Projection-Based Models for Capturing Human
Concepts of Motions
Yohei Kurata and Hui Shi
SFB/TR 8 Spatial Cognition, Universität Bremen
Postfach 330 440, 28334 Bremen, Germany{ykurata,shi}@informatik.uni-bremen.de

Abstract. Projection-based models, which distinguish spatial relations using aframe of spatial reference, can be used as a foundation for modeling humanconcepts of motions. In this paper, the existing projection-based models are
systematized using short code names that symbolize the models’ characteristics.
Then, through the observation of these code names, we detect some missing
types of models that are applicable to the modeling of motion concepts.

1Introduction

Projection-based models [1] are spatial models that adopt a frame of spatial reference[2], which partitions the space on/around one object (called relatum), and distinguishspatial relations based on the set of partitioned fields over which another object(called referent) extends. Two sorts of projection-based models can be used as afoundation for modeling human concepts of motions. One is the models whose
relatum is represented by a directed line (DLine), called DLine-relatum models. They
can describe where and how a landmark (referent) extends around/on a path (relatum)and, accordingly, they may capture such path-featured motion concepts as “gotoward” and “pass by”. Another useful one is point-referent models. They candescribe where a destination (referent) is located with respect to a landmark (relatum)and, accordingly, they may capture such goal-oriented motion concepts as “go to thefront of” and “go to the north of”. Modeling of such motion concepts is important forthe development of systems and machines that work together with ordinary people on
spatio-dynamic tasks. In the last two decades, a number of projection-based models
have been developed. This paper demonstrates that these models are systematizedusing short code names that symbolize the models’ characteristics (Section 2). Then,making use of these code names, we detect some missing types of models that areapplicable to the modeling of human motion concepts (Section 3).

2

Coding Projection-Based Models

The existing projection-based models have adopted a large variety of frames. One
distinctive difference of these frames is their shapes: -, -, and -shaped framescan be used when the relatum is represented by a point [1, 3, 4]; †- and ‡- shaped
frames can be used when the relatum is represented by a straight DLine or a pair ofpoints [5-7]; and -shaped frames can be used regardless of the relatum’s geometric
type [8]. In addition, the frames are categorized by their orientation factors [2]:• absolute frame, whose orientation is determined extrinsically by the environment;• intrinsic frame, whose orientation is determined by the relatum’s intrinsic
orientation (e.g., facing direction, moving direction); and• relative frame, whose orientation is determined by the direction from the thirdobject (viewer) to the relatum.
For instance, “London is to the north of Paris,” “Manhattan is on the left-hand side ofStatue of Liberty,” and “Sphinx sits on the left of the pyramid in my view” refer to thespatial relations defined by the absolute, intrinsic, and relative frames, respectively.
Table 1 summarizes the existing projection-based models and their characteristics.
As this table indicates, these models are characterized by a small number of criteria:
the frame’s shape, its orientation factor, and the geometric type of the referent and therelatum. Meanwhile, the viewer’s geometric type seems not important, because theviewer has been always represented by a point because its function is to specify aviewpoint. Based on this observation, we assigned a code name XyZm-nd to eachprojection-based model in accordance with the following naming rules:• X: geometric type of the referent—P (point), PD (directed point), L (line), LD(DLine), LSD (straight DLine), R (simple region), or A (arbitrary point-set object),• y: type of frame—a, i, or r (absolute/intrinsic/relative frame),• Z: geometric type of the relatum—either PD or LSD when an intrinsic frame isadopted (i.e., y = i), and anything (P, PD, L, LD, LSD, R, or A) otherwise,Table 1. Existing projection-based models, together with their code names (P: point, PD:
directed point, L: line, LSD: straight DLine, R: simple region, A: anonymous point-set object).

