The generation of internal contours of existing contour starts
from isolated contours or main arcs in state p:
Yos(1.2 3: Yo ^9 (211002)
Yo, (123) ^ YoA 9 G,1(10,20,02)
Wy, (1.2,3,4) —» Wy, A 9 (41:30)(10,20,02) (2)
Wpp(1.2,3,4) > Wpa À (41;30)(10,20,02)
Wyp(1,2,3,4,5) > Wyn À 9 (51:30)(10,20,30,40,02)
where symbol Y €(A, R)and W is arbitrary arc from
the external contour symbol set (A, R, U, J, V, T).
The second set of rules is connected with generation of adjacent
contours to the arcs by applying the rules for creating of
surrounding arcs. Initial set of production rules includes rules
for generation of adjacent contours from single contours of type
A or R.
A 9(1,2) — Y; A y Yc (011,102,220;330,003)
(040,004)
A 0 (1,2,3) > Y,A m Yc (011,102,220;330,003)
(040,004,050)
R,(1,2) 5 RR, Yc (011,102,220;330,003)
(040,004)
Ro(1,2,3) > R,Ry Ye (011,102,220;330,003)
(040,004,050)
G)
A separate set of rules is formed by rewriting rules for
generating of external or internal self-closed contours. The rules
for external touching contour have the form:
A 0 (1,2) 9 Ax Yc (12,21,30,03)(40,04)
A 0 (1,2) > A m Yc (12,21:30,03)(40,04,50)
Ro(1,2) 5 R« Yc(12,21,30,03)(40,04)
Ro (12) => Ry Yc (12,21;30,03)(40,04,50)
Such type of internal and external contours, attached in single
point, does not belong to special type of image description
because specified joint elements in grammar are arcs and
contours instead of connecting nodes. Similar form have the
rules for internal self-closed contour.
Ao(1,2) > Ap Yi (11,22;30,03)(40,04)
Aq (1,2) > Ap Yy(11,22;30,03)(40,04,50) s
Ro(12) => Rp Ye (11,22;30,03)(40,04)
Ro (1,2) = Rp Yy (11,22;30,03)(40,04,50)
The process of area cluster growing continues with generation
of an additional external arc in clockwise direction (according
to external contour arc connection). It could be divided into
four steps: generation of a moving arc with a fixed initial node,
moving the end node of the arc, transformation of isolated
external arcs into new type and scanning of contours of isolated
arcs for finding of entire isolated contours.
The generation of a moving arc could start from a node between
the arcs or from internal point of the arc. The rules are similar
for the arcs of type A and R. For arc of type A the rules have
the form:
International Archives of Photogrammetry and Remote Sensing. Vol. XXXI, Part B3. Vienna 1996
Ax — AxApy Yo Ax
Ax 2 AxArpy Yoy
Ax — RyRjYog
Ay — AxYcAg
WA, — WyYy Yo Ry
Wy Ax — Wy Yrs Yoy
Wy Ay — WxYiYcg
Wi Ay => WY A
(6)
where index X means arc of type K, M, C or B and
symbol Y arcs of type A or R and symbol W arc of type A, R,
U, J, V. The presentation of the rules for the arcs of type “roof”
is as follow:
Ry = RyRy Wey Ry
Ry = RyRy Wey
Ry > RyR, Yca
Ry Ry,YcRg
Wy Ry WyRy Yo, Rx
Wy Ry — WyRy Yoy
W,Ry — WyRjiYcg
WyRy — WyYcRy
(7)
An additional group of rules is connected with moving of the
node of external arc and finishing of moving:
Yco W, > W,Yca
Yea Wx Wx Wy Yo,
Yco Wy = Wig Yeu (8)
Yco Wy — Wy Wy Yoy
Yco Wy Wy Yyy
A special group of rules are connected with generation of the
arcs presenting visible walls. They could be produced starting
from a roof arc.
Ry > UcoRx
Ry >RyxUcoRx
UcoRx > RyUca
UcoRx > HisUcyRx
RiUcq > Hi Vey
RjUcoG Ry RIHg Uc Ry
RjUc!o Rx — RjHg Uc,
RjUco Ry — Hi; Rcs Ry (9)
RjUcoG Ry H;Rg Uc,
R;UcoG Ry > H,RysReyRx
R;UcoRy = RiR{J cq
RiJcaRx = R{R{R¢q
Rico > RyRey
RU co Ry — RjRERo4Ry
RjUcoYc — Hi coYc
R;UcoRxYc — HiRUcoYc
where symbol Y €(V, J, U).
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