Abstract

Many people suffer from different skin diseases, which can be diverse and varied. Most skin diseases cause disorders in the skin, such as changes in color, texture, and appearance manifesting in spots, swelling, scaling, ulcers, etc. One of the diseases that represents a serious health problem is skin cancer. The most dangerous skin cancer is malignant melanoma, which can cause death if not detected early. Therefore, development of new and accurate diagnosis methodologies to increase the chance of early detection is important. In this work, an analysis to discriminate between malignant melanoma and three types of benign skin lesions–melanocytic nevus, dermatofibroma, and seborrheic keratosis–is realized by calculating spectral indexes based on the real and imaginary parts of a fractional nonlinear filter obtained by affecting the modulus of the fractional Fourier transform by an exponent $k$. The fractional spectral indexes were calculated by working with selected sub-images obtained by dividing the input image. Also, a variation was implemented when the Hermite transform is used to calculate the fractional nonlinear filter. Discrimination between malignant melanoma and benign skin lesions was achieved with a 99.7% confidence level.

© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref]
  23. A. R. MacKenzie-Wood, G. W. Milton, and J. W. Launey, “Melanoma: Accuracy of clinical diagnosis,” Australas. J. Dermatol. 39(1), 31–33 (1998).
    [Crossref]
  24. M. Miller and A. B. Ackerman, “How accurate are dermatologists in the diagnosis of melanoma? degree of accuracy and implications,” Arch. Dermatol. 128(4), 559–560 (1992).
    [Crossref]
  25. B. Lindel and M. A. Hedblad, “Accuracy in the clinical diagnosis and pattern of malignant melanoma at a dermatological clinic,” J. Dermatol. 21(7), 461–464 (1994).
    [Crossref]
  26. C. M. Grin, A. W. Kopf, B. Welkovich, R. S. Bart, and M. J. Levenstein, “Accuracy in the clinical diagnosis of malignant melanoma,” Arch. Dermatol. 126(6), 763–766 (1990).
    [Crossref]
  27. A. M. Anderson, M. Matsumoto, M. I. Saul, A. M. Secrest, and L. K. Ferris, “Accuracy of skin cancer diagnosis by physician assistants compared with dermatologists in a large health care system,” JAMA Dermatol. 154(5), 569–573 (2018).
    [Crossref]

2018 (2)

A. Castro-Valdez and J. Álvarez-Borrego, “Identification of phytoplankton species using Hermite transform,” Ukr. J. Phys. Opt. 19(2), 106–120 (2018).
[Crossref]

A. M. Anderson, M. Matsumoto, M. I. Saul, A. M. Secrest, and L. K. Ferris, “Accuracy of skin cancer diagnosis by physician assistants compared with dermatologists in a large health care system,” JAMA Dermatol. 154(5), 569–573 (2018).
[Crossref]

2017 (3)

E. Guerra-Rosas, J. Álvarez-Borrego, and A. Angulo-Molina, “Identification of melanoma cells: a method based in mean variance of signatures via spectral densities,” Biomed. Opt. Express 8(4), 2185–2194 (2017).
[Crossref]

J. Q. Del Rosso, “A Closer Look at Seborrheic Keratoses: Patient Perspectives, Clinical Relevance, Medical Necessity, and Implications for Management,” J. Clin. Aesthet. Dermatol. 10(3), 16–25 (2017).

M. Zortea, E. Flores, and J. Scharcanski, “A simple weighted thresholding method for the segmentation of pigmented skin lesions in macroscopic images,” Pattern Recognit. 64, 92–104 (2017).
[Crossref]

2015 (1)

2014 (1)

A. Taloni, A. A. Alemi, E. Ciusani, J. P. Sethna, S. Zapperi, and C. A. M. La Porta, “Mechanical properties of growing melanocytic nevi and the progression to melanoma,” PLoS One 9(4), e94229 (2014).
[Crossref]

2012 (3)

L. Parish, S. Yazdanian, W. C. Lambert, and P. C. Lambert, “Dermatofibroma: a curious tumor,” Thomas Jefferson Univ. Jefferson Digit Commons Dep. 10(5), 268–270 (2012).

K. Korotkov and R. Garcia, “Computerized analysis of pigmented skin lesions: a review,” Artif. Intell. Med. 56(2), 69–90 (2012).
[Crossref]

J. A. Jaleel, S. Salim, and R. B. Aswin, “Artificial neural network based detection of skin cancer,” IJAREEIE. 1, 200–2005 (2012).

2011 (1)

A. G. Isai, B. G. Zapirain, and A. M. Zorrilla, “Melanomas non-invasive diagnosis application based on the ABCD rule and pattern recognition image processing algorithms,” Comput. Biol. Med. 41(9), 742–755 (2011).
[Crossref]

2010 (1)

M. M. Rahman and P. Bhattacharya, “An integrated and interactive decision support system for automated melanoma recognition of dermoscopic images,” Comput. Med. Imaging Graph. 34(6), 479–486 (2010).
[Crossref]

2009 (1)

S. Ogden and N. R. Telfer, “Skin cancer,” Medicine 37(6), 305–308 (2009).
[Crossref]

2008 (1)

B. Escalante-Ramírez, “The Hermite transform as an efficient model for local image analysis: An application to medical image fusion,” Comput. Electr. Eng. 34(2), 99–110 (2008).
[Crossref]

2001 (1)

M. Helfand, S. Mahon, and K. Eden, “Screening for skin cancer,” Am. J. Prev. Med. 20(3), 47–58 (2001).
[Crossref]

1999 (1)

H. M. Ozaktas, M. A. Kutay, and D. Mendlovic, “Introduction to the Fractional Fourier Transform and its Applications,” Adv. Imag. Electron. Phys. 106, 239–291 (1999).

