The present invention relates to a method, apparatus and system for optimizing an expression tree (101,902,1102) for compositing an image. Such an expression tree (101,902, 1102) can comprise at least two nodes. Each node is either a graphical element (102,104) or image compositing operator ((103,104) and has a region of the image represented by the node (102,103,104). In the method, for at least one node in the tree, several steps are carried out. The region represented by the node (103,104) is compared to a region representation data structure, which is preferably a quadtree representation, corresponding to one or more regions represented by at least one other node. A determination is then made if the region represented by the node (102,103,104) is totally or partially obscured by the one or more regions. If the region represented by the node is at least partially or totally obscured, the expression tree (101,902,1102) is modified. Modifying the expression tree (101,902,1102) involves applying a clipping operator (58,59) to the node if the region represented by the node is partially obscured. If the node is totally obscured, either removing the node if the node is a graphical element (102, 104) or applying a predetermined set of node replacement rules in accordance with the image compositing operator if the node (103) is a image compositing operator.
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17. An apparatus for optimising an expression tree, said expression tree for compositing an image and comprising at least three nodes, each said node of said tree being at least either a graphical element or a graphical operator, the apparatus comprising:
means for, comparing a first region of said node to a second region derived from at least one other node anywhere in said expression tree;
means for determining if said first region is totally or partially obscured by said second region; and
means for modifying the expression tree in the event that said first region is at least partially or totally obscured by said second region, to form an optimized expression tree in which an optimized part of said expression tree substantially represents unobscured portions of said first region.
24. An apparatus for optimizing an expression tree for compositing an image, said expression tree comprising a plurality of nodes, each said node being at least either a graphical element or a graphical operator, said apparatus comprising:
means for traversing the expression tree node by node;
means for determining at a current node if a first region of the image represented at said current node is obscured by a second region derived from at least one other node anywhere in said expression tree; and
means for modifying said expression tree in the event that said first region of said current node is partially or totally obscured by said second region to form an optimized expression tree in which an optimized part of said expression tree substantially represents unobsured unobscured portions of said first region.
1. A method of optimising an expression tree, said expression tree for compositing an image and comprising at least three nodes, each said node of said tree being at least either a graphical element or a graphical operator, the method comprising, for at least one node in said tree, the steps of:
comparing a first region of said node to a second region derived from at least one other node anywhere in said expression tree;
determining if said first region is totally or partially obscured by said second region; and
modifying the expression tree if said first region is at least partially or totally obscured by said second region, to form an optimised expression tree in which an optimised part of said expression tree substantially represents unobscured portions of said first region,
wherein said steps are performed by means of a programmed computer.
8. A method of optimising an expression tree for compositing an image, said expression tree comprising a plurality of nodes, each said node being at least either a graphical element or a graphical operator, said method comprising the steps of:
traversing the expression tree node by node; and
determining at a current node if a first region of the image represented at said current node is obscured by a second region derived from at least one other node anywhere in said expression tree, and modifying said expression tree in the event that said first region of said current node is partially or totally obscured by said second region, to form an optimised expression tree in which an optimised part of said expression tree substantially represents unobscured portions of said first region,
wherein said steps are performed by means of a programmed computer.
27. An apparatus for optimizing an expression tree for compositing an image, said expression tree comprising a plurality of nodes, each said node comprising at least either a graphical element or a graphical operator and having a region of the image represented by said node, said apparatus comprising:
means for traversing the expression tree node by node, said traversing means for each current node comprising a graphical operator, further comprising:
means for receiving a first region representation from a parent node;
means for passing to a first operand of said graphical operator a modified first region representation in accordance with a first predetermined modification rule for said operator;
means for returning to the graphical operator a second region representation of regions obscured by a sub-tree associated with the first operand;
means for passing to a second operand of said graphical operator a modified second region representation in accordance with a second predetermined modification rule for said operator;
means for returning to the graphical operator a third region representation of regions obscured by a sub-tree associated with the second operand; and
means for determining, in accordance with a set rule for said graphical operator, a final region representation to be returned to the parent to form an optimized expression tree in which said final region representation substantially represents an unobscured portion of said first region represented at the parent node a region within which said current node is capable of obscuring other nodes in said expression tree.
