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Figure from:Fingerprint image enhancement using multi-scale DDFB based diffusion filters and modified Hong filters

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5. Modified Hong algorithm

Figure 8 5. Modified Hong algorithm

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Fig. 1. These figure are taken from [8]. Sample image (a) is a well-defined images. Sample image (b) contains incomplete samples, region (a) contains well-defined sample, region (b) contains defected but recoverable sample, region (c) contains noise dominant unrecoverable sample. Sample image (c) contains cuts and bruises, include scratches, ridge breaks.
Fig. 1. These figure are taken from [8]. Sample image (a) is a well-defined images. Sample image (b) contains incomplete samples, region (a) contains well-defined sample, region (b) contains defected but recoverable sample, region (c) contains noise dominant unrecoverable sample. Sample image (c) contains cuts and bruises, include scratches, ridge breaks.
Fig. 2. Different types of diffusion.
Fig. 2. Different types of diffusion.
where D is a diffusion tensor. For 2D images this diffusion tensor is then assumed to be:
where D is a diffusion tensor. For 2D images this diffusion tensor is then assumed to be:
Fig. 4. Multi-scale DDFB flow control diagram. 3. Proposed multi-scale DDFB It is known that the directional image contains only features of similar direction with significantly less noise. To declare the local orientation among the directional images DDFB uses fixed block size energy comparison. Therefore, in this paper a multi-scale DDFB is used instead of simple DFB, it has the ability to adaptively change the local neighborhood size with the image local contrast and feature width, to obtain an optimal orientation estimate with the characteristics of noise robustness and feature localization. The block diagram of proposed multi-scale DDFB is shown in Fig. 4.
Fig. 4. Multi-scale DDFB flow control diagram. 3. Proposed multi-scale DDFB It is known that the directional image contains only features of similar direction with significantly less noise. To declare the local orientation among the directional images DDFB uses fixed block size energy comparison. Therefore, in this paper a multi-scale DDFB is used instead of simple DFB, it has the ability to adaptively change the local neighborhood size with the image local contrast and feature width, to obtain an optimal orientation estimate with the characteristics of noise robustness and feature localization. The block diagram of proposed multi-scale DDFB is shown in Fig. 4.
Fig. 5. (a)-(i) The 9 directional band images of DDFB.
Fig. 5. (a)-(i) The 9 directional band images of DDFB.
Fig. 7. (a)-(i) The 9 energy images of scales t=0.25, 0.375, ..., 1.25 respectively. These energy images are obtained by linearly combining the variance images on the basis of their respective strength measure. Fig. 6. (a)-(i) The 9 energy band images (variance) of scale-space at t=0.25, these images are obtained by convolving the Gaussian at scale t=0.25 with the band images of DDFB.
Fig. 7. (a)-(i) The 9 energy images of scales t=0.25, 0.375, ..., 1.25 respectively. These energy images are obtained by linearly combining the variance images on the basis of their respective strength measure. Fig. 6. (a)-(i) The 9 energy band images (variance) of scale-space at t=0.25, these images are obtained by convolving the Gaussian at scale t=0.25 with the band images of DDFB.
For calculating 11,512, s21,s22 we used 2nd order 5 x 5 truncated Gaussian derivatives which minimize the absolute error given by For calculating the rotated s11 and s12 from multi-scale DDFB ori- entation map we use following equation
For calculating 11,512, s21,s22 we used 2nd order 5 x 5 truncated Gaussian derivatives which minimize the absolute error given by For calculating the rotated s11 and s12 from multi-scale DDFB ori- entation map we use following equation
6. Experimental results
6. Experimental results
Fig. 11. (a) Sample image with noise distributed in four quadrants. (b)The absolute angle error of coherence enhancement diffusion. (c) The absolute angle error of multi-scale DDFB. Fig. 10. (a) The absolute angle error of coherence enhancement diffusion. (b) The absolute angle error of multi-scale DDFB.