1998 (1)

A. R. MacKenzie-Wood, G. W. Milton, and J. W. Launey, “Melanoma: Accuracy of clinical diagnosis,” Australas. J. Dermatol. 39(1), 31–33 (1998).
[Crossref]

1997 (1)

B. Javidi, W. Wang, and G. Zhang, “Composite Fourier-plane nonlinear filter for distortion-invariant pattern recognition,” Opt. Eng. 36(10), 2690–2696 (1997).
[Crossref]

1994 (1)

B. Lindel and M. A. Hedblad, “Accuracy in the clinical diagnosis and pattern of malignant melanoma at a dermatological clinic,” J. Dermatol. 21(7), 461–464 (1994).
[Crossref]

1992 (1)

M. Miller and A. B. Ackerman, “How accurate are dermatologists in the diagnosis of melanoma? degree of accuracy and implications,” Arch. Dermatol. 128(4), 559–560 (1992).
[Crossref]

1990 (2)

C. M. Grin, A. W. Kopf, B. Welkovich, R. S. Bart, and M. J. Levenstein, “Accuracy in the clinical diagnosis of malignant melanoma,” Arch. Dermatol. 126(6), 763–766 (1990).
[Crossref]

M. Jean-Bernard, “The Hermite Transform-Theory,” IEEE Trans. Acoust., Speech, Signal Process. 38(9), 1595–1606 (1990).
[Crossref]

Ackerman, A. B.

M. Miller and A. B. Ackerman, “How accurate are dermatologists in the diagnosis of melanoma? degree of accuracy and implications,” Arch. Dermatol. 128(4), 559–560 (1992).
[Crossref]

Aldridge, R. B.

L. Ballerini, R. B. Fisher, R. B. Aldridge, and J. Rees, “A Color and Texture Based Hierarchical K-NN Approach to the Classification of Non-melanoma Skin Lesions,” in M. E. Celebi and G. Schaefer (eds.), Color Medical Image Analysis, Lecture Notes in Computational Vision and Biomechanics 6, ISBN 978-94-007-5389-1, (Springer, 2013), 1–26.

Alemi, A. A.

A. Taloni, A. A. Alemi, E. Ciusani, J. P. Sethna, S. Zapperi, and C. A. M. La Porta, “Mechanical properties of growing melanocytic nevi and the progression to melanoma,” PLoS One 9(4), e94229 (2014).
[Crossref]

Alvarez-Borrego, J.

Álvarez-Borrego, J.

A. Castro-Valdez and J. Álvarez-Borrego, “Identification of phytoplankton species using Hermite transform,” Ukr. J. Phys. Opt. 19(2), 106–120 (2018).
[Crossref]

E. Guerra-Rosas, J. Álvarez-Borrego, and A. Angulo-Molina, “Identification of melanoma cells: a method based in mean variance of signatures via spectral densities,” Biomed. Opt. Express 8(4), 2185–2194 (2017).
[Crossref]

Anderson, A. M.

A. M. Anderson, M. Matsumoto, M. I. Saul, A. M. Secrest, and L. K. Ferris, “Accuracy of skin cancer diagnosis by physician assistants compared with dermatologists in a large health care system,” JAMA Dermatol. 154(5), 569–573 (2018).
[Crossref]

Angulo-Molina, A.

Aswin, R. B.

J. A. Jaleel, S. Salim, and R. B. Aswin, “Artificial neural network based detection of skin cancer,” IJAREEIE. 1, 200–2005 (2012).

Ballerini, L.

L. Ballerini, R. B. Fisher, R. B. Aldridge, and J. Rees, “A Color and Texture Based Hierarchical K-NN Approach to the Classification of Non-melanoma Skin Lesions,” in M. E. Celebi and G. Schaefer (eds.), Color Medical Image Analysis, Lecture Notes in Computational Vision and Biomechanics 6, ISBN 978-94-007-5389-1, (Springer, 2013), 1–26.

Bart, R. S.

C. M. Grin, A. W. Kopf, B. Welkovich, R. S. Bart, and M. J. Levenstein, “Accuracy in the clinical diagnosis of malignant melanoma,” Arch. Dermatol. 126(6), 763–766 (1990).
[Crossref]

Betta, G.

G. Betta, G. Di Leo, G. Fabbrocini, A. Paolillo, and P. Sommella, “Dermoscopic image-analysis system: estimation of atypical pigment network and atypical vascular pattern,” presented at the International Workshop on Medical Measuremet and Applications, Beneto, Italy, 20-21 Abril 2006.

Bhattacharya, P.

M. M. Rahman and P. Bhattacharya, “An integrated and interactive decision support system for automated melanoma recognition of dermoscopic images,” Comput. Med. Imaging Graph. 34(6), 479–486 (2010).
[Crossref]

Castro-Valdez, A.

