Image recognition in Matlab using Wavelets

Code used to load images from the path.

    These images are goind to be processed by using Wavelet 1-. The best Wavelet for this process is the Biorthogonal Wavelet 1-. In this test, we used this wavlet by changing the levels of decomposition, to obtain favorable results and to obtain weight matrices that are optimal for us to be used in a neural network. Another thing that was done was to distort the images by using transformation and distortion functions. These images must be analyzed with the wavelet in order to obtain their weights so as to train the neural network.

Functions used in the image treatment process.

Technical analysis

    In this section we are going to analyze the theoretical basis of the signature recognition  process. The first phase is about the conversion of the signature images into index matrices that characterizes those images in an unique way. These matrices are called weight matrices. To do this process, we are currently using Matlab, a mathmatical language that does these conversions using Wavelets.

    Wavelets are a set of tools and techniques that allows us to analyze images. Images are analyzed in both, scale an time aspect. When the descomposition is analyzed as a whole, compression processes are central and that is what we use to characterize signature images. One of the most recognized uses of Wavelets is the FBI digital fingerprint recognition based on compression.

    There are several techniques for the recognition of images or signals, since both image and signal are converted into a sinusoidal. One of these techniques is the Fourier analysis. This technique transforms the image into a sinusoidal function of time and frequency axes. Frequency is associated with the amplitude of the function. To higher frequency, lower amplitude.

    Fourier analysis has a problem. By transforming to the frequency domain, time information is lost. Fourier analysis takes a fixed interval and fits the sinusoidal function in that interval, compressing the ends. These is way is not possible to analyze abrupt changes, or what happends at the ends of the sinusoidal function.

When working with images, th analysis is done on shades of gray rather than on time, and we got the same problem.

    On the other hand, Wavelet analysis is based on variable size regions. Insted of using a time-frequency analysis, a time-scale analysis is used. Frequency and scale are related:

• • Fa = Fc / a * delta

  • delta = period

  • a = scale

  • Fc = frequency

  • Fa = portion of frequency

    The idea is to associate a wavelet with a portion of frequency of the sinusoidal function that corresponds to the image. This makes it possible to associate the layout of the Wavelet with the sinusoidal fuction of the image by approximation in a portion of the frequency. In this way the sinusoidal function can be characterized. To approximate thes traces between the wavelet and the sinusoidal function of the image, the wavelet is influenced by a factor in order to dilate or compress it and improve this approximation. This factor is the scale. Therefore, in wavelet analysis, frequency and scale are associated.

    Depending on the anaysis to be performed, we can choose between continuous or discrete wavelets. If the sinusoidal values are finite, not all values of the descomposition will be necessary to perform an exact reconstruction. In these cases a discrete analysis is enough and a continuous analysis would be redundant. In addition, a discrete analysis saves coding space. For image processing we hav done a discrete anaysis using a Biorthogonal wavelet.

References

• 1. http://coco.ccu.uniovi.es/immed/compresion/descripcion/spiht/discreta/discreta.htm

  2. “Validación segura de firmas hológrafas” - Nadina G. Battagliotti, Carolina E. Castillo 

  3. 1984-2009 The MathWorks, Inc.

Authors:

• 1. Carolina Castillo, IEEE Member and researcher @ AIGROUP, working in the PI1 Project. Teacher @ Universidad de Palermo.

  2. Laura Barone, researcher @ AIGROUP, working in the PI1 Project.