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![A 35-45 days giraffe embryo (457 days gestation) from [21].](profile/Marcelo-Walter/publication/220721453/figure/fig1/AS:305571254292483@1449865272560/A-35-45-days-giraffe-embryo-457-days-gestation-from-21.png)
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![Figure 2: A 35-45 days giraffe embryo (457 days gestation) from [21].](profile/Marcelo-Walter/publication/220721453/figure/fig1/AS:305571254292483@1449865272560/A-35-45-days-giraffe-embryo-457-days-gestation-from-21_Q320.jpg)
The giraffe and its patches, the leopard and its spots, the tiger and its stripes are spectacular examples of the integration of a pattern and a body shape. We present an approach that integrates a biologically-plausible pattern generation model, which can effectively deliver a variety of patterns characteristic of mammalian coats, and a body growt...
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... start of the pattern formation process is most likely as soon as the melanocytes have finished their migration from the neural crest, about 35 days for the giraffe (out of 457 days for the total gestation time). At this time the fetus already has a recognizable shape, as can be seen in Figure 2, which shows a giraffe embryo with an estimated age of 35 to 45 days. ...
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... & ¦ and $ ¦ are the world radius and length of the cylin- der, which can be easily derived from such measurements as the length and girth of features of the real animal or its pictures (see for instance the black lines labelled through used for the giraffe fetus shown in Figure 2) where: ...
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... section describes how the CM model presented in Section 3.2 is integrated with the shape control presented in the previous sec- tion. This will allow the synthesis of CM patterns directly on a shape-changing geometry, such as the body of the animal growing and illustrated in Figure 12. Figure 7 shows a schematic repre- sentation of the whole process of pattern formation development in connection with the body growing. ...
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... whole point of integrating the pattern formation and growth is that the two are tightly linked in the fetal stage and hopefully this approach will create more accurate models of patterned animals. Figure 12 shows four phases in the development of the giraffe pattern on the fetus at 35 days (estimated start of pattern develop- ment), 90 days, 150 days and 300 days. It should be compared to the pattern of the giraffe at birth. ...
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... that the shape gradually approximates the proportions of the newborn while the spots get bigger. Figure 13 shows the same fetus at 35 days, but put in a position similar to the real one shown in Figure 2, for easier com- parison (we do not suggest that the pattern is actually that visible on the embryo, just that it is there). From the fetus to the adult, the body size grows by a liner factor of 100, from ¢ ¡ ¤ £ to ¢ £ . ...
Citations
... In CG, the previously mentioned results from Turk [10] and Witkin&Kass [11] were seminal in bringing the attention of Turing's work on patterning to the graphics community. Later, Walter et al. [18] presented many animal coat patterns using a cell-based system simulated on a changing geometry due to growth. More recently, Malheiros and colleagues [12] showed how to simulate complex patterns with saturated RD on growing domains. ...
... Few works pursued the link between dynamic growth and appearance. Walter et al. [2001] showed that cell division driven by growth produced the characteristic pattern of a growing giraffe and the big cats. Albeit distinct from a RD model, its basis was the discrete simulation of cell proliferation as the focus of the growth processes, running over an expanding 3D surface. ...
Previous research in pattern formation using reaction-diffusion mostly focused on static domains, either for computational simplicity or mathematical tractability. In this work, we have explored the expressiveness of combining simple mechanisms as a possible explanation for pigmentation pattern formation, where tissue growth plays a crucial role. Our motivation is not only to realistically reproduce natural patterns but also to get insights into the underlying biological processes. Therefore, we present a novel approach to generate realistic animal skin patterns. First, we describe the approximation of tissue growth by a series of discrete matrix expansion operations. Then, we combine it with an adaptation of Turing's non-linear reaction-diffusion model, which enforces upper and lower bounds to the concentrations of the involved chemical reagents. We also propose the addition of a single-reagent continuous autocatalytic reaction, called reinforcement, to provide a mechanism to maintain an already established pattern during growth. By careful adjustment of the parameters and the sequencing of operations, we closely match the appearance of a few real species. In particular, we reproduce in detail the distinctive features of the leopard skin, also providing a hypothesis for the simultaneous productions of the most common melanin types, eumelanin and pheomelanin.
... Um dos poucos trabalhos a modelar um processo de formação de padrão concomitantemente ao crescimento é o de Walter et al. [14], no qual foram realizadas simulações sobre superfícies bi e tridimensionais utilizando um modelo alternativo à reação-difusão, o Mosaico de Clones [15]. Neste trabalho, o corpo dos modelos utilizados foi submetido a um crescimento a diferentes taxas em cada parte do corpo, a partir de medidas obtidas experimentalmente, obtendo resultados bastante similares aos reais. ...