A. Castro-Valdez and J. Álvarez-Borrego, “Identification of phytoplankton species using Hermite transform,” Ukr. J. Phys. Opt. 19(2), 106–120 (2018).
[Crossref]

Celebi, M. E.

N. C. F. Codella, D. Gutman, M. E. Celebi, B. Helba, M. A. Marchetti, S. W. Dusza, A. Kalloo, K. Liopyris, N. Mishra, H. Kittler, and A. Halpern, “Skin lesion analysis toward melanoma detection: A challenge at the 2017 International symposium on biomedical imaging (ISBI), hosted by the international skin imaging collaboration (ISIC),” Proc. - Int. Symp. Biomed. Imaging. (2018).

Ciusani, E.

A. Taloni, A. A. Alemi, E. Ciusani, J. P. Sethna, S. Zapperi, and C. A. M. La Porta, “Mechanical properties of growing melanocytic nevi and the progression to melanoma,” PLoS One 9(4), e94229 (2014).
[Crossref]

Codella, N. C. F.

N. C. F. Codella, D. Gutman, M. E. Celebi, B. Helba, M. A. Marchetti, S. W. Dusza, A. Kalloo, K. Liopyris, N. Mishra, H. Kittler, and A. Halpern, “Skin lesion analysis toward melanoma detection: A challenge at the 2017 International symposium on biomedical imaging (ISBI), hosted by the international skin imaging collaboration (ISIC),” Proc. - Int. Symp. Biomed. Imaging. (2018).

Del Rosso, J. Q.

J. Q. Del Rosso, “A Closer Look at Seborrheic Keratoses: Patient Perspectives, Clinical Relevance, Medical Necessity, and Implications for Management,” J. Clin. Aesthet. Dermatol. 10(3), 16–25 (2017).

Di Leo, G.

G. Betta, G. Di Leo, G. Fabbrocini, A. Paolillo, and P. Sommella, “Dermoscopic image-analysis system: estimation of atypical pigment network and atypical vascular pattern,” presented at the International Workshop on Medical Measuremet and Applications, Beneto, Italy, 20-21 Abril 2006.

Dusza, S. W.

N. C. F. Codella, D. Gutman, M. E. Celebi, B. Helba, M. A. Marchetti, S. W. Dusza, A. Kalloo, K. Liopyris, N. Mishra, H. Kittler, and A. Halpern, “Skin lesion analysis toward melanoma detection: A challenge at the 2017 International symposium on biomedical imaging (ISBI), hosted by the international skin imaging collaboration (ISIC),” Proc. - Int. Symp. Biomed. Imaging. (2018).

Eden, K.

M. Helfand, S. Mahon, and K. Eden, “Screening for skin cancer,” Am. J. Prev. Med. 20(3), 47–58 (2001).
[Crossref]

Escalante-Ramírez, B.

B. Escalante-Ramírez, “The Hermite transform as an efficient model for local image analysis: An application to medical image fusion,” Comput. Electr. Eng. 34(2), 99–110 (2008).
[Crossref]

Fabbrocini, G.

G. Betta, G. Di Leo, G. Fabbrocini, A. Paolillo, and P. Sommella, “Dermoscopic image-analysis system: estimation of atypical pigment network and atypical vascular pattern,” presented at the International Workshop on Medical Measuremet and Applications, Beneto, Italy, 20-21 Abril 2006.

Ferris, L. K.

A. M. Anderson, M. Matsumoto, M. I. Saul, A. M. Secrest, and L. K. Ferris, “Accuracy of skin cancer diagnosis by physician assistants compared with dermatologists in a large health care system,” JAMA Dermatol. 154(5), 569–573 (2018).
[Crossref]

Fisher, R. B.

L. Ballerini, R. B. Fisher, R. B. Aldridge, and J. Rees, “A Color and Texture Based Hierarchical K-NN Approach to the Classification of Non-melanoma Skin Lesions,” in M. E. Celebi and G. Schaefer (eds.), Color Medical Image Analysis, Lecture Notes in Computational Vision and Biomechanics 6, ISBN 978-94-007-5389-1, (Springer, 2013), 1–26.

Flores, E.

M. Zortea, E. Flores, and J. Scharcanski, “A simple weighted thresholding method for the segmentation of pigmented skin lesions in macroscopic images,” Pattern Recognit. 64, 92–104 (2017).
[Crossref]

Garcia, R.

K. Korotkov and R. Garcia, “Computerized analysis of pigmented skin lesions: a review,” Artif. Intell. Med. 56(2), 69–90 (2012).
[Crossref]

Grin, C. M.

C. M. Grin, A. W. Kopf, B. Welkovich, R. S. Bart, and M. J. Levenstein, “Accuracy in the clinical diagnosis of malignant melanoma,” Arch. Dermatol. 126(6), 763–766 (1990).
[Crossref]

Guerra-Rosas, E.

Gutman, D.

N. C. F. Codella, D. Gutman, M. E. Celebi, B. Helba, M. A. Marchetti, S. W. Dusza, A. Kalloo, K. Liopyris, N. Mishra, H. Kittler, and A. Halpern, “Skin lesion analysis toward melanoma detection: A challenge at the 2017 International symposium on biomedical imaging (ISBI), hosted by the international skin imaging collaboration (ISIC),” Proc. - Int. Symp. Biomed. Imaging. (2018).

