5.2. Sign Similarity Relation

The sign similarity relation is a parameterized, reflexive, symmetric and not transitive relation, that we introduce here to analyze the relative similarity between two sign instances, providing for the construction of matching procedures for signs and sign language expressions.

The sign similarity relation has to embody an admissible variation between the relative positions of the symbol instances within the two corresponding sign instances, taking into account a degree of significance for this variation (relatively to the symbol-boxes dimensions), as determined by the user.

The admissible variation in symbol instances positions is expressed in percentages by a so-called minimum degree of similarity, denoted by e.

Consider two symbol instances and , with and , respectively. and are said to be similar with at least degree e, denoted by , if and only if the following conditions hold:

Structural similarity:

which implies that

and

Admissible horizontal variation:

Admissible vertical variation:

where

Two sign instances and are said to be similar with at least degree e if and only there exists a bijection

such that for each

.

Example: Consider the three sign instances for the sign ìideaî in LIBRAS (see figure above). Observe that they contain three different instances for the symbol ìindexî, each one with a different y coordinate (all other symbol instances are exactly equal). Consider a situation where a user is searching for that sign in a text. Suppose he writes the first sign instance as the sign to be searched and that the other two instances are present in the text. The later two instances have some degree of similarity with respect to the first sign instance. In spite of the fact, in a strict sense, they are graphically different from the first instance. They may be considered to represent the same sign, depending on the minimum degree of similarity required by the user from the results of the matching process. With an intermediate degree of similarity, the second instance would match the first, while the third instance would not (the hand is too low in comparison with its position in the first sign instance). With a low degree of similarity, all instances would match. If the user required total similarity, no instance would match. The total degree of similarity ( ) requires that no difference be admitted between the two sign instances being compared.

Example: The similarity relation defined above does not take into account some important (and frequent) exceptions. Such exceptions are mainly related to symbols like the "arrow" symbol encountered in the sign ìideaî in LIBRAS (see figure above), whose position within the sign is absolutely not critical. Such symbols have most of their meaning completely encoded in their shapes and transformations, and the place where they are put in the sign-boxes is essentially irrelevant. For instance, the "arrow" symbol in the sign for "idea" means that the right hand moves in the horizontal plane, in the indicated direction, and this information is the same, wherever the "arrow" is placed in the sign-box. In such cases, the relative position of the symbol-box within the sign-box is not important. In the examples of the figure above, even if a rigorous or a total degree of similarity is required, the match process should find that those three sign instances are similar. On the other hand, for symbols like the ìasteriskî, almost no variation of the its position should be allowed, since it indicates a position where two components of the sign (head, hands, etc.) touch each other, when the sign is performed, and even low degrees of variations may imply linguistically relevant differences between the signs.

Remark: SWML, as currently defined, has all information needed to allow the matching procedure sketched here to be fully performed. The treatment of exceptions is to be embedded in the matching process, requiring from SWML only that it identifies symbol instances completely, which it already does.