Source Steven Seitz Convention larger values correspond to brighter content A

# Source steven seitz convention larger values

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(Source: Steven Seitz) Convention: larger values correspond to brighter content. A color image is defined similarly as a 3 component vector-valued function: x ( s 1 , s 2 ) = r ( s 1 , s 2 ) g ( s 1 , s 2 ) b ( s 1 , s 2 ) . 78

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Image representation – Types of images – Digital imagery Digital imagery Raster images Sampling: reduce the 2d continuous space to a discrete grid Ω Z 2 Gray level image: Ω R (discrete position to gray level) Color image: Ω R 3 (discrete position to RGB) 79
Image representation – Types of images – Digital imagery Bitmap image Quantization: map each value to a discrete set [0 , L - 1] of L values ( e.g., round to nearest integer) Often L = 2 8 = 256 ( 8 bit images unsigned char ) Gray level image: Ω [0 , 255] ( 255 = 2 8 - 1 ) Color image: Ω [0 , 255] 3 Optional: assign instead an index to each pixel pointing to a color palette (format: .png , .bmp ) 80

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Image representation – Types of images – Digital imagery Digital imagery Digital images: sampling + quantization: -→ 8bit images can be seen as a matrix of integer values We will refer to an element s Ω as a pixel location, x ( s ) as a pixel value, and the pair ( s, x ( s )) as a pixel (“picture element”). 81
Image representation – Types of images – Digital imagery Functional representation: x : Ω Z d R K d : dimension ( d = 2 for pictures, d = 3 for videos, . . . ) K : number of channels ( K = 1 monochrome, 3 colors, . . . ) s = ( i, j ) : pixel position in Ω x ( s ) = x ( i, j ) : pixel value(s) in R K 82

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Image representation – Types of images – Digital imagery Functional representation: x : Ω Z d R K d : dimension ( d = 2 for pictures, d = 3 for videos, . . . ) K : number of channels ( K = 1 monochrome, 3 colors, . . . ) s = ( i, j ) : pixel position in Ω x ( s ) = x ( i, j ) : pixel value(s) in R K Array representation ( d = 2 ): x ( R K ) n 1 × n 2 n 1 × n 2 : n 1 : image height, and n 2 : width x i,j R K : pixel value(s) at position s = ( i, j ) : x i,j = x ( i, j ) 82
Image representation – Types of images – Digital imagery For d > 2 , we speak of multidimensional arrays : x ( R K ) n 1 × ... × n d d is called dimension, rank or order, In the deep learning community: they are referred to as tensors (not to be confused with tensor fields or tensor imagery). 83

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Image representation – Types of images – Digital imagery Vector representation: x ( R K ) n n = n 1 × n 2 : image size (number of pixels) x k R K : value(s) of the k -th pixel at position s k : x k = x ( s k ) 84
Image representation – Types of images – Digital imagery Color 2d image: Ω Z 2 [0 , 255] 3 Red, Green, Blue (RGB), K = 3 RGB: Usual colorspace for acquisition and display There exist other colorspaces for different purposes: HSV (Hue, Saturation, Value), YUV, YCbCr. . . 85

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Image representation – Types of images – Digital imagery Spectral image: Ω Z 2 R K Each of the K channels is a wavelength band For K 10 : multi-spectral imagery For K 200 : hyper-spectral imagery Used in astronomy, surveillance, mineralogy, agriculture, chemistry 86
Image representation – Types of images – Digital imagery The Horse in Motion (1878, Eadweard Muybridge) Gray level video: Ω Z 3 R 2 dimensions for space 1 dimension for time 87

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Image representation – Types of images – Digital imagery
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