Halpern, A.

N. C. F. Codella, D. Gutman, M. E. Celebi, B. Helba, M. A. Marchetti, S. W. Dusza, A. Kalloo, K. Liopyris, N. Mishra, H. Kittler, and A. Halpern, “Skin lesion analysis toward melanoma detection: A challenge at the 2017 International symposium on biomedical imaging (ISBI), hosted by the international skin imaging collaboration (ISIC),” Proc. - Int. Symp. Biomed. Imaging. (2018).

Hedblad, M. A.

B. Lindel and M. A. Hedblad, “Accuracy in the clinical diagnosis and pattern of malignant melanoma at a dermatological clinic,” J. Dermatol. 21(7), 461–464 (1994).
[Crossref]

Helba, B.

N. C. F. Codella, D. Gutman, M. E. Celebi, B. Helba, M. A. Marchetti, S. W. Dusza, A. Kalloo, K. Liopyris, N. Mishra, H. Kittler, and A. Halpern, “Skin lesion analysis toward melanoma detection: A challenge at the 2017 International symposium on biomedical imaging (ISBI), hosted by the international skin imaging collaboration (ISIC),” Proc. - Int. Symp. Biomed. Imaging. (2018).

Helfand, M.

M. Helfand, S. Mahon, and K. Eden, “Screening for skin cancer,” Am. J. Prev. Med. 20(3), 47–58 (2001).
[Crossref]

Isai, A. G.

A. G. Isai, B. G. Zapirain, and A. M. Zorrilla, “Melanomas non-invasive diagnosis application based on the ABCD rule and pattern recognition image processing algorithms,” Comput. Biol. Med. 41(9), 742–755 (2011).
[Crossref]

Jaleel, J. A.

J. A. Jaleel, S. Salim, and R. B. Aswin, “Artificial neural network based detection of skin cancer,” IJAREEIE. 1, 200–2005 (2012).

Javidi, B.

B. Javidi, W. Wang, and G. Zhang, “Composite Fourier-plane nonlinear filter for distortion-invariant pattern recognition,” Opt. Eng. 36(10), 2690–2696 (1997).
[Crossref]

Jean-Bernard, M.

M. Jean-Bernard, “The Hermite Transform-Theory,” IEEE Trans. Acoust., Speech, Signal Process. 38(9), 1595–1606 (1990).
[Crossref]

Jiang, M.

T. Y. Tan, L. Zhang, and M. Jiang, “An intelligent decision support system for skin cancer detection from dermoscopic images,” 12th Int Conf Nat Comput Fuzzy Syst Knowl Discov. (2016).

Kalloo, A.

N. C. F. Codella, D. Gutman, M. E. Celebi, B. Helba, M. A. Marchetti, S. W. Dusza, A. Kalloo, K. Liopyris, N. Mishra, H. Kittler, and A. Halpern, “Skin lesion analysis toward melanoma detection: A challenge at the 2017 International symposium on biomedical imaging (ISBI), hosted by the international skin imaging collaboration (ISIC),” Proc. - Int. Symp. Biomed. Imaging. (2018).

Kittler, H.

N. C. F. Codella, D. Gutman, M. E. Celebi, B. Helba, M. A. Marchetti, S. W. Dusza, A. Kalloo, K. Liopyris, N. Mishra, H. Kittler, and A. Halpern, “Skin lesion analysis toward melanoma detection: A challenge at the 2017 International symposium on biomedical imaging (ISBI), hosted by the international skin imaging collaboration (ISIC),” Proc. - Int. Symp. Biomed. Imaging. (2018).

Kopf, A. W.

C. M. Grin, A. W. Kopf, B. Welkovich, R. S. Bart, and M. J. Levenstein, “Accuracy in the clinical diagnosis of malignant melanoma,” Arch. Dermatol. 126(6), 763–766 (1990).
[Crossref]

Korotkov, K.

K. Korotkov and R. Garcia, “Computerized analysis of pigmented skin lesions: a review,” Artif. Intell. Med. 56(2), 69–90 (2012).
[Crossref]

Kutay, M. A.

H. M. Ozaktas, M. A. Kutay, and D. Mendlovic, “Introduction to the Fractional Fourier Transform and its Applications,” Adv. Imag. Electron. Phys. 106, 239–291 (1999).

La Porta, C. A. M.

A. Taloni, A. A. Alemi, E. Ciusani, J. P. Sethna, S. Zapperi, and C. A. M. La Porta, “Mechanical properties of growing melanocytic nevi and the progression to melanoma,” PLoS One 9(4), e94229 (2014).
[Crossref]

Lambert, P. C.

L. Parish, S. Yazdanian, W. C. Lambert, and P. C. Lambert, “Dermatofibroma: a curious tumor,” Thomas Jefferson Univ. Jefferson Digit Commons Dep. 10(5), 268–270 (2012).

Lambert, W. C.

L. Parish, S. Yazdanian, W. C. Lambert, and P. C. Lambert, “Dermatofibroma: a curious tumor,” Thomas Jefferson Univ. Jefferson Digit Commons Dep. 10(5), 268–270 (2012).

