A. Rosenfeld, "Picture Languages - Formal Models for Picture Recognition", Academic Press, New York, 1979.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....plane by unit lines. A well known example for this kind of technique is the Freeman s chain code [FRE61] that represents unit lines in 4 (or 8) directions and which is used for contour line descriptions. There are other description models, some of which are similar to the chain code scheme (see [ROS79]) There are no applications of picture grammars to visual inspection reported in the literature, since they are of very theoretical structure and rather for constructing pictures than for analyzing images. In this chapter the proposed new visual inspection concept was described. Following a ....

A. Rosenfeld, "Picture Languages - Formal Models for Picture Recognition", Academic Press, New York, 1979.

....of points representation for any set of voxels, with the centres of the voxels de ning the vertices of the graphs and the edges representing voxel adjacency. See Figure 3.3. In arriving at the medial surface axis of S via thinning, we must preserve the topology of the image . It can be shown [64] that any operation that reassigns voxels of S to S will preserve the topology of in 2 dimensions if and only if the operation preserves the number of objects O(S) and number of cavities C(S) Things are much more complicated in 3 dimensions due to the presence of holes (tunnels) In ....

A. Rosenfeld. Picture Languages : Formal Models for Picture Recognition. Academic Press, 1979.

....condition, are themselves good de nitions of complexity, and not necessarily correlated with the complexity of recognizing a completed picture. 10 2. 3 Deterministic Finite Automata, or DFA s The automata in the next two sections were introduced by Blum and Hewitt [6] The reader may consult [51] for a review. De nition. A 4 way deterministic nite state automaton, or 4 way DFA, consists of a nite set of states S, an initial state s 0 2 S, a subset S accept S, and a transition function F : A S S f ; #; g. F describes how the DFA changes its state and moves one step up, down, ....

....if there exists a 4 way NFA which recognizes it. Recall that in one dimension, DFA s and NFA s are equivalent. In two or more dimensions, NFA s are more powerful: Proposition. The class of NFA languages properly contains the DFA languages. Proof. Containment is obvious; we take an example from [51] which is NFA but not DFA. Let the alphabet be f0; 1; 2g, and consider squares of non 0 s on a background of 0 s, where the squares have odd side and their center site is a 2. 13 After con rming that it is in a square as we did before, an NFA can recognize this by moving diagonally from one ....

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A. Rosenfeld, Picture Languages: Formal Models for Picture Recognition. Academic Press, 1979.

....[IN77] We will follow [GR92] and denote this set of languages REC. While DFAs, NFAs, AFAs and REC are all equivalent to the regular languages in one dimension, in two or more dimensions they become distinct: DFA NFA AFA REC where all of these inclusions are strict. We recommend [LMN98,GR96,IT91,Ros79] for reviews of these classes. A bibliography of papers in the subject is maintained by Borchert at [BB] Note that we restrict our automata to move within the picture they are trying to recognize. For DFAs, it is known that allowing them to move outside the picture into a eld of blanks does ....

....of papers in the subject is maintained by Borchert at [BB] Note that we restrict our automata to move within the picture they are trying to recognize. For DFAs, it is known that allowing them to move outside the picture into a eld of blanks does not increase their computational power [Ros79]. For NFAs this is known for 1 n pictures [LMN98] and for AFAs the question is open. However, we allow them to sense the boundary of the rectangle, and make di erent transitions accordingly. Similarly, when de ning a language in REC we allow its local pre image to forbid blocks containing ....

A. Rosenfeld, Picture Languages: Formal Models for Picture Recognition. Academic Press, 1979.

.... collage grammar; iterated function system; chaincode grammar; turtle interpretation 1 Introduction During the last two decades picture generation has become a large field whose manyfold aspects are studied in mathematics as well as in practical and theoretical computer science (see, e.g. [30, 24, 21, 2, 27, 29]) The area attracts the interest of numerous researchers from diverse directions, which is no surprise because one can find in this area a great number of intellectually appealing mathematical and computational problems, interesting applications like the modelling of plant development and, one ....

Azriel Rosenfeld. Picture Languages: Formal Models for Picture Recognition. Academic Press, New York, 1979.

....languages [3] or the languages recognizable by non deterministic online tesselation acceptors [5] While DFAs, NFAs and h(LLL)s are equivalent in one dimension, in two or more they become distinct: DFA # NFA # h(LLL) where these inclusions are strict. Reviews of these classes are given in [8, 4, 7, 11], and a bibliography of papers in the subject is maintained by Borchert at [2] A fair amount is known about the closure properties of these classes as well. The DFA, NFA, and h(LLL) languages are all closed under intersection and union using straightforward constructions. The situation for ....

A. Rosenfeld (1979) Picture Languages: Formal Models for Picture Recognition. Academic Press.

....condition, are themselves good definitions of complexity, and not necessarily correlated with the complexity of recognizing a completed picture. 2. 3 Deterministic Finite Automata, or DFA s The automata in the next two sections were introduced by Blum and Hewitt [6] The reader may consult [46] for a review. Definition. A 4 way deterministic finite state automaton, or 4 way DFA, consists of a finite set of states S, an initial state s 0 2 S, a subset S accept ae S, and a transition function F : A Theta S S Theta f ; #; g. F describes how the DFA changes its state and moves one ....

....if there exists a 4 way NFA which recognizes it. Recall that in one dimension, DFA s and NFA s are equivalent. In two or more dimensions, NFA s are more powerful: Proposition. The class of NFA languages properly contains the DFA languages. Proof. Containment is obvious; we take an example from [46] which is NFA but not DFA. Let the alphabet be f0; 1; 2g, and consider squares of non 0 s on a background of 0 s, where the squares have odd side and their center site is a 2. After confirming that it is in a square as we did before, an NFA can recognize this by moving diagonally from one ....

[Article contains additional citation context not shown here]

A. Rosenfeld, Picture Languages: Formal Models for Picture Recognition. Academic Press, 1979.

....pattern features on which the grammar should be based. Bounding and interior image curves were typical, but the graph matching rapidly became intractable. Missing and bogus edges were a problem, and the complexity of curve possibilities exceeded the grammars. With the exception of array grammars [44], little progress was made. Research continues on graph isomorphism algorithms for vision applications, but examples are still typically based on graphs derived from feature points and image curves [19] Probability measures have also been placed on images and image curves in an attempt to provide ....

A. Rosenfeld. Picture Languages: Formal Models for Picture Recognition. Academic Press, New York, 1979.

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