Geon-Driven Shape Models for Holistic

Semantics

Amitabha Mukerjee Hemant Muley

Amitabha Mukerjee

Department of Computer Science and Engineering

Indian Institute of Technology, Kanpur

Kanpur- 208 016, India.

Hemant Muley

Senior Project Associate

Mechanical Engineering Department,

Indian Institute of Technology, Kanpur

Kanpur- 208 016, India.

Email: hemantmuley@yahoo.com

Corresponding Author :

Amitabha Mukerjee

Phone: +91 512 597489 (O) 597995 (Lab)

Fax: +91 512 597995, 590725

Email: amit@cse.iitk.ac.in

Abstract

Cognitive theories of 3D shape decomposition have posited simple

volumetric primitives (Geon Structural Description or GSD). In this

work, we adapt these Geon models for 3D holistic shape design and

present a methodology for evaluating holistic aspects of 3D shape, such

as aesthetics, via user-interactive optimisation. The conceptual design

space is defined through a set of constraints on the parameters of the

decomposition. The preliminary shapes are evaluated by combining a

computable measure of their function with a subjective evaluation by

the user (for aesthetics etc). An important aspect in these early stages

of design is the ability of the user to redefine the design specification

itself; this is achieved by redefining either the parameter ranges, or the

geonic-decomposition itself. Results using an example of the common

household faucet are demonstrated on a 3D shape design tool OASIS

implemented on top of a standard CAD package.

KEYWORDS : Computer Aided Conceptual Design, Aesthetics Optimiza-

tion, Design Evolution, Interactive Genetic Algorithms, Variational 3D Shape,

Parametric Design.

Geon-Driven Shape Models forHolistic Semantics

1 Subjective Semantics for Holistic Shape

An important part of what a design means to the end user lies in its holistic

effect, which includes emotional, aesthetic and other aspects of experience

that are difficult to quantify. However, because of its strong emotional link,

these holistic factors often hold the key for the success of a given product in

the market.

In attempting to capture these aspects in a CAD context, one encounters

a difficulty regarding the nature of aesthetics that has been widely debated by

Philosophers : the objective group following Aristotle have held that aesthet-

ics inheres in the object and judgments can be independent of the observer,

while others such as Hume have argued for a subjective perception of beauty.

Kant, in his “Critique of Judgment” mediates between these two positions,

asserting that aesthetic judgment can have universal agreement despite be-

ing subjective in nature. This debate has also been observed in work on

aesthetics within the CAD tradition, with a group considering aesthetics as

decomposable in terms of object characteristics, and another group incorpo-

rating user feedback as part of the aesthetic evaluation.

In this work, we adopt the user-feedback approach towards capturing

aesthetic intent, and demonstrate a conceptual level aesthetic design tool

which incorporates the following novel aspects:

• Cognitive model of Shape : Decomposing the geometry into a cogni-

tively relevant set of components.

• Conceptual Design Space : Define the shape for any conceptual design

1

by constraining the parameter set that defines the conceptual class.

• Interactive Aesthetics Optimization : Use a combined objective func-

tion including both aesthetic (subjective) and functional (computed)

evaluation.

Brick Claw Cone Cylinder Fry

Horn Lemon Noodle Soap Wedge

Figure 1: Geons (“geometric ions”) component shapes described in terms

of four qualitative attributes (symmetry, size, edge and axis) of generalized

cylinders. These ten shapes have been proposed as fundamental shape prim-

itives by Biederman([1, 29]).

1.1 Cognitive Shape Model

How does one cognitively represent shape? An influential class of theories,

originating with Marr and Nishimara [18] holds that we construct a descrip-

tion of the object’s 3D structure from simple components. When needed

in tasks such as visual recognition, this structural description can be re-

constructed from all possible views, so that any given retinal image can be

matched. In Biederman’s well known Geon Structural Description (GSD)

version of this theory [1], structural descriptions are obtained by combining

simple 3D volumes called geons (Figure 1), along with the spatial relations

2

between them. While the use of geons as models for visual recognition has

given rise to some debate over the relevance of the viewpoint [29], psycholog-

ical evidence including verbal descriptions of 3D shapes, edge deletions from

wireframe drawings, and depth rotated images being recognized in constant

time appear to provide strong evidence for geonic decomposition in the men-

tal model, even though in certain object recognition tasks (where the geons

are not sufficiently distinguished) it may be merged with other viewpoint

specific metric data. In conceptual design, in particular, it is this non-metric

inherent shape aspect that is of the greatest interest, and this is what we

attempt to capture in this work.

