10-04-2017, 08:15 PM
ABSTRACT
We present a system for the visualization of an important signal processing technique- a Gabor Filter bank s response to an image. To do this, one must overcome the problem that no multi-dimensional space can be shown in a a single, static graph. We use an interactive widget to change the visible range of the projected dimensions, and additional graphics which summarize the responses in the projected dimensions. Thus, though we view this four-dimensional space through 2-dimensional projections, we allow the user to understand all dimensions, not just the plane of projec- tion. We found that the implemented system helped in get- ting a better understanding of Gabor filter responses. We think that use of a domain dependent interaction tool and additional summarization graphics may be useful in a more general Information Visualization setting.
General Terms Gabor Filters, Information Visualization, High Dimensional Data
Keywords Gabor Filters, Information Visualization, High Dimensional Data
1. INTRODUCTION
Spatial frequencies and their orientations are important char- acteristics of textures in images. Figure 2 shows examples of spatial textures with characteristic frequency and orien- tations. The frequency characteristics of images can be an- alyzed using spectral decomposition methods like Fourier analysis. We will illustrate spectral analysis for the simpler case of 1D signals. Consider the sinusoid shown in Fig- ure 1(a). The magnitude of its Fourier spectrum is shown in Figure 1(b) - the peak corresponds to the frequency of _The authors wish to thank Ben Shneiderman and Mustafa Bilgic for review and discussion about the work. the sinusoid. Figure 1© shows another sinusoid whose fre- quency is double that of the previous one; Figure 1(d) shows the magnitude of its spectrum. Suppose we add these two si- nusoids then we will obtain a signal as shown in Figure 1(e). Doing a spectral analysis on this would show the composi- tion of the signal - the two peaks in Figure 1(f) correspond to the component sinusoids. Fourier analysis has proven to be one of the most powerful tools in signal processing. However, a key problem with Fourier analysis is that spectral features from different parts of the image are mixed together. Many image analysis applications, e.g. object recognition, track- ing, etc., require spatially localized features. Gabor filters are a popular tool for this task of extracting spatially local- ized spectral features
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