Launey, J. W.

A. R. MacKenzie-Wood, G. W. Milton, and J. W. Launey, “Melanoma: Accuracy of clinical diagnosis,” Australas. J. Dermatol. 39(1), 31–33 (1998).
[Crossref]

Levenstein, M. J.

C. M. Grin, A. W. Kopf, B. Welkovich, R. S. Bart, and M. J. Levenstein, “Accuracy in the clinical diagnosis of malignant melanoma,” Arch. Dermatol. 126(6), 763–766 (1990).
[Crossref]

Lindel, B.

B. Lindel and M. A. Hedblad, “Accuracy in the clinical diagnosis and pattern of malignant melanoma at a dermatological clinic,” J. Dermatol. 21(7), 461–464 (1994).
[Crossref]

Liopyris, K.

N. C. F. Codella, D. Gutman, M. E. Celebi, B. Helba, M. A. Marchetti, S. W. Dusza, A. Kalloo, K. Liopyris, N. Mishra, H. Kittler, and A. Halpern, “Skin lesion analysis toward melanoma detection: A challenge at the 2017 International symposium on biomedical imaging (ISBI), hosted by the international skin imaging collaboration (ISIC),” Proc. - Int. Symp. Biomed. Imaging. (2018).

MacKenzie-Wood, A. R.

A. R. MacKenzie-Wood, G. W. Milton, and J. W. Launey, “Melanoma: Accuracy of clinical diagnosis,” Australas. J. Dermatol. 39(1), 31–33 (1998).
[Crossref]

Mahon, S.

M. Helfand, S. Mahon, and K. Eden, “Screening for skin cancer,” Am. J. Prev. Med. 20(3), 47–58 (2001).
[Crossref]

Marchetti, M. A.

N. C. F. Codella, D. Gutman, M. E. Celebi, B. Helba, M. A. Marchetti, S. W. Dusza, A. Kalloo, K. Liopyris, N. Mishra, H. Kittler, and A. Halpern, “Skin lesion analysis toward melanoma detection: A challenge at the 2017 International symposium on biomedical imaging (ISBI), hosted by the international skin imaging collaboration (ISIC),” Proc. - Int. Symp. Biomed. Imaging. (2018).

Matsumoto, M.

A. M. Anderson, M. Matsumoto, M. I. Saul, A. M. Secrest, and L. K. Ferris, “Accuracy of skin cancer diagnosis by physician assistants compared with dermatologists in a large health care system,” JAMA Dermatol. 154(5), 569–573 (2018).
[Crossref]

Mendlovic, D.

H. M. Ozaktas, M. A. Kutay, and D. Mendlovic, “Introduction to the Fractional Fourier Transform and its Applications,” Adv. Imag. Electron. Phys. 106, 239–291 (1999).

Miller, M.

M. Miller and A. B. Ackerman, “How accurate are dermatologists in the diagnosis of melanoma? degree of accuracy and implications,” Arch. Dermatol. 128(4), 559–560 (1992).
[Crossref]

Milton, G. W.

A. R. MacKenzie-Wood, G. W. Milton, and J. W. Launey, “Melanoma: Accuracy of clinical diagnosis,” Australas. J. Dermatol. 39(1), 31–33 (1998).
[Crossref]

Mishra, N.

N. C. F. Codella, D. Gutman, M. E. Celebi, B. Helba, M. A. Marchetti, S. W. Dusza, A. Kalloo, K. Liopyris, N. Mishra, H. Kittler, and A. Halpern, “Skin lesion analysis toward melanoma detection: A challenge at the 2017 International symposium on biomedical imaging (ISBI), hosted by the international skin imaging collaboration (ISIC),” Proc. - Int. Symp. Biomed. Imaging. (2018).

Ogden, S.

S. Ogden and N. R. Telfer, “Skin cancer,” Medicine 37(6), 305–308 (2009).
[Crossref]

Ozaktas, H. M.

H. M. Ozaktas, M. A. Kutay, and D. Mendlovic, “Introduction to the Fractional Fourier Transform and its Applications,” Adv. Imag. Electron. Phys. 106, 239–291 (1999).

Paolillo, A.

G. Betta, G. Di Leo, G. Fabbrocini, A. Paolillo, and P. Sommella, “Dermoscopic image-analysis system: estimation of atypical pigment network and atypical vascular pattern,” presented at the International Workshop on Medical Measuremet and Applications, Beneto, Italy, 20-21 Abril 2006.

Parish, L.

L. Parish, S. Yazdanian, W. C. Lambert, and P. C. Lambert, “Dermatofibroma: a curious tumor,” Thomas Jefferson Univ. Jefferson Digit Commons Dep. 10(5), 268–270 (2012).

Rahman, M. M.

M. M. Rahman and P. Bhattacharya, “An integrated and interactive decision support system for automated melanoma recognition of dermoscopic images,” Comput. Med. Imaging Graph. 34(6), 479–486 (2010).
[Crossref]

Rees, J.

