Spots Concept for Problems of Artificial Intelligence and Algorithms of Neuromorphic Systems

Simonov, Nikolai A.

doi:10.1134/s106373972005008x

Cited by 5 publications

(24 citation statements)

References 25 publications

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“…Namely, they introduced the concepts of 4-intersection [44] and 9-intersection [45] matrixes, which are logical matrices that encode the spatial relations between spatial regions. Notice that these matrixes are similar but differ from the L4 numbers proposed in [27,28] because authors of [44,45] consider also relations with the boundaries. Clementini et al [46] generalized 9-intersection matrixes, replacing intersections for the crisp boundary with the intersections for broad boundaries.…”

Section: Introductionmentioning

confidence: 80%

“…The elementary relations can be formalized using logical L4 numbers [27]. For spots 𝑎𝑎, 𝑎𝑎 and their environments 𝑎𝑎 �, 𝑎𝑎 � the L4 number ⟨𝑎𝑎|𝑎𝑎⟩ is defined as a table…”

Section: Definition Of L4 Numbersmentioning

confidence: 99%

“…The mathematical apparatus of the spot model is based on the L4 numbers, rather than on real numbers. As far as the basis of this apparatus is described in more detail in the previous works [27,28], here we will briefly outline the main content and reveal the meanings of the concepts introduced there. Table 1.…”

Section: Definition Of L4 Numbersmentioning

confidence: 99%

“…In [27,28], the basis of spots is defined as a collection of "known" spots that can be in some mutual ER. The representation of a spot by their ER on the basis spots is a mapping or imaging of the spot on this basis.…”

Section: Elementary Relationsmentioning

confidence: 99%

“…A new mathematical model of spots is proposed in [27,28] for representation and processing incomplete, inaccurate or qualitative information. In particular, it allows to create algorithms of a new type for AI and build neuromorphic systems, which operates in the way that is close to the human thinking.…”

Section: Introductionmentioning

confidence: 99%

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Application of the Model of Spots for Inverse Problems

Simonov¹

2022

Preprint

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This article proposes application of a new mathematical model of spots for solving inverse problems using a learning method, which is similar to using the deep learning. In general, the spots represent vague figures in abstract “information spaces” or crisp figures with lack of in-formation about their shapes and are adequate for representation human mental images and reasoning in Artificial Intelligence (AI). However, crisp figures are regarded as a special and limiting case of spots. A basic mathematical apparatus, basing on L4 numbers, has been developed for the representation and processing of qualitative information of elementary spatial relations between spots. Also, we defined L4 vectors, L4 matrices, and mathematical operations on them. Developed apparatus can be used in AI, in particular, for knowledge representation and for modeling qualitative reasoning and learning. Another application area is the solution of inverse problems by learning. For example, this can be applied to image reconstruction using ultrasound, X-ray, magnetic resonance, or radar scan data. The introduced apparatus was verified by solving problems of reconstruction of images, utilizing only qualitative data of its elementary relations with some scanning figures. This article also demonstrates application of spot-based inverse Radon algorithm for binary image reconstruction.

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Section: Introductionmentioning

confidence: 80%

Section: Definition Of L4 Numbersmentioning

confidence: 99%

Section: Definition Of L4 Numbersmentioning

confidence: 99%

Section: Elementary Relationsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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