Fig. 1. Flotation machine vision system

Fig. 2. NSST multiscale decomposition of bubble images

Fig. 3. Three dimensional diagram of bubble images. (a) Original image; (b) low frequency subband image

Fig. 4. Fractional order differential valley detection templates

Fig. 5. Implementation flow chart

Fig. 6. Bubble delineation steps and experimental results. (a) Bubble image; (b) low frequency subband image; (c) high frequency scale 1; (d) high frequency scale 2; (e) high frequency scale 3; (f) low frequency subband boundary; (g) modulus maximum for scale 1; (h) modulus maximum for scale 2; (i) modulus maximum for scale 3; (j) high frequency scale boundary; (k) traditional valley detection; (l) adaptive valley detection; (m) multiscale boundary fusion; (n) boundary refining; (o) final result

Fig. 7. Comparison of bubble delineation results of different methods. (a) Bubble image; (b) detection result of Sobel; (c) detection result of Canny; (d) detection result of Gauss Laplacian; (e) threshold segmentation result of iteration method; (f) OTSU result; (g) result of K neighbor clustering segmentation; (h) result of marked-based watershed segmentation; (i) detection result of adaptive valley; (j) result of proposed method

Fig. 8. (a) Different types of bubble images; (b) results of Ref. [9]; (c) results of Ref. [11]; (d) results of Ref. [12]; (e) results of proposed method