L. Ballerini, R. B. Fisher, R. B. Aldridge, and J. Rees, “A Color and Texture Based Hierarchical K-NN Approach to the Classification of Non-melanoma Skin Lesions,” in M. E. Celebi and G. Schaefer (eds.), Color Medical Image Analysis, Lecture Notes in Computational Vision and Biomechanics 6, ISBN 978-94-007-5389-1, (Springer, 2013), 1–26.

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J. A. Jaleel, S. Salim, and R. B. Aswin, “Artificial neural network based detection of skin cancer,” IJAREEIE. 1, 200–2005 (2012).

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A. M. Anderson, M. Matsumoto, M. I. Saul, A. M. Secrest, and L. K. Ferris, “Accuracy of skin cancer diagnosis by physician assistants compared with dermatologists in a large health care system,” JAMA Dermatol. 154(5), 569–573 (2018).
[Crossref]

Scharcanski, J.

M. Zortea, E. Flores, and J. Scharcanski, “A simple weighted thresholding method for the segmentation of pigmented skin lesions in macroscopic images,” Pattern Recognit. 64, 92–104 (2017).
[Crossref]

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A. M. Anderson, M. Matsumoto, M. I. Saul, A. M. Secrest, and L. K. Ferris, “Accuracy of skin cancer diagnosis by physician assistants compared with dermatologists in a large health care system,” JAMA Dermatol. 154(5), 569–573 (2018).
[Crossref]

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A. Taloni, A. A. Alemi, E. Ciusani, J. P. Sethna, S. Zapperi, and C. A. M. La Porta, “Mechanical properties of growing melanocytic nevi and the progression to melanoma,” PLoS One 9(4), e94229 (2014).
[Crossref]

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G. Betta, G. Di Leo, G. Fabbrocini, A. Paolillo, and P. Sommella, “Dermoscopic image-analysis system: estimation of atypical pigment network and atypical vascular pattern,” presented at the International Workshop on Medical Measuremet and Applications, Beneto, Italy, 20-21 Abril 2006.

Taloni, A.

A. Taloni, A. A. Alemi, E. Ciusani, J. P. Sethna, S. Zapperi, and C. A. M. La Porta, “Mechanical properties of growing melanocytic nevi and the progression to melanoma,” PLoS One 9(4), e94229 (2014).
[Crossref]

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T. Y. Tan, L. Zhang, and M. Jiang, “An intelligent decision support system for skin cancer detection from dermoscopic images,” 12th Int Conf Nat Comput Fuzzy Syst Knowl Discov. (2016).

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S. Ogden and N. R. Telfer, “Skin cancer,” Medicine 37(6), 305–308 (2009).
[Crossref]

Wang, W.

B. Javidi, W. Wang, and G. Zhang, “Composite Fourier-plane nonlinear filter for distortion-invariant pattern recognition,” Opt. Eng. 36(10), 2690–2696 (1997).
[Crossref]

Welkovich, B.

C. M. Grin, A. W. Kopf, B. Welkovich, R. S. Bart, and M. J. Levenstein, “Accuracy in the clinical diagnosis of malignant melanoma,” Arch. Dermatol. 126(6), 763–766 (1990).
[Crossref]

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L. Parish, S. Yazdanian, W. C. Lambert, and P. C. Lambert, “Dermatofibroma: a curious tumor,” Thomas Jefferson Univ. Jefferson Digit Commons Dep. 10(5), 268–270 (2012).

Zapirain, B. G.

A. G. Isai, B. G. Zapirain, and A. M. Zorrilla, “Melanomas non-invasive diagnosis application based on the ABCD rule and pattern recognition image processing algorithms,” Comput. Biol. Med. 41(9), 742–755 (2011).
[Crossref]

Zapperi, S.

A. Taloni, A. A. Alemi, E. Ciusani, J. P. Sethna, S. Zapperi, and C. A. M. La Porta, “Mechanical properties of growing melanocytic nevi and the progression to melanoma,” PLoS One 9(4), e94229 (2014).
[Crossref]

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B. Javidi, W. Wang, and G. Zhang, “Composite Fourier-plane nonlinear filter for distortion-invariant pattern recognition,” Opt. Eng. 36(10), 2690–2696 (1997).
[Crossref]

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T. Y. Tan, L. Zhang, and M. Jiang, “An intelligent decision support system for skin cancer detection from dermoscopic images,” 12th Int Conf Nat Comput Fuzzy Syst Knowl Discov. (2016).

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A. G. Isai, B. G. Zapirain, and A. M. Zorrilla, “Melanomas non-invasive diagnosis application based on the ABCD rule and pattern recognition image processing algorithms,” Comput. Biol. Med. 41(9), 742–755 (2011).
[Crossref]

Zortea, M.

M. Zortea, E. Flores, and J. Scharcanski, “A simple weighted thresholding method for the segmentation of pigmented skin lesions in macroscopic images,” Pattern Recognit. 64, 92–104 (2017).
[Crossref]

Adv. Imag. Electron. Phys. (1)

H. M. Ozaktas, M. A. Kutay, and D. Mendlovic, “Introduction to the Fractional Fourier Transform and its Applications,” Adv. Imag. Electron. Phys. 106, 239–291 (1999).