11. A method of optimising an expression tree for compositing an image, said expression tree comprising a plurality of nodes, each said node comprising:
at least either a graphical element or a graphical operator and having a region of the image represented by said node, said method comprising the steps of:
traversing the expression tree node by node and at each current node comprising a graphical operator applying the sub-steps of:
(i) receiving a first region representation from a parent node;
(ii) passing to a first operand of said graphical operator a modified first region representation in accordance with a first predetermined modification rule for said operator;
(iii) returning to the graphical operator a second region representation of regions obscured by a sub-tree associated with the first operand;
(iv) passing to a second operand of said graphical operator a modified second region representation in accordance with a second predetermined modification rule for said operator;
(v) returning to the graphical operator a third region representation of regions obscured by a sub-tree associated with the second operand; and
(vi) determining, in accordance will a set rule for said graphical operator, a final region representation to be returned to the parent node to form an optimised expression tree in which said final region representation substantially represents an unobscured portion of the first region represented at the parent node a region within which said current node is capable of obscuring other nodes in said expression tree,
wherein said steps are performed by means of a programmed computer.
2. The method as recited in
3. The method as recited in
removing the node; and
if the node has a parent node which has a graphical operator, selecting a node replacement rule from a predetermined set of node replacement rules in accordance with said graphical operator and applying said rule.
4. The method as recited in
if the parent node is an “over” graphical operator and the current node is at a left branch of the parent node, replacing the parent node with a right subtree of the parent node;
if the parent node is an “over” graphic graphical operator and the current node is at a right branch of the parent node, replacing the parent node with a left subtree of the parent node;
if the parent node is an “in” graphical operator, removing the parent node and any subtrees branching off the parent node;
if the parent node is a “ratop” graphical operator and the current node is at a left branch of the parent node, removing the parent node and any subtrees branching off the parent node;
if the parent node is a “ratop” graphical operator and the current node is at a right branch of the parent node, replacing the parent node with a left subtree of the parent node;
if the parent node is an “out” graphical operator and the current node is at a left branch of the parent node, removing the parent node and any subtrees branching off the parent node;
if the parent node is an “out” graphical operator and the current node is at a right branch of the parent node, replacing the parent node with a left subtree of the parent node;
if the parent node is a “plusC” graphical operator and the current node is at a left branch of the parent node, replacing the parent node with a right subtree of the parent node;
if the parent node is a “plusC” graphical operator and the current node is at a right branch of the parent node, replacing the parent node with a left subtree of the parent node;
if the parent node is a “plusW” or an “Xor” graphical operator and the current node is at a left branch of the parent node, replacing the parent node with a right subtree of the parent node; and
if the parent node is an “plusW” or an “Xor” graphical operator and the current node is at a right branch of the parent node, replacing the parent node with a left subtree of the parent node.
5. The method as recited in any one of
6. The method as recited in
7. The method as recited in
9. The method as recited in claim ti, wherein said modityinig modifying includes removing said current rode or replacing said current node with another node of the expression tree.
10. The method as recited in claim 7 8, wherein said modifying further includes clipping, or marking for clipping at a later time, said first region represented by said current node.
