Tree Skeleton Research Articles

Topological volume skeletonization and its application to transfer function design

Topological volume skeletonization is a novel approach for automating transfer function design in visualization by extracting the topological structure of a volume dataset. The skeletonization process yields a graph called a volume skeleton tree, which consists of volumetric critical points and their connectivity. The resultant graph provides critical field values whose color and opacity are accentuated in the design of transfer functions for direct volume rendering. Visually pleasing results of volume visualization demonstrate the feasibility of the present approach.

Vascular tree object segmentation by deskeletonization of valley courses

In this paper, we propose a valley-course-based image segmentation technique for tree-like object delineation, as an alternative to the traditional centerline-based methods. This technique consists of valley-course extraction, skeleton pruning and deskeletonization. Valley courses, constructed from valley points that are obtained by star-pattern scanning over an image, offer a natural manner of identifying tree skeletons. Unattached segments are removed using morphological operations. A structured tree is then constructed from the skeletons by using a tree pruning/spanning algorithm. A fleshy tree-like object is obtained by a deskeletonization procedure, which consists of extracting tree boundary in vicinity of the skeletons in the original image. The tree boundary is determined by identifying paired edge points at a valley point. A derivative-free edge identification approach is proposed, which defines an edge point at a side-slope by a relative intensity drop with respect to the local background. An empirical formula using a logarithmic function of local intensity contrast offers desirable characteristics of adaptability and stability. The adaptability of edge points to the local background is attributed to the compression behavior of logarithmic function. Furthermore, stability to noise is resulted because derivative operations are not used. The segmentation technique was validated using coronary angiographic images.

Statistics of merging peaks of random Gaussian fluctuations: skeleton tree formalism

Cosmological bound objects are generally considered to be formed from the local maxima of cosmological density fluctuations, which are often assumed to be Gaussian random fields. In order to study the statistics of those objects that are the result of hierarchical merging, we propose skeleton tree formalism, which can analytically distinguish episodic merging from continuous accretion in the mass-growth processes. This distinction was not clear in the extended Press–Schechter (PS) formalism. Skeleton tree formalism is a natural extension of peak theory, which is an alternative formalism for the statistics of bound objects. Fluctuation-field smoothing with a Gaussian filter produces a landscape by adding the extra dimension of the filter-resolution scale to the spatial coordinate of the fluctuation. In this landscape, a smoothed peak is nesting alongside the neighbouring peak and appears as a critical point called a sloping saddle, which can be interpreted as a destroyed object during a merger event in the context of the hierarchical structure formation. The topological properties of the landscape can be abstracted as skeleton trees, which consist of the line process of the smoothing peaks and the point process of the sloping saddles. According to this abstract topological picture, in this paper, we present the concept and the basic results of skeleton tree formalism in describing (1) the distinction between accretion and a merger in the hierarchical structure formation from various initial random Gaussian fields; (2) the instantaneous number density of the sloping saddles, which gives the destruction rate in the mergers; (3) the number densities of all the peaks, nesting and non-nesting, with simple and analytical distinguishing definitions; (4) the self-consistency of the formalism in reproducing the statistics, including the conservation equation, of all the peaks; (5) the instantaneous number density of the reforming objects, which is derived from the conservation formula of the non-nesting peak; and (6) the mean growth history of the objects, which is reproduced from the rates of destruction, reformation, and from the relative accretion growth.

Age-dependent bark photosynthesis of aspen twigs

The photosynthetic performance of trembling aspen (Populus tremula L.) twigs and leaves was studied in relation to selected structural features of aspen bark. PFD transmittance of intact periderm was reduced by about 90% in current-year twigs through peridermal thickening. However, because of drastic changes within the bark microstructure, PFD transmittance increased in 1-year-old twig segments up to 26% of the incident PFD. On a unit surface area basis, the chlorophyll content of young twigs (425 mg Chl m–2) almost reached that of leaves (460 mg Chl m–2). The chlorophyll content of aspen bark chlorenchyma was clearly age-dependent, even increasing in current-year twigs with advancing internodal age. The low bark chlorophyll a/b ratios (about 2.6 compared with 3.9 in leaves) indicate that bark chloroplasts are shade-adapted. Positive net photosynthesis was not found in aspen twigs, but apparent respiration was distinctly reduced in the light due to light-driven carbon refixation (bark photosynthesis) within the chlorenchymal tissues. Under constant microclimatic conditions, dark respiration rates were strongly correlated with stem-internal CO2 refixation. In accordance with increasing dark respiration rates, the efficiency of this carbon recycling was generally greater in the metabolically more active, younger twig segments than in older segments; carbon refixation rates reached up to 80% of dark respiration values. At least in young twigs and branches and thus in the light-exposed outer parts of tree crowns, respiratory CO2 losses by the tree skeleton could efficiently be reduced. Refixation of carbon dioxide may be of great importance for carbon budgets in the environmentally controlled or pathogen-induced leafless states of deciduous aspen trees.