Figure 2: A simple faucet is represented in Geon Structural Description

(GSD) with a cylinder for the inlet, two cylinders for the knob, and a noodle

(a curved cylinder) as its spout. A table-lamp may have a base and stem

that are cylinders, with a conical shade.

The GSD theory has been widely used in object recognition, where one

of the key issues has been that of obtaining a decomposition of a shape into

geonic components [27, 31]. However, it does not seem to have been widely

3

used as a model for the inchoate early-conceptualization of shape in CAD.

Intrinsically however, it is more difficult to construct a GSD model of a 3D

shape (since it may have multiple geonic decompositions), whereas given a

GSD model as may apply to a designers concept, it is easy to visualize or

display it (fig. 2). An early instance of the use of geons for conceptual design

may be found in [20], which uses generalized cylinders as geons and defines

conceptual shapes for simple 3D assemblies. On the other hand, Gregoire et

al [11] attempt to decompose a CAD model into its constituent geons.

A large related body of research in a similar direction attempts to use the

idea of design features as the basic shape primitive [13, 7, 6]. Features have

considerable importance in terms of being able to relate to part function and

manufacturing process design, and a case can also be made that humans are

cognitively aware of entities such as “slots” as rectangloid holes. The main

advantage of the geon model, is that it provides the designer with a small

finite lexicon of primitive shapes, whereas the set of features can be very

large and complex; in fact any two designers can never agree on a complete

set. Also the geon model as proposed here uses a well-defined structure for

joins whereas joining of features remains less studied (however, see [4], for a

join model that uses linguistic concepts such as “adjacent to” or “left of”).

1.1.1 Subjective Shape Aesthetics

As mentioned above, there are two philosophical approaches to aesthetics,

a: to construct an objective model of aesthetics as a function of the shape,

colour, and other attributes and b: subjective evaluation in which users di-

rectly provide the aesthetic assessment. The objective approach requires con-

structing a mapping from the design parameters to the aesthetics; in terms

of shape, this is possible only for simpler geometries such as in 2D orthogonal

4

Inlet cylinder+brick cylinder+brick brick

Knob cylinder+cylinder cylinder+cone+cone cylinder+cylinder

Spout fry+fry fry+cone wedge+cylinder

Inlet brick fry cone

Knob cylinder+cone+cone cylinder+cone+cone cone+cone

Spout fry+cylinder fry+cone fry+cone

Figure 3: Six faucets created using differing geonic components. Changing

the parametrization and join-constraints of the geons results in completely

different design instantiations.

shapes [22, 2, 19, 24]. A recent attempt for more general geometries is the

Fiores-II project [9, 23, 3] which attempts to correlate aesthetics in terms of

curve properties such as acceleration, sharpness, tension etc. The subjective

approach which is adopted in this work involves obtaining human feedback

and using these to guide the design evolution process. In recent years, in-

teractive evaluation is becoming popular (see survey in [28]) and examples

include [8, 21, 16]. Shape holistic feedback on complex geometries from users

is combined with traditional evaluation functions which may be based on

tools such as Finite Element Analysis or Computational Fluid Dynamics etc.

5

This process is implemented in the tool OASIS (Optimization of Aesthetic

Shape via Interactive Search) which works with I-DEAS.

1.2 Conceptual Design

Capturing the flexibility of conceptual design, requires the ability to model

the classes of shape as opposed to the unambiguous models [26] of traditional

Computer-Aided Design (CAD). While there have been many attempts to

approach this (see [12] for a review and an early co-variance approach), the

first step towards the dream was possible only after the Variational Geometry

models [17] were incorporated into the stream of Parametric Design. Despite

this flurry of progress (see a recent review by Hsu and Woon [15]), work

on Computer Aided Conceptual Design (CACD) remains largely confined to

the laboratory. Why should this be so? A recent survey points to three

factors [14]:

the problems originate in the endeavor in academia to introduce

abstract models, to develop highly specialized non-integral tools,

and to give preference to automated, rather than highly interac-

tive means.