Modelos de reação-difusão são amplamente usados na simulação de formação de padrõesem seres vivos, sendo aplicados tanto como explicação destes fenômenos quantopara a geração de texturas em computação gráfica. No entanto, poucos estudos levamem conta a influência da forma da superfície sobre o padrão resultante. Neste trabalhorealizamos simulações com o modelo de reação-difusão não-linear de Turing emsuperfícies bidimensionais utilizando diferentes parâmetros e formatos de superfície.Nossos resultados mostram que a forma possui um efeito relevante sobre o padrão finalresultante, permitindo a transição de pintas para listras, a alteração da estabilidadee da robustez do sistema, e a obtenção de padrões geometricamente regulares.
... In fact, Computer Graphics has been widely using RD and CA as base models to generate pigmentation patterns. Further pioneering work on forms [8], growth [6] and simulation [29] made modeling natural phenomena a diverse and multidisciplinary area. However, most of the techniques were still very specific to the fields they dealt with, being sometimes ad hoc and quite complex. ...
... We have coupled uniform growth and saturated RD, imposing a limit only to U. To make the growth rate consistent over the simulated tissue, we further constrained the pattern into a growing square domain, and explicitly seeded the prepattern with uniformly spaced spots. Note that previous results for both giraffe and rosettes were only possible with cascade RD processes or more specialized computations [16,26,29,30]. Figure 1 shows another experiment, where a simulation is run to generate the texture for a specific moray eel species, Muraena melanotis. We again employed saturated RD, involving U and V . ...
This paper describes a novel model for coupling continuous chemical diffusion and discrete cellular events inside a biologically inspired simulation environment. Our goal is to define and explore a mini- malist set of features that are also expressive, enabling the creation of complex and plausible 2D patterns using just a few rules. By not being constrained into a static or regular grid, we show that many different phenomena can be simulated, such as traditional reaction- diffusion systems, cellular automata, and pigmentation patterns from living beings. In particular, we demonstrate that adding chemical saturation increases significantly the range of simulated patterns us- ing reaction-diffusion, including patterns not possible before such as the leopard rosettes. Our results suggest a possible universal model that can integrate previous pattern formation approaches, providing new ground for experimentation, and realistic-looking textures for general use in Computer Graphics.
... All of the previous procedural or data driven techniques discussed so far, uses some form of skeletal structure to drive the animation. In an alternate approach, the actual polygonal mesh itself has also been used by various researcher for animation output (James and Twigg, 2005;Shi et al., 2007;Walter et al., 2001). Whereas Kry et al. (2009) in his paper discusses the use of model deformations to generate the gait patterns to achieve motion. ...
Computer generated animation has become extremely popular in current
era involved not only in movies and games, but mainstream television,
education, scientific visualizations, Sports are but few noteworthy areas
of its application. Even though majorly two types of animation techniques
are used in the general industry; namely key-frame and motion capture,
there are various other techniques of generating autonomous animation.
In this survey paper we discuss the major techniques and approaches
towards procedurally generating autonomous animation of Quadruped
characters in specific. Initially we discuss various techniques used in
generating skeletons and creating a character rig for quadrupeds. The
various animation techniques are then discussed from footprint generation
to data driven methods and finally physics and dynamics based approached
and algorithms. All these methodologies tend to provide best possible
solution for solving the problem of generating involuntary and autonomous
animation of quadruped characters. In the end, a more suitable hybrid
technique is proposed which will be more practically feasible and user
friendly so it can be easily implemented.
... This analogy confers the RD model the status of a computational framework in which geometrical operations can be performed. In this paper, we introduce a model setup that exhibits a construction of the Voronoi diagram, considered as a fundamental geometrical structure that can be used to computationally reproduce many natural formations, like soap bubbles [7], bone cells [8] and pattern formation in some mammalian models [9]. ...
In this paper, a new method to solve computational problems using reaction diffusion (RD) systems is presented. The novelty relies on the use of a model configuration that tailors its spatiotemporal dynamics to develop Voronoi diagrams (VD) as a part of the system’s natural evolution. The proposed framework is deployed in a solution of related robotic problems, where the generalized VD are used to identify topological places in a grid map of the environment that is created from sensor measurements. The ability of the RD-based computation to integrate external information, like a grid map representing the environment in the model computational grid, permits a direct integration of sensor data into the model dynamics. The experimental results indicate that this method exhibits significantly less sensitivity to noisy data than the standard algorithms for determining VD in a grid. In addition, previous drawbacks of the computational algorithms based on RD models, like the generation of volatile solutions by means of excitable waves, are now overcome by final stable states.
... [Witkin and Kass (1991)] used a reactiondiffusion equation to generate stripe patterns. [Walter et al. (2001)] used a biological model to reproduce the texture of animal skin. ...