Skeleton Trees for the Efficient Decoding of Huffman Encoded Texts

A new data structure is investigated, which allows fast decoding of texts encoded by canonical Huffman codes. The storage requirements are much lower than for conventional Huffman trees, O(log^2 n) for trees of depth O(log n), and decoding is faster, because a part of the bit-comparisons necessary for the decoding may be saved. Empirical results on large real-life distributions show a reduction of up to 50% and more in the number of bit operations. The basic idea is then generalized, yielding further savings.

Breathing Like a Mountain

I couldn't speak about Gulaga for about 3 months after being there. Not even to myself! The experience of this sacred mountain seemed so powerful that I knew it needed time to be integrated - its own time, that is. I have been involved in Outdoor Education for about 15 years, mostly with adolescents, through schools. And yes, the camps were worthwhile, albeit short, especially in the area of personal development, my particular area of interest. But what gave me the biggest buzz, was when kids really connected with their surroundings - went beyond normal experiences, beyond words, to experience some sense of Otherness'. Like being up before dawn & staggering up some mountain to get a breathtaking sight of creation unfolding; or canoeing on the Kangaroo River in a drowned river, valley surrounded by tree skeletons that in the heavy mist were indistinguishable as to whether they were above or below water, with the haunting tune of a didgeridoo lending an even more surreal atmosphere. When kids became awed at the raw beauty & power of Nature, this is what I always hoped for. Of course you cannot always plan for those "gifts of grace", but I tried. I'd always incorporate 'solo' time; we'd enter deep silence through caves; star gaze for hours on clear nights; write poetry, share poetry; cultivate awareness, etc. But this aspect was so infinitesimally small & really I was out of step with most of the programs that jam-packed so much into the day leaving precious little time for quiet reflection, Or hurtled kids through the bush on mountain bikes. Or created dozens of initiative tasks that could just as easily been done on the school oval. I never felt at ease with 'using' the bush to satisfy outcome - based programs. How different was this to viewing the earth as a resource to be plundered - and let's face it, taking 130 kids into a fragile area en masse, or into any area en masse, is very plundering!! Anyway, I guess I was seeking a deeper connection with the earth myself. And this is where Gulaga comes in. It was called a pilgrimage. A pilgrimage at Easter to Mount Gulaga on the south coast of NSW. I was reluctant to go but I went anyway. I was hanging on by the thinnest of threads until the end of the term when I was to go on long service leave for 12 months. I promised myself that I would give no energy out to others. That effectively meant I spent a lot of time in silence. It probably prepared me for the transition of leaving the city behind and entering into the wilderness, what some have referred to as entering into wilderness psychologically as well as physically (Greenway 1995). Mountains have always been known as sacred places, places that make our spirits soar. They join heaven and earth. People have always made pilgrimages to mountains for this very reason. They are holy sites, places to experience replenishment, to breathe in the universe. The word 'spirit' comes from the Latin word 'spirarae' which means 'to breathe together' (Swan 1996) Dulumunmun (Uncle Max), a Yuin elder, was to be our guide on this pilgrimage to Gulaga. His Yuin ancestors have sung this land since the beginning of time. He started telling the Dreamtime stories a few hours out of Sydney. We not only heard but saw the stories of Koorakari, Wind Spirit, stories about Creation, about the Birthing Law, about the Circle of Life. It gave new meaning to the study of a sacred text. And I felt my relationship to the land changing, deepening. …

Regeneration of Natural Pine Forest - Review of Work Done After the 1989 Fire in Mount Carmel, Israel

In September 1989 a fire burned a large natural Pinus halepensis Mill. forest on Mt. Carmel, Israel. This paper summarizes the main results of five years of research, in which the effects of natural factors and management on the development of the forest and the vegetation were studied. It was found that the burned pine tree skeletons were correlated with the spatial pattern of seed germination.. Fewer pine seedlings were found one year after the fire near the burned trunks, but the survival and growth rate of these young pine trees was higher in the following four years. Pine ash was found to inhibit post-fire seed germination, offering a possible explanation for the apparent effect of the old burned trees on the spatial pattern of the new pine seedlings. Both laboratory experiments and field measurements indicate that the high pH of the ash, is the main factor responsible for the inhibition of germination. We examined several management regimes designed to enhance the growth of the young post-fire pine trees and assess their influence on the recovery of the forest. The results revealed that four years after fire, and three years after treatments, forest regeneration was mainly affected by the natural process while management had only a marginal effect. Management such as cutting and leaving, or cutting and removing the burned trunks and twigs from the plots, had almost no effect on species composition and cover. However, thinning of Pinus and Cistus seedlings increased survival and growth of remaining seedlings.

