages of the proposed method are two-fold: firstly, it produces a motion field whose density is locally adaptive, thus allowing the transmission of a smaller number of motion vectors. Moreover, it reduces the BBME task when a more detailed estimation would not produce a significant improvement, thus achieving a lower computational load that makes it particularly suited to the implementation of real-time video codecs.

Adaptive multiwavelet initialization

The multiwavelet concept uses a set of scaling functions and a set of wavelets to generate an orthogonal multichannel multiresolution pyramid decomposition for finite energy signals. The multiple scaling functions extract the lowpass information of the input data set, and the multiwavelets extract the bandpass information. When the lowpass filters associated with the scaling functions are cascaded, a multiresolution pyramid decomposition/reconstruction system is formed with each pyramid convolution operator having several inputs and several outputs. However, there is only one data set available to initialize this process. This paper addresses the question of how to modify the data set using prefilters so that its decomposition contains the most useful information for the chosen application. The best prefilters are determined by the minimization of the energy of preselected decomposition components. The resulting decomposition is, therefore, signal adaptive, and under appropriate conditions, perfect reconstruction of the input data set can be achieved with a proper postfiltering. The detailed discussions in the paper are focussed on the two-wavelet and two-scaling function case; the general multiwavelet case is addressed at the end of the paper. A compression example is provided to demonstrate the performance of the optimally initialized multiwavelet method and to compare it with a single wavelet method and another multiwavelet initialization method proposed by other authors.

A multiresolution approach for contour extraction from brain images.

Many image registration methods use head surface, brain surface, or inner/outer surface of the skull to estimate rotation and translation parameters. The inner surface of the skull is also used for intracranial volume segmentation which is considered the first step in segmentation and analysis of brain images. The surface is usually characterized by a set of edge or contour points extracted from cross-sectional images. Automatic extraction of contour points is complicated by discontinuity of edges in the back of the eyes and ears and sometimes by a previous surgery or an inadequate field of view. We have developed an automated method for contour extraction that connects discontinuities using a multiresolution pyramid. Steps of the method are: (1) Contour points are found by an edge-tracking algorithm; (2) A multiresolution pyramid of contour points is constructed; (3) Contour points of reduced images are found; (4) From the continuous contour found at the lowest resolution, contour points at a higher resolution are found; (5) Step 4 is repeated until contour points at the highest resolution (original image) are found. The method runs fast and has been successful in extracting contours from MRI and CT images. We illustrate the method and its performance using MRI and CT images of the human brain.

Multiresolution locally expanded HONN for handwritten numeral recognition

In this paper, we propose a neural network architecture, multiresolution locally expanded high order neural network (MRLHONN) to solve the problem of handwritten numeral recognition. In this recognition scheme, the multiresolution representation of character image is input into a high order neural network (HONN), while in each resolution, only neighboring pixels are expanded to produce high order input. The property of this architecture is that, the local expansion alleviate the problem of large connecting weight set, and the multiresolution representation remedy the inadequacy of local expansion. Two forms of multiresolution representations, quadtree representation and Gaussian pyramid, were used in experiments. The recognition results demonstrate the efficiency of the proposed architecture.

Digital Television Broadcasting: Nondisruptive Improvement over Time

The Federal Communications Commission (FCC) decided, at an early date, that it was important for the digital broadcasting system to be upgradeable over time. Therefore, it established, as an important desideratum for the system to be chosen, that it could be improved in a nondisruptive manner i.e., without making the original equipment obsolete. An effective way to do this is to formulate a single baseline system that produces standard-definition imagery, and to carry out any later upgrading exclusively by adding one or more enhancement signals. Enhanced receivers would extract all data streams to create improved imagery. This approach to upgrading permits the manufacture of digital receivers (and set-top converters for NTSC receivers) of the lowest possible cost since high-definition decoding and signal-processing capability is unnecessary If the enhancement signals are transmitted by means of nonuniform constellation, then they will appear to be random noise to baseline receivers, guaranteeing that such receivers will continue to be usable regardless of the exact nature of the enhancement signal(s). While it would be preferable for the baseline system to be progressively scanned, it would be possible to permit both interlaced (I) and progressive (P) baseline formats to be used and yet to design enhanced receivers in such a way that they would operate properly with both. The source coding required in such a system is already well known by such names as pyramid coding, layered coding, or multiresolution coding. Channel-coding methods are also described that permit receivers to extract data from the transmitted signal in accordance with the local SNR and their signal-processing capabilities.

Multiresolution Vector Quantization for Video Coding

In this work, we propose a coding technique that is based on the generalized block prediction of the multiresolution subband decomposition of motion compensated difference image frames. A segmentation mask is used to distinguish between the regions where motion compensation was effective and those regions where the motion model did not succeed. The difference image is decomposed into a multiresolution pyramid of subbands where the highest resolution subbands are divided into two regions, based on the information given by the segmentation mask. Only the coefficients of the regions corresponding to the motion model failure are considered in the highest resolution subbands. The remaining coefficients are coded using a multiresolution vector quantization scheme that exploits inter-band non-linear redundancy. In particular, blocks in one subimage are predicted from blocks of the adjacent lower resolution subimage with the same orientation. This set of blocks plays the role of a codebook built from coefficients inside the subband decomposition itself. Whenever the inter-band prediction does not give satisfactory results with respect to a target quality, the block coefficients are quantized using a lattice vector quantizer for a Laplacian source.

Iterative multiresolution algorithm for image reconstruction from the magnitude of its Fourier transform

Iterative algorithms are currently the most effective approaches to solving a number of difficult signal reconstruction and recovery problems, and all of these algorithms suffer from stagnation and computational complexity. We propose a new multiresolution iterative approach that employs the concept of a multiresolution pyramid. This method attempts to solve the problem of image reconstruction from the measurement of the image’s Fourier modulus by decomposing the problem onto different resolution grids, which enables the iterative algorithm to avoid stagnation by providing a better initial guess and enabling a higher likelihood of arriving at a global minimum while dramatically reducing the computational cost. Results on both synthetic and real-world images are shown; a performance comparison with the direct iterative algorithm demonstrates the effectiveness of our approach in terms of convergence, robustness and computational efficiency.