12. The method as recited in
(a) where the graphic operator is an “over” or a “plusC” operator, the final region representation to be returned to the parent node is determined from a union of the second region representation and the third region representation;
(b) where the graphic operator is an “in” operator, the final region representation to be returned to the parent node is determined from an intersection of the second region representation and the third region representation;
(c) where the graphic operator is a “ratop” operator, the final region representation to be returned to the parent node is the second region representation;
(d) where the graphic operator is an “out” operator, the final region representation to be returned to the parent node is determined from a difference of the second region representation and a region representation comprising at least a region represented by a bounding box of a node at a right subtree of the current node; and
(e) where the graphic operator is an “Xor” or a “plusW” operator the final region representation to be returned to the parent node is determined from a union of the second region representation less a region representation comprising at least a region represented by a bounding box of a node at a right subtree of the current node and the third region representation less a region representation containing a bounding box of a node at a right subtree of the current node.
13. The method as recited in
passing substantially the first region representation as the modified first region representation in the event that the graphical operator is an “over”, “in”, “ratop”, “plusC”, “plusW”, “Xor”, or “out” (visit left operand first)” or alike operators operator; and
if the graphical operator is an “out (visit right operand first)” operation, passing as the modified first region representation a union of the first region representation with the second region representation.
14. The method as recited in
passing substantially the first region representation as the modified second region representation in the event that the graphical operator is an “in”, “ratop”, “out”, “plusC”, “plusW”, or “Xor” or alike operators operator; and
in the event that the graphical operator is an “over” operator passing as the modified second region representation union of the first region representation with the second region representation.
15. The method as recited in any one of
16. The method as recited in
a right operand of an “over” operator and the “over” operator node does not need to return an image representation to its parent node;
a left operand of an “in”, “plusC”, “plusW” or “Xor” operator and said operator node does not need to return an image representation to its parent node;
a right operand of an “in”, “plusC”, “plusW” or “Xor” operator and said operator node does not need to return an image representation to its parent node;
a left operand of an “out” or “ratop” operator and said operator node does not need to return an image representation to its parent node;
a right operand of a “ratop” operator;
a root of the expression tree;
an operand of an image warp, affine transformation or convolution operator; and
an operand of a colour transformation that does not preserve opaqueness or if said transformation node does not need to return an image representation to its parent node.
18. The apparatus as recited in
19. The apparatus as recited in
means for removing the node; and
means for selecting a node replacement rule from a predetermined set of node replacement rules in accordance with said graphical operator and applying said rule if the node has a parent node which has a graphical operator and the node is totally obscured.
20. The apparatus as recited in
if the parent node is an “over” graphical operator and the current node is at a left branch of the parent node, replacing the parent node with a right subtree of the parent node;
if the parent node is an “over” graphic graphical operator and the current node is at a right branch of the parent node, replacing the parent node with a left subtree of the parent node;
if the parent node is an “in” graphical operator, removing the parent node and any subtrees branching off the parent node;
if the parent node is a “ratop” graphical operator and the current node is at a left branch of the parent node, removing the parent node and any subtrees branching off the parent node;
if the parent node is a “ratop” graphical operator and the current node is at a right branch of the parent node, replacing the parent node with a left subtree of the parent node;
if the parent node is an “out” graphical operator and the current node is at a left branch of the parent node, removing the parent node and any subtrees branching off the parent node;
if the parent node is an “out” graphical operator and the current node is at a right branch of the parent node, replacing the parent node with a left subtree of the parent node;
if the parent node is a “plusC” graphical operator and the current node is at a left branch of the parent node, replacing the parent node with a right subtree of the parent node;
if the parent node is a “plusC” graphical operator and the current node is at a right branch of the parent node, replacing the parent node with a left subtree of the parent node;
if the parent node is a “plusW” or an “Xor” graphical operator and the current node is at a left branch of the parent node, replacing the parent node with a right subtree of the parent node; and
if the parent node is a “plusW” or an “Xor” graphical operator and the current node is at a right branch of the parent node, replacing the parent node with a left subtree of the parent node.