Parallel Implementation of Tree Skeletons

Trees are a useful data type, but they are not routinely included in parallel programming systems, in part because their irregular structure makes partitioning and scheduling difficult. We present a method for algebraically constructing implementations of tree skeletons, high-level homomorphic operations that execute in parallel. Many computations on binary trees can be performed inO(logn) parallel time usingnprocessors, even taking account of communication costs. We extend these results to trees with arbitrary and variable degree. Then we show that it is possible to implement a distributed version of homomorphisms on binary trees, takingO(n/p+ log2p) parallel time onp < nprocessors, for trees of any skew and taking full account of communication costs. Under slightly stronger restrictions on the underlying functions, this can be improved toO(n/p+ logp). Furthermore, the technique for deriving distributed versions is algebraic, allowing the automatic generation of code for SPMD and data-parallel architectures.

Visual simulation of botanical trees based on virtual heliotropism and dormancy break

AbstractRealistic image synthesis of botanical trees has many applications. Since the generation of ‘tree skeletons’ having natural visual impressions is essential to realistic image synthesis, various methods of modelling skeletons, especially growth models, have been presented. However, no one has succeeded in simulating natural tree features which appear in a growth process, such as generation of a round tree crown, a weeping bough, an irregular branching pattern, or regeneration of a crown.This paper demonstrates, by showing several simulated examples, that a growth model having the abilities of heliotropism and dormancy break, which produces shapes of trees adapted to changes in the light environment, is effective in the CG simulation of realistic tree skeletons.

Three-dimensional knowledge driven reconstruction of coronary trees

A knowledge-driven approach to the three-dimensional reconstruction of coronary artery trees by means of two X-ray projections is proposed. The spatial reconstruction of the tree skeleton is discussed. A binary tree model of the arterial structure and its projections is employed. Consequently, the reconstruction of the three-dimensional tree skeleton is achieved by (a) matching the skeletons of corresponding pairs of vascular segments in the two views and (b) back-projecting the coupled skeleton projections. From a geometrical point of view, the matching problem is, in general, ill-conditioned. For this reason, additional information sources were used. Thus, the matching phase is accomplished by using both the imaging geometry information, as well as anatomical and topological knowledge, about the coronary arteries coded in a rule base. As far as the back-projection phase is concerned, an algorithm was developed based on: (1) the imaging geometry, (2) the bounding of the back-projection error and (3) a contiguity criterion.

On the multistage Bayes classifier

This paper deals with the decision rules of a multistage classifier based on a decision tree scheme. For the given tree skeleton and features to be used, the optimal (Bayes) decision rules (strategy) for performing the classification at each nonterminal node are derived and discussed. Since, in a general case, the risk minimization leads to the involved (inseparable by analytical methods) optimal decision rules, the separability problem of multistage recognition strategy is discussed and sufficient conditions for the separability of the multistage Bayes classifier are given. The separable suboptimal strategy is proposed and compared with the optimal one in respect of classification accuracy. The primary results are illustrated by simple examples.

Design of speaker identification schemes for large number of speakers

Design of speaker identification schemes for a small number of speakers (around 10) with a high degree of accuracy in controlled environment is a practical proposition today. When the number of speakers is large (say 50–100), many of these schemes cannot be directly extended, as both recognition error and computation time increase monotonically with population size. The feature selection problem is also complex for such schemes. Though there were earlier attempts to rank order features based on statistical distance measures, it has been observed only recently that the best two independent measurements are not the same as the combination in two's for pattern classification. We propose here a systematic approach to the problem using the decision tree or hierarchical classifier with the following objectives: (1) Design of optimal policy at each node of the tree given the tree structure i.e., the tree skeleton and the features to be used at each node. (2) Determination of the optimal feature measurement and decision policy given only the tree skeleton. Applicability of optimization procedures such as dynamic programming in the design of such trees is studied. The experimental results deal with the design of a 50 speaker identification scheme based on this approach.