Abstract
When considering perceptions, the observation scale and resolution are closely related properties. There is consensus on considering resolution as the density of the elementary pieces of information in a specified information space. On the other hand, with the concept of scale, several conceptions compete for a consistent meaning. Scale is typically regarded as a way to indicate the degree of detail in which an observation is performed. Surprisingly, there is not a unified definition of scale as a description’s property. This paper offers a precise definition of scale and a method to quantify it as a property associated with the interpretation of a description. To complete the parameters needed to describe the perception of a description, the concepts of scope and resolution are also revealed with an exact meaning. A model describing a recursive process of interpretation, based on evolving steps of scale, scope and resolution, is introduced. The model relies on the conception of observation scale and its association to the selection of symbols. Five experiments illustrate the application of these concepts, showing that resolution, scale and scope integrate the set of properties to define any point of view from which an observation is performed and interpreted. The results obtained for descriptions expressed in one and two dimensions, are the basis for a comparison of the perceivable symbolic information from different interpretations of the same descriptions. In conclusion, this study provides a framework for building models of our interpretation process and suggests ways to understand some mechanisms in the formation of information from initially meaningless symbols.
Highlights
The ‘anatomy’ of a description has been the subject of intense discussion
This paper offers a novel conception of scale, pointing out clear differences with the concepts of resolution and scope
The Fundamental Scale Algorithm (FSA) is developed for one-dimensional descriptions, these results strongly suggest that languages evolve to develop their capacity to organize symbols to effectively convey information
Summary
The ‘anatomy’ of a description has been the subject of intense discussion. Three abstract entities have been recognized as essential [1,2] for the construction of descriptions in any language or communication system: resolution, scale and scope. Even though Benz et al did not directly define scale as a property of the way a photograph is observed, they did recognize that the same photography may be given different interpretations. Grossmann, Morlet, Strömberg, Daubechies, Meyer, Mallat and Zhong are some researchers involved in the development of the Wavelet Transform and the Scale-space theory; a field devoted to the representation and processing of signals In this field, the scale represents a parameter used to define the “degree of smoothing” applied to the processed signals. Enhancing the observation of a system’s description has been typically restricted to the grouping of information-elements into spaces topologically congruent This approach has proved to be of limited utility because it restricts the effects of varying parameters within the process of interpreting descriptions. The proposed concepts of scale, resolution and scope are used to evaluate descriptions of different nature. Discussion and conclusions about the implications of the proposed meaning of scale and the interpretation process are presented
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