In this work, we attempt to avoid these three pitfalls, and introduce an

interactive tool that is integrated with a leading commercial CAD system

and demonstrate this process on clearly defined mechanical CAD examples.

We construct computational models by mapping the notion of geons to

simple 3D primitives, and constraining their relative join poses through a set

of 3D motion parameters. The resulting model can then be placed in the

canon of traditional CAD practice, thus enabling the designer to harness a

powerful set of tools with which she can communicate and optimize her shape

6

ideas. The method requires the user to define an early model of the overall

shape, defined in terms of a few simple primitives, the shapes and relative

poses of which are specified by a set of constraints defined on the independent

geometric parameters (called driving parameters). Subsequently, the use of

interactive evaluation for aesthetics permits optimization and visualization

of a variety of shapes at an early stage of design. This permits a clearer

perspective of the design space, with the possibility of its re-evaluation. By

varying the geon types and the join geometries a wide variety of shapes can

be obtained with a limited vocabulary of part geometries. Figure 3 shows

six different concepts for the design of a faucet, that can be built up quickly

using simple geonic components.

2 Interactive Evolutionary Optimization

Genetic Algorithms (GA) is an iterative multi-front optimization procedure,

which has found wide applicability in design optimization, as can be seen in

the overviews [25, 10]. This work uses an interactive version of GA in order

to obtain user inputs on the aesthetics of the part. Similar approaches have

been used in fashion design [16], music composition [30], dam design [8], and

architectural layout design [19]. We incorporate a hybrid objective function

including both the user choice as well as a computed measure of functional

effectiveness. However, obtaining user’s choices for more complex geometries

is constrained by the number of visualizations that can be shown simultane-

ously, and also in the user’s consistency in evaluating shapes.

7

Initial Shape Space

IncrementalyEvolving DesignSpace

Final Design

Original Shape

Figure 4: Re-defining Design Specifications. As the designer explores the

design, new constraints emerge or new deficiencies may be observed in the

design specifications. This process is known as Visual Emergence and helps

the designer to refine the design space, possibly several times.

2.1 Design Space Re-Definition

One of the important benefits of an interactive optimization system such as

OASIS may be the facilitation of design space re-definition through direct

shape visualization (Figure 4).

It is the experience of most designers that the Design Specification (DS)

itself evolves as the designer explores further with the various attributes of the

design. This Visual Emergence is the result of active exploration of the design

space. In our experience with OASIS, we commonly find the three following

types of re-definition occurring during this early optimization interaction:

• Re-Defining the Design Specifications : Often the design space is deter-

mined by the range given to the various parameters. Here, occasionally

the optimum will appear at an extremity of the design space, so that

it becomes prudent to redefine the ranges of the parameters so as to

expand it in this direction, and reduce some of the values that are far

8

from this point so as to reduce the total search. A diagram showing

this conceptual process is shown in Figure 4.

• Changing the Parametrization : Another common issue is that once the

design is completely visualizable in 3D certain flaws come to the notice

of the designer, and these can then be rectified in the DS. Figure 5

shows an example where a part of the design space consists of invalid

designs – these were then reformulated to obtain a new DS.

• Redefining the Optimization Objective : The user, after some explo-

ration, realizes that the objective function does not capture some im-

portant aspects and changes the objective function. OASIS permits

changes in both DS and optimization objective between generations of

the run (which are slower than traditional GA due to the interactive

component).

3 Water Faucets

As an example task, we now take up the detailed design of a basin faucet

modeled using simple geonic elements for the inlet, outlet and knob. Each

of these design elements has a set of driving geometric parameters, in terms

of which all other shape parameters as well as joining constraints can be

defined.