Geometric modeling has been one of the most researched areas in the medical domain. Today, there is not a well established methodology to model the shape of an organ. There are many approaches available and each one of them have different strengths and weaknesses. Most state of the art methods to model shape use surface information only. There is an increasing need for techniques to support volumetric information. Besides shape characterization, a technique to differentiate objects by shape is needed. This requires computing statistics on shape. The current challenge of research in life sciences is to create models to represent the surface, the interior of an object, and give statistical differences based on shape. In this work, we use a technique for shape modeling that is able to model surface and internal features, and is suited to compute shape statistics. Using this technique (s-rep), a procedure to model the human cerebral cortex is proposed. This novel representation offers new possibilities to analyze cortical lesions and compute shape statistics on the cortex. The second part of this work proposes a methodology to parameterize the interior of an object. The method is flexible and can enhance the visual aspect or the description of physical properties of an object. The geometric modeling enhanced with physical parameters is used to produce simulated magnetic resonance images. This image simulation approach is validated by analyzing the behavior and performance of classic segmentation algorithms for real images.
... Beaucoup de méthodes de génération de formes ont vu le jour dans la communauté d'imagerie numérique utilisant différents concepts souvent basés sur la vie artificielle ou la biologie : les procédés de réactiondiffusion [WK91,WFM01], les automates cellulaires [Dew88], les algorithmes génétiques [Sim94, LLD08, Lug09] et les fractales pour la synthèse de forme [Jac93] dont les L-system [Smi84,PHM96]. Nous ne rentrerons pas dans une description détaillée de ces méthodes car elles s'écartent de notre problématique. ...
Le modèle physique masses interactions est puissant pour la simulation de comportements dynamiques très divers et pour la production de mouvements expressifs, riches et d'une grande complexité. En revanche, une difficulté inhérente à ce type de formalisme pour la production d'images animées réside dans le fait que les masses ponctuelles n'ont pas de spatialité ; il est donc difficile de produire des séquences d'images animées par le rendu direct des masses ponctuelles décrivant le mouvement. D'une manière générale, il est donc nécessaire de développer des méthodes qui étendent la spatialité de ces masses ponctuelles pour compléter la chaîne de production d'images animées par modèle physique particulaire. Une méthode, proposée par le laboratoire ICA, répond à ce type de problématique en permettant d'étendre la spatialité des masses ponctuelles en considérant l'interaction physique entre ces masses et un milieu. Il s'agit d'une métaphore du procédé physique de la gravure. Celle ci a permis de produire des images animées convaincantes de divers phénomènes visuels. Nous présentons dans ce document un élargissement de cette méthode notamment au cas 3D, ainsi qu'à de nouveaux comportements. De plus, l'algorithme de cette méthode a été parallélisé, ce qui nous a permis d'obtenir des simulations calculées en temps réel en utilisant la puissance actuelle des cartes graphiques. Afin de maitriser au mieux les possibilités de la méthode, nous avons développé un logiciel comprenant une interface graphique manipulable et interactive permettant de modéliser avec aisance différents comportements. Cette méthode a été intégrée dans des installations interactives artistiques multi-sensorielles fournissant un comportement dynamique riche et configurable, tout en permettant une interaction en temps réel avec le spectateur.
... In several cases, there is a close relationship between material and the model surface. In [25], Walter et al. modeled the creation of different patterns found on mammalian coats and their behavior as the body grows. Xu et al. [29] applied salient feature curves to texture synthesis resulting in shape-revealing textures that stress the importance of shape characteristics. ...
Texture mapping is an important technique for adding visual details to geometric models. Image-based texture mapping is the most popular approach, but it relies on pre-computed images which often limit their use to static effects. For adding dynamic effects, procedural-based texturing is more adequate. Since it rely on functions to describe texturing patterns, procedural texturing allows for a more compact representation and control of visual effects by a simple change of parameters. In this work we describe GeoTextures, an approach that uses geodesic distance fields defined from multiple sources at different locations over a model surface to place, advect, and combine procedural visual effects over complex surfaces. The use of geodesics extends the scope of common procedural textures which are usually limited to using spatial 3D coordinates or 2D texture coordinates. We illustrate the flexibility of our real-time approach with a range of visual effects, such as time-based propagation of weathering phenomena, transparency effects, and mesh displacement over surfaces with smooth silhouettes using hardware based tessellation available in current graphics cards.
... In such cases, taking into account surface attributes in the texturing process allows for more appealing results. In [4], Walter et al. modeled the creation of different patterns found on mammalian coats as well as its behavior as the body grows. Xu et al. [5] applied surfaces salient feature curves to texture synthesis resulting in shape-revealing textures which reinforce or even highlights the shape essential characteristics. ...
Texture mapping is an important technique to add visual detail to geometric models. As an alternative to traditional image-based texture mapping, procedural textures are described by a function, with interesting properties such as compact representation, resolution independency and parametric adjustment of the visual appearance. Procedural textures are usually defined in the 2D texture space, making the result dependent on texture mapping coordinates assigned to the model, or in the 3D object space, implying in no correlation with the surface model. In this work we introduce GeoTextures, an approach that uses the geodesic distance, defined from multiple sources over the model, as a parameter that is taken into account by time-varying procedural textures. The use of geodesic distances allows the process to be both independent from the mapping of texturing coordinates and also conforming with the model surface. We validate the proposal by applying real-time procedural textures in complex surfaces.