Am. J. Prev. Med. (1)

M. Helfand, S. Mahon, and K. Eden, “Screening for skin cancer,” Am. J. Prev. Med. 20(3), 47–58 (2001).
[Crossref]

Arch. Dermatol. (2)

M. Miller and A. B. Ackerman, “How accurate are dermatologists in the diagnosis of melanoma? degree of accuracy and implications,” Arch. Dermatol. 128(4), 559–560 (1992).
[Crossref]

C. M. Grin, A. W. Kopf, B. Welkovich, R. S. Bart, and M. J. Levenstein, “Accuracy in the clinical diagnosis of malignant melanoma,” Arch. Dermatol. 126(6), 763–766 (1990).
[Crossref]

Artif. Intell. Med. (1)

K. Korotkov and R. Garcia, “Computerized analysis of pigmented skin lesions: a review,” Artif. Intell. Med. 56(2), 69–90 (2012).
[Crossref]

Australas. J. Dermatol. (1)

A. R. MacKenzie-Wood, G. W. Milton, and J. W. Launey, “Melanoma: Accuracy of clinical diagnosis,” Australas. J. Dermatol. 39(1), 31–33 (1998).
[Crossref]

Biomed. Opt. Express (2)

Comput. Biol. Med. (1)

A. G. Isai, B. G. Zapirain, and A. M. Zorrilla, “Melanomas non-invasive diagnosis application based on the ABCD rule and pattern recognition image processing algorithms,” Comput. Biol. Med. 41(9), 742–755 (2011).
[Crossref]

Comput. Electr. Eng. (1)

B. Escalante-Ramírez, “The Hermite transform as an efficient model for local image analysis: An application to medical image fusion,” Comput. Electr. Eng. 34(2), 99–110 (2008).
[Crossref]

Comput. Med. Imaging Graph. (1)

M. M. Rahman and P. Bhattacharya, “An integrated and interactive decision support system for automated melanoma recognition of dermoscopic images,” Comput. Med. Imaging Graph. 34(6), 479–486 (2010).
[Crossref]

IEEE Trans. Acoust., Speech, Signal Process. (1)

M. Jean-Bernard, “The Hermite Transform-Theory,” IEEE Trans. Acoust., Speech, Signal Process. 38(9), 1595–1606 (1990).
[Crossref]

IJAREEIE. (1)

J. A. Jaleel, S. Salim, and R. B. Aswin, “Artificial neural network based detection of skin cancer,” IJAREEIE. 1, 200–2005 (2012).

J. Clin. Aesthet. Dermatol. (1)

J. Q. Del Rosso, “A Closer Look at Seborrheic Keratoses: Patient Perspectives, Clinical Relevance, Medical Necessity, and Implications for Management,” J. Clin. Aesthet. Dermatol. 10(3), 16–25 (2017).

J. Dermatol. (1)

B. Lindel and M. A. Hedblad, “Accuracy in the clinical diagnosis and pattern of malignant melanoma at a dermatological clinic,” J. Dermatol. 21(7), 461–464 (1994).
[Crossref]

JAMA Dermatol. (1)

A. M. Anderson, M. Matsumoto, M. I. Saul, A. M. Secrest, and L. K. Ferris, “Accuracy of skin cancer diagnosis by physician assistants compared with dermatologists in a large health care system,” JAMA Dermatol. 154(5), 569–573 (2018).
[Crossref]

Medicine (1)

S. Ogden and N. R. Telfer, “Skin cancer,” Medicine 37(6), 305–308 (2009).
[Crossref]

Opt. Eng. (1)

B. Javidi, W. Wang, and G. Zhang, “Composite Fourier-plane nonlinear filter for distortion-invariant pattern recognition,” Opt. Eng. 36(10), 2690–2696 (1997).
[Crossref]

Pattern Recognit. (1)

M. Zortea, E. Flores, and J. Scharcanski, “A simple weighted thresholding method for the segmentation of pigmented skin lesions in macroscopic images,” Pattern Recognit. 64, 92–104 (2017).
[Crossref]

PLoS One (1)

A. Taloni, A. A. Alemi, E. Ciusani, J. P. Sethna, S. Zapperi, and C. A. M. La Porta, “Mechanical properties of growing melanocytic nevi and the progression to melanoma,” PLoS One 9(4), e94229 (2014).
[Crossref]

Thomas Jefferson Univ. Jefferson Digit Commons Dep. (1)

L. Parish, S. Yazdanian, W. C. Lambert, and P. C. Lambert, “Dermatofibroma: a curious tumor,” Thomas Jefferson Univ. Jefferson Digit Commons Dep. 10(5), 268–270 (2012).

Ukr. J. Phys. Opt. (1)

A. Castro-Valdez and J. Álvarez-Borrego, “Identification of phytoplankton species using Hermite transform,” Ukr. J. Phys. Opt. 19(2), 106–120 (2018).
[Crossref]

Other (5)

T. Y. Tan, L. Zhang, and M. Jiang, “An intelligent decision support system for skin cancer detection from dermoscopic images,” 12th Int Conf Nat Comput Fuzzy Syst Knowl Discov. (2016).

N. C. F. Codella, D. Gutman, M. E. Celebi, B. Helba, M. A. Marchetti, S. W. Dusza, A. Kalloo, K. Liopyris, N. Mishra, H. Kittler, and A. Halpern, “Skin lesion analysis toward melanoma detection: A challenge at the 2017 International symposium on biomedical imaging (ISBI), hosted by the international skin imaging collaboration (ISIC),” Proc. - Int. Symp. Biomed. Imaging. (2018).