relative

P[5][9]relative
intrinsic

P

Models of cardinal directions [1, 8]

absolute

A

Dipole Calculus [10, 11]ViewerSingle Cross [5]Relatum

Class

ReferentFramePP

PrP1-8LSD–

PrP1-8PiLSD 3-12

A–

AaA1-8intrinsic

LSD ×2–LSDiLSD 0-2

Ternary Point Configuration Calculus(TPCC) [4]relative

PP

P

PrP1-24

Bipartite Arrangements [6]intrinsic

LSD

LSD

–

LSDiLSD 3-12

P–

PaP1-4n

Model

Double Cross

ShapeCode Name2

P×22Star Calculus [3],,…

absoluteP

Oriented Point Relation Algebra [12],,…

intrinsic

PD×2–

PDiPD 1-nintrinsic

PPD–

PiPD 1-nintrinsic

PLSD–

PiLSD m-n

Ego Orientation [7]Orientation Calculi [7],…
,…

2• m/n: number of fields over/around the relatum, respectively, and• d: number of XyZm-n patterns that composes a single relation (omitted if d =1).
The rightmost column in Table 1 shows the code names assigned to the existingmodels. For instance, Single Cross [5] is assigned a code name PrP1-8, whichindicates that this model considers a point-like referent placed in a relative frame,
which is centered at a point-like relatum and defines one field over the point-likerelatum and eight fields around it. Double Cross [5, 9] has two code names: PrP1-82
and PiLSD 3-12. PrP1-82 reflects its original definition in [5] where spatial relations aredefined as the synthesis of two Single Cross relations (PrP1-8), whereas PiLSD 3-12reflects the reformulated definition in [9] that considers point-DLine relations.

3Projection-Based Models for Modeling Motion Concepts

As introduced in Section 1, DLine-relatum models and point-referent models arepotentially useful for modeling human concepts of motions. Each DLine-relatum
model is given a code name like XiLD m-n or XiLSD m-n. The model may be used tocapture where and how a landmark X extends around/on a path LD/LSD. We currently
have PiLSD m-n (Double Cross in [9], Orientation Calculi [7]) and LSDiLSD m-n(Bipartite Arrangements [6]), while RiLSD m-n and LiLSD m-n are missing. The modelsof RiLSD m-n and LiLSD m-n may capture path-featured motions concepts that presume
the landmark’s spatial extension, such as “go into” and “go across.” Thus, thesemodels are particularly useful when handling the motions in a small-scale space (e.g.,apartments). On the other hand, each point-referent model is given a code name like
PyZm-n. The model may be used to capture the relative location of the destination P
with respect to a landmark Z. We currently have PaAm-n (Cardinal Direction [1, 8]),PiPD m-n (Ego Orientation [7]), PiLSD m-n (Double Cross in [9], Orientation Calculi[7]), and PrPm-n (Single Cross [5] and TPCC [4]). Thus, for every geometric type oflandmarks, we can consider a point-referent model that adopts an absolute or intrinsicframe (recall that the relatum is limited to PD or LSD when the intrinsic frame isadopted). On the other hand, as for the point-referent models with a relative frame,PrLm-n (and its variants PrLD m-n and PrLSD m-n) and PrRm-n are missing. The modelsof these categories can be used for modeling motion concepts in which the goal isassociated with linear or region-like landmarks. For instance, two point-referent
models, categorized into PrL1-4 and PrR1-4, may illustrate whether the goal is locatedon the left, right, front, or back of a linear landmark (e.g., a station platform) and aregion-like landmark (e.g., a park) as seen from the mover’s start point, respectively.

4Conclusions

DLine-relatum models and point-referent models, both subsets of projection-basedmodels, are useful for qualitative characterizations of spatial movements using
landmarks. This paper demonstrated that these models are systematized by short codenames that reflect the models’ prominent characteristics. The comparison of the codenames leaded to the identification of four missing types of models—RiLSD m-n,

LiLSD m-n, PrLm-n, and PrRm-n—that are potentially useful for modeling motion
concepts. Currently we are developing a series of models that belong to RiLSD m-n andapplying these models to the modeling of a number of motion concepts that concern
region-like landmarks in an effective way [13]. The exploration of the other potential
models that belong to LiLSD m-n, PrLm-n or PrRm-n are also desirable for enriching thefoundation for handling human concepts of motions computationally.
Among the models reviewed in this paper, TPCC [4] introduces a new concept ofprojection-based modeling—near-far distinction. Although nearness is a subjective
concept, TPCC expediently defines near and far fields based on the viewer-relatum
distance, as this yields some nice properties in its calculus [4]. It is an interesting topic
to apply such a near-far distinction to other projection-based models and analyze how
it improves the calculus, as well as the modeling capability of spatial concepts.
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