In practice, coming up with this high-level shape parametrization is one

of the most important tasks for a designer in using conceptual design tools

such as OASIS. In fact, it is quite likely that the parametrization and the

constraint set would keep changing as the user viewed each defined constraint

space. Our parametrization is shown in Figure 6 and Figure 7, and was

9

Figure 5: Changing the parametrization. In this faucet, the parameter θ0 is

defined as (θ2 + 10 − 0.25 × θ1) but results in self-intersection for θ1 > 40◦.

The design space is then re-defined by defining the constraint as θ0 is equal

to (π - θ1).

arrived at after much exploration in the design space typified by the invalid

design shown in Figure 5.

Figure 6: Inlet and Outlet of the faucet with the driving parameters set as

{Wi ,Hi} and {Wo ,Ho ,Lo, θ1 , θ2} respectively. Combining these, we have

the constraints Wi = Wo , Hi = Ho .

10

Figure 7: Complete Faucet with Knob. Knob radius {Rb} is added to the

driving parameter set {Wo ,Ho ,Lo, θ1 , θ2}.

A design instance is obtained by instantiating the driving parameters

and this represents an individual in a population of design instances for the

interactive genetic algorithm. For evaluating the functioning of the faucet, we

seek to maximize the flow-rate of water coming out subject to the constraints

on its driving parameters. This is given as, Q = A(2gHnet)1/2, where “g” =

gravitational acceleration, Hnet = H - Hf where, H = pressure head between

the water source and the outlet of the faucet, A = cross-section area of the

outlet, Hf = head loss due to friction and bends and Hnet = net pressure

head. Other considerations such as weight minimization or ergonomic factors

have not been considered in this demonstration. The combined fitness for a

faucet in a population is,

Combined fitness = (1− wi)f1 + wif2

where f1 = Functional objective fitness and the weight 0 ≤ wi ≤ 1 indicates

the relative importance of the user’s evaluation f2. In practice, this balance

11

depends on how important is functional optimality; if this is very important,

one can use a lower wi, but where style is everything, one can even try wi = 1,

which leads to a purely user-driven design evaluation.

In our implementation, we use a real-coded version of GA with 5 design

parameters(Wo ,Ho ,Lo , θ1 , θ2 ) (as shown in Figure 7). The crossover and

mutation probabilities were chosen as 0.95 & 0.05 respectively, and real-

code distribution indexes as for crossover 2 & 20 for mutation. The initial

population of faucets (randomly generated) along with the second generation

is shown in Figure 8. The fourth population of faucets as shown in Figure

9 still contains some faucets (e.g. [A] and [E]) which are assigned negative

fitness by user. However, by generation ten, the faucets in the population

are all very similar, converging nearly to the users perception of aesthetics.

Figure 8: First randomly initialized and second evolved population (after

user’s feedback) of faucets.

12

Figure 9: Fourth and final (tenth) generations showing the evolved shapes

of faucets based on user’s feedback. While there are still some negatively

assessed shapes in the fourth population, by the tenth the shapes appear to

have converged to what the user finds acceptable.

4 Conclusion

In this work we have attempted to capture that part of design meaning

which lies in its holistic effect, and includes emotional, aesthetic and other

aspects of experience that are difficult to quantify. We have reported a

subjective system for evaluating the holistic aspects of design. An important

innovation is the use of a cognitively plausible set of primitives (geons) in

defining at the decomposition structure for conceptual design. By permitting

the user to interact directly at early phases of design, such approaches are

likely to present significant savings in the lifetime costs and also faster design

turnaround times. Compared to other systems handling conceptual design

or aesthetics in restricted domains, our approach permits the user to define

a wide class of shapes over a rich set of algebraic surfaces, and may thus be

considered a general-purpose holistic design tool.

13

In integrating several objectives (e.g. aesthetics and functional) a more

informative approach may be to present the user with a set of solutions

where no solution is better than(dominates) another for all the objectives.

Such solutions lie on the non-dominated front, and visualizing this set of

solutions can provide the user with an overview of a high-information content

boundary in the parameter space. This work is currently being integrated

with a multi-criteria evolutionary optimization method [5] for obtaining such

pareto-fronts.