Fig. 11. (a) Sample image with noise distributed in four quadrants. (b)The absolute angle error of coherence enhancement diffusion. (c) The absolute angle error of multi-scale DDFB. Fig. 10. (a) The absolute angle error of coherence enhancement diffusion. (b) The absolute angle error of multi-scale DDFB.
Fig. 14. (a) Original image. (b) Coherence enhancement diffusion results on (a). (c) Multi-scale DDFB results on (a). (d) Binarization of (a). (e) Binarization of (b). (f) Binarization of (c). Fig. 13. (a) Original image. (b) Coherence enhancement diffusion results on (a) (c) Multi-scale DDFB results on (a). (d) Binarization and minutiae points of (a). (e Binarization and minutiae points of (b). (f) Binarization and minutiae points of (c).
Fig. 14. (a) Original image. (b) Coherence enhancement diffusion results on (a). (c) Multi-scale DDFB results on (a). (d) Binarization of (a). (e) Binarization of (b). (f) Binarization of (c). Fig. 13. (a) Original image. (b) Coherence enhancement diffusion results on (a) (c) Multi-scale DDFB results on (a). (d) Binarization and minutiae points of (a). (e Binarization and minutiae points of (b). (f) Binarization and minutiae points of (c).
Fig. 12. (a) Original image. (b) Coherence enhancement diffusion results on (a). (c) Multi-scale DDFB results on (a). (d) Binarization and minutiae points of (a). (e) Binarization and minutiae points of (b). (f) Binarization and minutiae points of (c).
Fig. 12. (a) Original image. (b) Coherence enhancement diffusion results on (a). (c) Multi-scale DDFB results on (a). (d) Binarization and minutiae points of (a). (e) Binarization and minutiae points of (b). (f) Binarization and minutiae points of (c).
Fig. 17. (a) Original image. (b) Output simple coherence enhancement diffusion applied on (a). (c) Output of simple Hong applied on (a). (d) Output of proposed method (modified Hong then modified coherence enhancement diffusion) applied on (a). (e) Binarization and minutiae points of (a). (f) Binarization and minutiae points of (b). (g) Binarization and minutiae points of (c). (h) Binarization and minu- tiae points of (d).
Fig. 17. (a) Original image. (b) Output simple coherence enhancement diffusion applied on (a). (c) Output of simple Hong applied on (a). (d) Output of proposed method (modified Hong then modified coherence enhancement diffusion) applied on (a). (e) Binarization and minutiae points of (a). (f) Binarization and minutiae points of (b). (g) Binarization and minutiae points of (c). (h) Binarization and minu- tiae points of (d).
Fig. 16. (a) Original image. (b) Output of simple coherence enhancement diffusion applied on (a). (c) Output of simple Hong applied on (a). (d) Output of proposed method (modified Hong then modified coherence enhancement diffusion) applied on (a). (e) Binarization and minutiae points of (a). (f) Binarization and minutiae points of (b). (g) Binarization and minutiae points of (c). (h) Binarization and minu- tiae points of (d).
Fig. 16. (a) Original image. (b) Output of simple coherence enhancement diffusion applied on (a). (c) Output of simple Hong applied on (a). (d) Output of proposed method (modified Hong then modified coherence enhancement diffusion) applied on (a). (e) Binarization and minutiae points of (a). (f) Binarization and minutiae points of (b). (g) Binarization and minutiae points of (c). (h) Binarization and minu- tiae points of (d).
Fig. 15. (a) Original image. (b) Output simple coherence enhancement diffusion applied on (a). (c) Output of simple Hong applied on (a). (d) Output of proposed method (modified Hong then modified coherence enhancement diffusion) applied on (a). (e) Binarization and minutiae points of (a). (f) Binarization and minutiae points of (b). (g) Binarization and minutiae points of (c). (h) Binarization and minu- tiae points of (d).
Fig. 15. (a) Original image. (b) Output simple coherence enhancement diffusion applied on (a). (c) Output of simple Hong applied on (a). (d) Output of proposed method (modified Hong then modified coherence enhancement diffusion) applied on (a). (e) Binarization and minutiae points of (a). (f) Binarization and minutiae points of (b). (g) Binarization and minutiae points of (c). (h) Binarization and minu- tiae points of (d).