21. The apparatus as recited in any one of
22. The apparatus as recited in
23. The apparatus as recited in
25. The apparatus as recited in
26. The apparatus as recited in
28. The apparatus as recited in
(a) where the graphic operator is an “over” or a “plusC” operator, the final region representation to be returned to the parent node is determined from a union of the second region representation and the third region representation;
(b) where the graphic operator is an “in” operator, the final region representation to be returned to the parent node is determined from an intersection of the second region representation and the third region representation;
(c) where the graphic operator is an a “ratop” operator, the final region representation to be returned to the parent node is the second region representation;
(d) where the graphic operator is an “out” operator, the final region representation to be returned to the parent node is determined from a difference of the second region representation and a region representation comprising at least a region represented by a bounding box of a node at a right subtree of the current node; and
(e) where the graphic operator is an “Xor” or a “plusW” operator the final region representation to be returned to the parent node is determined from a union of the second region representation less a region representation comprising at least a region represented by a bounding box of a node at a right subtree of the current node and the third region representation less a region representation containing a bounding box of a node at a right subtree of the current node.
29. The apparatus as recited in
passing substantially the first region representation as the modified first region representation in the event that the graphical operator is an “over”, “in”, “ratop”, “plusC”, “plusW”, “Xor”, or “out” (visit left operand first)” or alike operators operator; and
if the graphical operator is an “out (visit right operand first)” operation, passing as the modified first region representation a union of the first region representation with the second region representation.
30. The apparatus as recited in
passing substantially the first region representation as the modified second region representation in the event that the graphical operator is an “in”, “ratop”, “out”, “plusC”, “plusW”, or “Xor” or alike operators operator; and
in the event that the graphical operator is an “over” operator, passing as the modified second region representation a union of the first region representation with the second region representation.
31. The apparatus as recited in any one of
32. The apparatus as recited in
a right operand of an “over” operator and the “over” operator node does not need to return an image representation to its parent node;
a left operand of an “in”, “plusC”, “plusW” or “Xor” operator and said operator node does nor need to return an image representation to its parent node;
a right operand of an “in”, “plusC”, “plusW” or “Xor” operator and said operator node docs not need to return an image representation to its parent node;
a left operand of an “out” or “ratop” operator and said operator node does not need to return an image representation to its parent node;
a right operand of a “ratop” operator;
a root of the expression tree;
an operand of an image warp, affine transformation or convolution operator; and
an operand of a colour transformation that does not preserve opaqueness or if said transformation node does not need to return an imap representation to its parent node.
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,
function obscure(node, need_result, q0)
begin
case node's type begin
primitive →
if q0 obscures the node's bounding box then
return obscured.
else if q0 partially obscures the node's bounding box and
there is advantage in clipping the primitive (eg., it is an image,
edge blend, box, all, or path primitive) then
begin
Clip if the overhead of clipping is worth the saving in not gen-
erating and compositing the clipped pixels.
Obtain a clip path from q0. This clip path remains associated with
q0 while it exists, so that it is only ever created once.
Tag the node as requiring clipping to this path.
end
if need_result then
begin
if the primitive is a good obscurer (a large opaque image, box or all:
a large opaque path containing a single, simple, convex edge)
then
Construct a quadtree from the primitive's boundary.
return this quadtree.
else
return empty quadtree.
end
colour transformation →
if q0 obscures the node's bounding box then
return obscured.
else if q0 partially obscures the node's bounding box then
begin
Clip, as we expect the overhead of clipping to be worth the saving
in not transforming the clipped pixels.
Obtain a clip path from q0. This clip path remains associated with
q0 while it exists, so that it is only ever created once.
Tag the node as requiring clipping to this path.
end
Determine whether the transformation preserves opaqueness
(opacity 1 maps to opacity 1), and whether it preserves invisbility
(opacity 0 maps to opacity 0).
call obscure(node's operand, transformation preserves opaqueness
and need_result, q0), obtaining quadtree q1 if requested. If
opaqueness is not preserved, then we can't know what areas will
be obscured after the transformation is applied, so there is no
point asking for a quadtree.
if operand is obscured then
begin
Note that if the operand is said to be obscured, then it is only the
visible parts (opacity # 0) that are guaranteed to be obscured.
if transformation preserves invisibility then
return obscured.
else
begin
Determine what the transformation will transform invisible
(opacity = 0) to.
