Reasoning on the Patterns of Spatial Arrangements between a Path and a Region-Like Landmark

Universität
BremenHui Shi and Yohei Kurata
SFB/TR 8 Spatial Cognition, Universität Bremen / {shi, ykurata}@informatik.uni-bremen.de

Research Goal

Inversion, Homing, and Shortcut

We develop a foundation of spatial reasoning
on the patterns of path-landmark arrangements
modeled by RfDL3-12
RightFront

Leftat-Exit

Exit

Rightat-Exit

Left-ofInteriorInterior

StraightFront

Right-ofInterior

Leftat-Entry

Entry

Rightat-Entry

LeftBack

StraightBack

RightBack(i) Composition of a Double Cross Pattern and an RfDL3-12 Pattern

I walked until a yard comes to my left.
Now I got some questions:i)
RaLeftFront

Composition

If I turn back to the bus stop, in which
direction I see the yard?

Dad, I’m between a bus
stop and a shopii) If I walk toward somewhere in the yard, inwhich direction I see the bus stop?

biii) If I walkinlk towardd somewherehi theh yardddirectly from the bus stop, in which
direction I would see my current location?

baThe composition ab : c ; bc : R returns all possible ab : R

Given ab : RDerivation
Process• Homing returns all possible bx : a ( x ∈ R )• Shortcut returns all possible ax : b (x ∈ R )ab : c

For instance, givenbaaaa

Rightat-Exit∧

Interior

RightFront

Right-ofInterior

Leftat-Entry

Entry

Rightat-Entry

LeftBack

StraightBack

RightBack• RfDL3-12 is useful for capturing the motion concepts that concern thedirection and extent of the landmark as seen from the path [3, 4]

bx : aba : R…

(ii) Composition of Two RfDL3-12 Patterns
Derivation
Processes

Inversion

HomingShortcutbab : Rab : R• Shortcut in Double Cross
returns all possible ac : beither one iseeither one isbx : a ( x ∈ R )either one is[5] Zimmermann & Freksa (1996) Qualitative Spatial Reasoning Using Orientation, Distance, and Path Knowledge. Applied Intelligence 6:49-58.

• Homing in Double Cross
returns all possible bc : aR2

The green is to theright back of my ball

Now I noticed that a bunker is behind the hole.
So, if I go back to the teeing ground, in which
direction I see the bunker with respect to this ball?

Shortcut in Double Cross [5]either one is[4] Shi & Kurata (2008) Modeling Ontological Concepts of Motions with Two Projection-Based Spatial Models. Workshop on Behavioral
Monitoring and Interpretation.

Given ab : cxb

ab : Reither one isba : R[3] Kurata & Shi (2008) Interpreting Motion Expressions in Route Instructions Using Two Projection-Based Spatial Models. KI-2008.

R1
R1

Homing in Double Cross [5][2] Freksa (1992) Using Orientation Information for Qualitative Spatial Reasoning. International Conference GIS, LNCS 639, 162-178. Springer.

∧ax : ba[1] Kurata & Shi (2008) RfDL: Models for Capturing Directional and Topological Characteristics of Path-Landmark Arrangements. Workshop onMoving Objects.

∧What other possibilities?

e.g., ‘go toward …’, ‘pass … on the left’, ‘go until … comes to the right’,‘go across …’, ‘go into …’, and ‘go out of…’

References

Conditions for ab : Rempty

at least one isb

at least one isb

at least one is

Exit

Left-ofInterior

Given ab : c and bc : x ,the composition inDouble
Cross returns
D bl Ct
all possible ab : x.

either one isRxb

is an extension of Double Cross [2]Leftat-Exit;either one isRx

either one isRRÆ 3 fields on the path + 12 fields around the path

StraightFront;

Composition in Double Cross [2]• RfDL
front-side-back,and entry-interior-exit
f 3-12 considers left-right,
ff
distinctions with respect to the path

LeftFront

bc : R;• RfDL = Region-in-the-frame-of-Directed-Line• Essentially, RfDL3-12So, where’s the shopwith respect to me
and the bus stop?

The answer to this question is derived computationally by the composition ofa Double Cross pattern ab : c and an RfDL3-12 pattern bc : R• Inversion returns ba : R• The finest model in the RfDL model series [1], which consists of eightmodels that categorize the spatial arrangements between a straightpath and a region-like landmark with different levels of granularities

sc

The answer to these questions are derived computationally by the inversion,
homing, and shortcut of an RfDL3-12 pattern ab : R , respectively

What is RfDL3-12?

I can see you in the rightfront of the bus stop

Rax : b ( x ∈ R )The answer to this question is derived computationally by the composition oftwo RfDL3-12 patterns ab : R1 and bx : R2 (x ∈ R1 )The composition ab : R1 ; bx : R2 (x ∈ R1 ) returns all possible ab : R2
This composition is derived in the similar way as (i), considering the synthesis of
the results of the Double Cross composition ab : x; bc : y where x and y moves in
R1 and R2, respectively