Self-organizing tree models Based on Palubicki et al., “Self-oganizing tree models for image synthesis” in SIGGRAPH 2009 As part of CS 658 Mike Jones

Your reading What questions and comments did you have for this paper? What problem are they trying to solve? What have others done and why is that inadequate? How did they solve the problem? How is their solution a solution? Did you believe it? What’s next?

Objectives After class today you should be able to Compare Palubicki’s space colonization algorithm with Runion’s. Outline all of the factors and parameters which go into creating a tree in Palubicki’s model. Argue for or against Palubicki’s model in a specific hypothetical use scenario.

The Problem Genetic branching patterns are part but not all of the story. Nature vs. Nurture

Their Solution Self-organization This is more important than I thought on first reading. Architectural and self-organizing components Architectural: form determined by branching pattern Self-organizing: structure arises from individual “decisions” (fates in this case) Signaling Procedural brushes

Self-organization Mandelbrot’s fractal tree on the left. Note that branch segments get smaller with each generation. (Generation given by color). Ulam’s approach on the right. Branch segment length is constant, but buds have different fates. Buds that might collide with the tree die. The fact that bud fates change based on “decisions” based on local conditions is what makes this self-organizing. This isn’t new in tree modeling but “they advance[] this class of models beyond the visually rudimentary models in previous work.” Image from Palubicki et al. “Self-organizing tree models in image synthesis” in SIGGRAPH 2009

User Control “difficult to model older trees with irregular but harmoniously balanced crowns.” Self-organization within a confined space solves this problem. Quote from Palubicki et al. “Self-organizing tree models in image synthesis” in SIGGRAPH 2009 Image from Reeves and Blau “Approximate and probabilistic algorithms for shading and rendering structured particle systems” in SIGGRAPH 1985

Vocabulary Monopoidal Sympoidal Endogenous Exogenous Acropetal Basipetal Image from Palubicki et al. “Self-organizing tree models in image synthesis” in SIGGRAPH 2009

Space Colonization “The key modification is the introduction of buds as the only locations that can produce new branches.” Delete markers in the occupancy zone Move in average direction toward markers in the perception volume. Theta, rho and r set by user. Image from Palubicki et al. “Self-organizing tree models in image synthesis” in SIGGRAPH 2009

Shadows Q = max (C – s + a, 0) Q is light exposure C = all available light. Shadow contributed by a single bud is a/(b^q) where a = user defined parameter b = user defined parameter q = depth under the bud Sum up all the shadow contributions in each voxel to get the light distribution in the crown. q Image from Palubicki et al. “Self-organizing tree models in image synthesis” in SIGGRAPH 2009

Bud Fate Sylleptic is the simplest case. Why? Apical control is required to obtain excurrent forms. Why? Sylleptic: new branches in the same season as the supporting stem was created. Proleptic: new branches in the next year after supported stem was created Sympoidal: development moves to lateral branches and axial bud dies or becomes a flower Excurrent form: main trunk. Image from Palubicki et al. “Self-organizing tree models in image synthesis” in SIGGRAPH 2009

Apical Control: Extended BH Originally purely endogenous. Is their approach purely endogenous? User sets alpha and lambda Q is the light resource V is the growth inducing hormone Metamers = floor(v), internode lengths = v/n Image from Palubicki et al. “Self-organizing tree models in image synthesis” in SIGGRAPH 2009

Apical control: priority model What the difference in hormone distribution between extended BH and the priority model? 0.5 + 0.7 + 0.9 = 2.1 0.6 + 0.5 = 1.1 1.1 + 2.1 = 3.2 Average exposure per bud is used to seed the priority model. Image from Palubicki et al. “Self-organizing tree models in image synthesis” in SIGGRAPH 2009

Apical control: priority model Grey circles are priorities within different axes. Vertical axis is the primary axis. Top distribution is based only on light exposure Bottom distribution has apical control Image from Palubicki et al. “Self-organizing tree models in image synthesis” in SIGGRAPH 2009

Apical control: priority model N = number of buds supported by that axis. V_i = hormone going to bud i on the priority list. V = amount of hormone going into the axis. W = weight (see function below) Q_i = light at bud i. As before, v_base = alpha Q_base. Image from Palubicki et al. “Self-organizing tree models in image synthesis” in SIGGRAPH 2009

Apical control: priority model N = number of buds supported by that axis. V_i = hormone going to bud i on the priority list. V = amount of hormone going into the axis. W = weight (see function below) Q_i = light at bud i. As before, v_base = alpha Q_base. What the difference in hormone distribution between extended BH and the priority model? Image from Palubicki et al. “Self-organizing tree models in image synthesis” in SIGGRAPH 2009

What would it take to grow a tree?

Shedding Branches If a branch is too shaded, it can fall off.

Sketching Trees Image from Palubicki et al. “Self-organizing tree models in image synthesis” in SIGGRAPH 2009

Results Image from Palubicki et al. “Self-organizing tree models in image synthesis” in SIGGRAPH 2009

Results Image from Palubicki et al. “Self-organizing tree models in image synthesis” in SIGGRAPH 2009

Results Image from Palubicki et al. “Self-organizing tree models in image synthesis” in SIGGRAPH 2009

Benes’ Model

Wrap-up How does Palubicki’s model compare to Benes’ model? How does Palubicki’s model compare to Runions 07 model? How does Palubicki’s model compare to Reeves and Blau?