Replace this node by an “all” primitive of this colour/opacity.
if need_result then
return a quadtree constructed from the all's boundary.
return
end
end
if need_result then
if transformation preserves opaqueness then
return quadtree q1.
else
return empty quadtree.
affine transformation, image warp →
if q0 obscures the node's bounding box then
return obscured.
else if qO partially obscures the node's bounding box then
begin
Clip, as we expect the overhead of clipping to be worth the saving
in not generating and compositing the the clipped pixels.
Obtain a clip path from q0. This clip path remains associated with
q0 while it exists, so that it is only ever created once.
Tag the node as requiring clipping to this path.
end
call obscure(node's operand, false, empty quadtree). We cannot
pass q0 down the tree or accept a result unless we
inverse/transform the quadtrees through the transformation.
image convolution →
if q0 obscures the node's bounding box then
return obscured.
call obscure(node's operand, false, empty quadtree).
binary operator →
if q0 obscures the node's bounding box then
return obscured.
case node's operator begin
over →
call obscure(node's left operand, true, q0), obtaining area qL obscured
by left operand.
call obscure(node's right operand, need_result, if left operand
is obscured then q0 else q0∪qL), obtaining area qR, obscured
by right operand if need_result.
if left operand is obscured and right operand is obscured then
return obscured.
else if left operand is obscured then
begin
Replace this node with its right operand.
if need_result then
return qR.
end
else if right operand is obscured then
begin
Replace this node with its left operand.
if need_result then
return qL.
end
else
if need result then
return qL∪qR.
end
in →
call obscure(node's left operand, need_result, q0), obtaining area qL
obscured by left operand if need_result.
if left operand is obscured then
return obscured.
call obscure(node's right operand, need_result, q0), obtaining area qR
obscured by right operand if need_result.
if right operand is obscured then
return obscured.
if need result then
return qL∩qR.
out →
call obscure(node's right operand. true, q0), obtaining area qR
obscured by right operand.
call obscure(node's left operand, need_result, if right operand is
obscured then q0 else q0∪qR), obtaining area qL obscured by
left operand if need_result.
if left operand is obscured then
return obscured.
else if right operand is obscured then
begin
Replace this node with its left operand.
if need_ result then
return qL.
end
else
if need_result then
return qL-B(right operand).
end
ratop →
call obscure(node's left operand, need result, q0), obtaining area qL
obscured by left operand if need_result.
if left operand is obscured then
return obscured.
call obscure(node's right operand, false, q0).
if right operand is obscured then
Replace this node with its left operand.
if need_result then
return qL.
plusC →
call obscure(node's left operand, need_result, q0), obtaining area qL
obscured by left operand if need_result.
call obscure(node's right operand, need result, q0), obtaining area qR
obscured by right operand if need_result.
if left operand is obscured and right operand is obscured then
return obscured.
else if left operand is obscured then
begin
Replace this node with its right operand.
if need_result then
return qR.
end
else if right operand is obscured then
begin
Replace this node with its left operand.
if need_result then
return qL.
end
else
if need_result then
return qL↑qR.
end
plusW, Xor →
call obscure(node's left operand, need_result, q0), obtaining area qL
obscured by left operand if need_result.
call obscure(node's right operand, need_result, q0), obtaining area qR
obscured by right operand if need_result.
if left operand is obscured and right operand is obscured then
return obscured.
else if left operand is obscured then
begin
Replace this node with its right operand.
if need_result then
return qR.
end
else if right operand is obscured then
begin
Replace this node with its left operand.
if need_result then
return qL.
end
else
begin
if need_result then
return (qL-B(rightoperand)) ∪ (qR-B(leftoperand)).
end
end case binary operator
end case node type
end
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