SYMBOLIC TRANSFORMS A New Method For Image Classification

SYMBOLIC TRANSFORMS A New Method For Image Classification and Compression With applications in l. Robotic Vision, l. Face Recognition, l. Pattern Matching Theophanes E. Raptis rtheo@dat. demokritos. gr

Main Idea: Pixels -> Symbolic Alphabets Stage 1: Define Input appropriately l Stereoscopic Cameras (Contour Information) l Other types of preprocessing – filtering according to image type (medical, natural, faces, etc. ) l Define objective information (color, depth, grayscale). Encode inputs appropriately. l

Stage 2: Encodings Interpreter l Translate rows and columns as hypothetical distribution functions (“wavefunctions”) l Use the discrete analogue of Feynman Integrals or Partition Functions over distribution functions (histograms). l 4 methods available: Symbolic “Position””Momentum” variables, Symbolic “Phase Space”, Symbolic “Hamiltonians” l

l l l a) b) c) d) e) Stage 3: Post-processing For a set of images or “pixel sets”, pass each one through ST and get a unique chaotic chirp signal over all bases. Signal comparison possible through Direct overlap Specral Distance methods Histogram-Spatiogram Distances Hilbert-Huang Trasnforms -> Hilbert Spectrum. IMF modes. Phase Space Reconstruction-Poincare Plane projections -> Linear Discriminator Neural Nets

Examples l Stage 1(Filtered Input) Stage 2(Complex Matrices) l Stage 3 (Output Complex Signal)

Compression Ratio l l Using a truncation procedure running through all bases from binary up to 1024 symbols output signal >= N kb, N being the number of bytes per floating point. Ratio ≈ (D 1 x. D 2)/N for a [D 1, D 2] Image Array. Compression Lossy: ST non-invertible or Inverse non-unique. Signal storage in a recurrent Neural Net possible. Ideal for robotic vision recognition-identification.