A limitation of the current subjective approach is that interactive evalu-

ation often limits the search owing to human fatigue. One of the solutions

to this problem may be to show single individuals representative of a shape

class [16], obtained by finding “nearby” designs in the parameter-space of

the geonic models.

In OASIS as it is currently implemented, the process of re-defining the

design space requires an aborting of the current run and redefining the space

anew. This looses all of the experiences of the previous design space, which

needs to be carried onto the next phase of design. This requires a complete

algebraic constraint handler, which was not provided since the main intent

was as a demonstration vehicle; however such equation solvers are already

present in any parametric design engine, and it would be straightforward to

integrate such solutions fairly easily in practice.

One question that arises naturally when using a cognitively plausible

decomposition is whether one can define computational paradigms for user

preferences based on this decomposition. As an example, one may evaluate

the knob and the faucet outline on stylistic norms such as measures of line

crispness, acceleration or tension [23] as well as other shape attributes such as

aspect ratio, to evolve norms for stylistic homogeneity between the different

14

components in a generalized faucet model. This is likely to be an imporant

line of research involving aesthetic constraints that relate different design

components – e.g. the outlet would need to be longer if one has adopted an

airier profile on the knob. While aesthetics has been thought of as a holistic

aspect, would it be possible to define it on the components of the shape, a

study that we may call Decompositional Aesthetics? A suggestion towards

this possibility may indeed turn out to be one of the main contributions of

this work.

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List of Figures

1 Geons (“geometric ions”) component shapes described in terms of

four qualitative attributes (symmetry, size, edge and axis) of gen-

eralized cylinders. These ten shapes have been proposed as funda-

mental shape primitives by Biederman([1, 29]). . . . . . . . . . . . 2

18

2 A simple faucet is represented in Geon Structural Description (GSD)

with a cylinder for the inlet, two cylinders for the knob, and a noo-

dle (a curved cylinder) as its spout. A table-lamp may have a base

and stem that are cylinders, with a conical shade. . . . . . . . . . . 3

3 Six faucets created using differing geonic components. Changing the

parametrization and join-constraints of the geons results in com-

pletely different design instantiations. . . . . . . . . . . . . . . . . 5

4 Re-defining Design Specifications. As the designer explores the de-

sign, new constraints emerge or new deficiencies may be observed

in the design specifications. This process is known as Visual Emer-

gence and helps the designer to refine the design space, possibly

several times. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

5 Changing the parametrization. In this faucet, the parameter θ0 is

defined as (θ2 + 10 − 0.25 × θ1) but results in self-intersection

for θ1 > 40◦. The design space is then re-defined by defining the

constraint as θ0 is equal to (π - θ1). . . . . . . . . . . . . . . . . . . 10

6 Inlet and Outlet of the faucet with the driving parameters set as

{Wi ,Hi} and {Wo ,Ho ,Lo , θ1 , θ2} respectively. Combining these,

we have the constraints Wi = Wo , Hi = Ho . . . . . . . . . . . . . . 10

7 Complete Faucet with Knob. Knob radius {Rb} is added to the

driving parameter set {Wo ,Ho ,Lo , θ1 , θ2}. . . . . . . . . . . . . . . 11

8 First randomly initialized and second evolved population (after user’s

feedback) of faucets. . . . . . . . . . . . . . . . . . . . . . . . . . . 12

9 Fourth and final (tenth) generations showing the evolved shapes of

faucets based on user’s feedback. While there are still some neg-

atively assessed shapes in the fourth population, by the tenth the

shapes appear to have converged to what the user finds acceptable. 13

19

Biographical Notes of Authors :

1. Amitabha Mukerjee did his B.Tech. (’79) from the Indian Institute of

Technology, Kharagpur and his PhD from the University of Rochester (’85).

He is currently a professor in Computer Science and Engineering at the

Indian Institute of Technology, Kanpur, India, where he works on Spatial

Cognition, Geometric Modelling, and Robotics.

2. Hemant Muley, is a Senior Project Associate at Indian Institute of Tech-

nology, Kanpur, India. He completed his M.Tech. in Mechanical Engineering

from I.I.T. Kanpur in May 2003. His research interests are CAD, Geometric

Modeling and Computer Aided Conceptual Design.