A novel visual codebook model based on fuzzy geometry for large-scale image classification

• This paper aims to overcome the drawbacks of traditional visual words.
• Fuzzy visual word and fuzzy feature are defined using n-dimensional fuzzy geometry.
• A new similarity measure between fuzzy features and fuzzy visual words is designed.
• Two modified image classification frameworks based on Fuzzy codebook are proposed.
• Experimental results demonstrated their advantages against traditional algorithms.

The codebook model has been developed as an effective means for image classification. However, the inherent operation of assigning visual words to image feature vectors in traditional codebook approaches causes serious ambiguities in image classification. In particular, the nearest word may not be the best fit to a feature, and multiple words may be equally appropriate for one specific feature. To resolve these ambiguities, we propose a novel visual codebook model based on the n-dimensional fuzzy geometry (n-D FG) theory, where all visual words and features are modeled as fuzzy points in the n-D FG space, and appropriate uncertainty is introduced to each fuzzy point to enhance the representation capacity. This n-D FG-codebook model not only inherits advantages from the fuzzy set theory, but also facilitates the analysis and determination of the relationship between visual words and features in geometric form. By explicitly taking into account the ambiguities, we propose a novel measure of similarity between the visual words and fuzzy features. Following the proposed codebook model and the novel similarity measure, we develop two useful image classification algorithms by modifying popular image coding algorithms (i.e. SPM and LLC). Finally, experimental results demonstrate that the classification accuracy of the proposed algorithms is dramatically improved for a standard large-scale image database. For example, with a codebook size of 256, the proposed algorithms achieve similar performance as traditional algorithms with a codebook size of 1024, indicating that the proposed algorithms reduce the computational cost by 75% while achieving almost identical classification accuracy to traditional algorithms. Thus, the proposed algorithms represent a more efficient and appropriate scheme for big image data.