American Cancer Society. Cancer Facts & Figures. 2014.

G. Betta, G. Di Leo, G. Fabbrocini, A. Paolillo, and P. Sommella, “Dermoscopic image-analysis system: estimation of atypical pigment network and atypical vascular pattern,” presented at the International Workshop on Medical Measuremet and Applications, Beneto, Italy, 20-21 Abril 2006.

L. Ballerini, R. B. Fisher, R. B. Aldridge, and J. Rees, “A Color and Texture Based Hierarchical K-NN Approach to the Classification of Non-melanoma Skin Lesions,” in M. E. Celebi and G. Schaefer (eds.), Color Medical Image Analysis, Lecture Notes in Computational Vision and Biomechanics 6, ISBN 978-94-007-5389-1, (Springer, 2013), 1–26.

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Figures (8)

Fig. 1.
Fig. 1. Skin lesions images. (a) DF. (b) MEL. (c) MN. (d) SK.
Fig. 2.
Fig. 2. Segmentation process, where ${\bullet} $ is a point to point multiplication. (a) Original grayscale image. (b) Mask. (c) Segmented image.
Fig. 3.
Fig. 3. Image division. (a) Sub-masks $Mas{k_q}({x,\;y} )$. (b) Corresponding sub-images $I{({x,\;y} )_q}.$
Fig. 4.
Fig. 4. Sub-images selected for having information greater than or equal to one-third of its area.
Fig. 5.
Fig. 5. FrFT representation in the space-frequency plane.
Fig. 6.
Fig. 6. (a) Hermite transform of melanoma image. (b) Diagram of coefficient orders.
Fig. 7.
Fig. 7. Results of the fractional spectral indexes of sub-images. (a) $\overline {index_1^{SSFR}} $. (b) $\overline {index_2^{SSFR}} $. (c) $\overline {index_3^{SSFR}} $. (d) $\overline {index_4^{SSFR}} $.
Fig. 8.
Fig. 8. Results of the fractional spectral indexes when working with the HT of sub-images. (a) $\overline {index_1^{SSFR}} $. (b) $\overline {index_2^{SSFR}} $. (c) $\overline {index_3^{SSFR}} $. (d) $\overline {index_4^{SSFR}} $.

Tables (6)

Tables Icon

Table 1. Optimum orders for each fractional spectral index using sub-images.

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Table 2. Optimum orders for each fractional spectral index using the HT of the sub-images.

Tables Icon

Table 3. Fractional spectral indexes intervals for melanoma images.

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Table 4. Fractional spectral indexes Intervals for the melanoma images implementing the Hermite transform.

Tables Icon

Table 5. Sensitivity and Specificity for FrNLF

Tables Icon

Table 6. Sensitivity and Specificity for FrNLF with Hermite

Equations (19)

Equations on this page are rendered with MathJax. Learn more.

M a s k ( x , y ) = { 1 i f I g r a y ( x , y ) > T 0 i f I g r a y ( x , y ) T ,
T = max ( σ 2 ) .
A M a s k = x , y M a s k ( x , y ) , if M a s k ( x , y ) > 0.
A M a s k q = x , y M a s k q ( x , y ) , if M a s k q ( x , y ) > 0 ,
A M a s k q 1 3 [ A r e a q ] ,
G α ( u ) = F α { g ( x ) } = 1 j c o t α e j π u 2 c o t α g ( x ) e j π x 2 c o t α e j 2 π u x c s c α d x ,
p = α π / π 2 2 .
N L F { g ( x ) } = | G ( u ) | k e j ϕ ( u ) ,
N L F p { g ( x ) } = | G p ( u ) | k e j ϕ ( u ) .
W ( x , y ) = ( β , γ ) S v ( x β , y γ ) ,
L ( x , y ) = 1 W ( x , y ) ( β , γ ) S L ( x , y ) v ( x β , y γ ) .
v 2 ( x , y ) G M , N M ( x , y ) G L , K L ( x , y ) d x d y = δ N L δ M K ,
v ( x , y ) = 1 2 π σ 2 exp [ x 2 + y 2 2 σ 2 ] ,
G N M , M ( x , y ) = 1 2 N ( N M ) ! M ! H M ( x σ ) H N M ( y σ ) ,
L m , n m ( β , γ ) = L ( x , y ) D M , N M ( x β , y γ ) d x d y .
S S F R 1 q = { 1, if Re [ N L F p { I q ( x , y ) } ] 0 0, otherwise } , S S F R 2 q = { 1, if Re [ N L F p { I q ( x , y ) } ] < 0 0, otherwise } , S S F R 3 q = { 1, if Im [ N L F p { I q ( x , y ) } ] 0 0, otherwise } , S S F R 4 q = { 1, if Im [ N L F p { I q ( x , y ) } ] < 0 0, otherwise } ,
i n d e x n q S S F R = A M a s k q S S F R n q ,
i n d e x n S S F R ¯ = 1 Q i n d e x n q S S F R Q ,
m e a n ( i n d e x n S S F R ¯ ) = m = 1 76 i n d e x n m S S F R ¯ 76 ,