Abstract
In this paper we propose a new method for removing specular reflection from multispectral dermatological images which is based on blind source separation using Non-negative Matrix Factorization. The key idea of our method is based on a first step which consists to estimate the number of sources involved, by applying a Principal Component Analysis, then a first version of these sources by applying an Independent Component Analysis to our images. We exploit this first version of the sources in a second step to initialize our Non-negative Matrix Factorization algorithm instead of the random initialization that is used by most of the existing methods and that considerably affects their performances. In order to quantify numerically the performance of our method, we also propose a new protocol to artificially mix a specular reflection image with a diffuse reflection image. The tests effected on real and artificial multispectral dermatological images have shown the good performance of our method compared to two of the most used methods.
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Notes
- 1.
As the reflectance function \(F(u,\lambda )\) physically represents all phenomena produced by the interaction between light and skin, it is in principle described by an exponential model representing the absorption of the different components of the skin [14].
- 2.
We show that the BSS problem is an ill-posed inverse problem which admits an infinity of solutions so that it is essential to add hypotheses on the sources and/or on the mixing coefficients, which gave rise to 3 families of methods. These three families are based respectively on Independent Component Analysis (ICA), Sparse Component Analysis (SCA) and Non-negative Matrix Factorisation (NMF) (See [9] for more details).
- 3.
A signal is said to be sparse in a given representation domain if there are some areas of that domain where it is inactive.
- 4.
That is 3 bands corresponding to the visible range (RGB) and 3 bands corresponding to the infrared range.
- 5.
We recall that this number of principal components is none other than the number of non-zero (or significant) eigenvalues of the covariance matrix associated to the image. In practice, we choose a threshold below which an eigenvalue is considered to be zero (see Results section).
- 6.
For example, for a matrix of size \(m\times n\), this vectorisation consists in juxtaposing its rows one after the other which gives us a vector of length “\(m\cdot n\)”.
- 7.
Indeed, BSS methods based on ICA can be classified into two families [9]. The first family includes the methods that exploit higher order statistics and assume that the source signals are statistically independent at higher orders (for example, the methods JADE [6] and FasICA [16]). The second family includes the methods that exploit second-order statistics and assume that the source signals are statistically independent at second order only (for example, the methods AMUSE [29] and SOBI [3]).
- 8.
This is for example the case of audio signals.
- 9.
This is the case for most of the real sources, using any BSS method.
- 10.
Indeed, for all other BSS approaches, the separation is performed in two steps: the estimation of the separation matrix, then that of the sources.
- 11.
In other words, in our case the number of spectral bands M of our image must be superior than or equal to the number of sources which is equal to \(N_d+1\).
- 12.
Note that, we could very well propose a criterion exploiting the distribution of the specular reflection which is known for its sparseness, in order to identify it automatically.
- 13.
In our computations, any eigenvalue of the covariance matrix (associated to the image) having a value less than \(10^{-3}\) is considered as null.
- 14.
- 15.
Knowing that, we performed tests for different values of \(N_d\), and we found that the method [2] gives good results for \(N_d=2\).
- 16.
Indeed, the criterion based on the visual analysis of the treated images is a qualitative criterion and it is difficult with the naked eye to compare in a precise way between two treated images. This comparison becomes even more difficult, if not impossible, when the two images are very close in terms of elimination the specular reflection.
- 17.
i.e. the real RGB image consisting only of the diffuse reflection.
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Zokay, M., Saylani, H. (2022). Removing Specular Reflection in Multispectral Dermatological Images Using Blind Source Separation. In: Yang, G., Aviles-Rivero, A., Roberts, M., Schönlieb, CB. (eds) Medical Image Understanding and Analysis. MIUA 2022. Lecture Notes in Computer Science, vol 13413. Springer, Cham. https://doi.org/10.1007/978-3-031-12053-4_54
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