| Summary: | This paper proposes the transformation <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi mathvariant="bold-italic">S</mi><mo>→</mo><mover accent="true"><mi mathvariant="bold-italic">C</mi><mo>→</mo></mover></mrow></semantics></math></inline-formula>, where <b>S</b> is a digital gray-level image and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mover accent="true"><mi mathvariant="bold-italic">C</mi><mo>→</mo></mover></semantics></math></inline-formula> is a vector expressed through the textural space. The proposed transformation is denominated Vectorial Image Representation on the Texture Space (VIR-TS), given that the digital image <b>S</b> is represented by the textural vector <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mover accent="true"><mi mathvariant="bold-italic">C</mi><mo>→</mo></mover></semantics></math></inline-formula>. This vector <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mover accent="true"><mi mathvariant="bold-italic">C</mi><mo>→</mo></mover></semantics></math></inline-formula> contains all of the local texture characteristics in the image of interest, and the texture unit <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mover accent="true"><mi mathvariant="bold-italic">T</mi><mo>→</mo></mover></semantics></math></inline-formula> entertains a vectorial character, since it is defined through the resolution of a homogeneous equation system. For the application of this transformation, a new classifier for multiple classes is proposed in the texture space, where the vector <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mover accent="true"><mi mathvariant="bold-italic">C</mi><mo>→</mo></mover></semantics></math></inline-formula> is employed as a characteristics vector. To verify its efficiency, it was experimentally deployed for the recognition of digital images of tree barks, obtaining an effective performance. In these experiments, the parametric value λ employed to solve the homogeneous equation system does not affect the results of the image classification. The VIR-TS transform possesses potential applications in specific tasks, such as locating missing persons, and the analysis and classification of diagnostic and medical images.
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