Image processing, analysis and machine Vision reading notes-------Chapter II image and its expression and properties

2.1 Some concepts of image representation

Images and signals are commonly used to describe mathematical models.

Continuous image function

The value of the image function corresponds to the brightness of the image point. The image of the human eye retina or TV camera sensor itself is two d (2D). We refer to this image, which records the luminance information pair, as a brightness image. The brightness image is a perspective projection of the 3D scene.

Image processing typically takes a static image and time t as a constant. A monochrome static image is represented by a continuous image function f (x, y), where the variable is a planar two coordinate. The digital image function used by computerized image processing is usually represented as a matrix, so its coordinates are integers. The definition field of an image function is an area of the plane R

r={(x, y), 1<=x<=xm,1<=y<=yn}

Where Xm,yn represents the largest image coordinate. The customary image coordinate direction is the normal Cartesian form (horizontal x, longitudinal axis y, left lower origin).

The range of image functions is limited, in monochrome images the lowest values correspond to black, while the highest values correspond to white, and the luminance values between them are gray levels.

The quality of digital image increases with the increase of space, spectrum, radiometric measurement and time resolution. The spatial resolution is determined by the proximity of the image plane to the sampling point, the spectral resolution is determined by the frequency bandwidth of the light obtained by the sensor, and the radiometric resolution corresponds to the number of distinguishable gray orders, and the time resolution depends on the time sampling interval obtained by the image.

2.2 Image Digitization

Digital imaging refers to a matrix that samples continuous function f (x, y) as a single m row n column. The image is quantized to an integer number for each successive sample value, and the continuous range of the image function f (x, y) is divided into k intervals. The finer the sampling and quantification (i.e., the larger the m,n,k), the better the approximation of the continuous function f (x, y).

Image function Sampling has two problems, one is to determine the sampling interval, that is, the distance of the adjacent two sampled image points, and the other is to set the sampling point of the geometric arrangement (sampling raster).

2.2.1 Sampling

A continuous image is digitized at the sampling point, which is arranged on a plane, and its relations are called rasters. So a digital image is a data structure, usually a matrix. In practice, the grid is usually square or positive hexagonal.

An infinitely small sample point in a raster corresponds to a cell of a digitized image, also known as a pixel or an image element.

2.2.2 Quantification

In image processing, the sampled image value FS (jδx,kδy) is represented by a number. The process of converting the continuous numerical value (brightness) of an image function to its digital equivalent is quantized (quantization).

Most digital image processing instruments use K-Interval quantization method. If you use a B-bit to represent the value of the pixel brightness, then the brightness level is k=2b.

When the quantization level is insufficient, a pseudo-outline appears in the image's main problem.

2.3 Digital Image Properties

Measurement and topological properties of 2.3.1 digital images

A digital image consists of a finite number of pixels that reflect the luminance information at a particular location in the image.

Any function that satisfies the following three conditions is a "distance" (or measure):

D (p,q) >=0, when and only if P=q D (p,q) =0 identity

D (p,q) =d (q,p) symmetry

D (p,r) <=d (p,q) +d (q,r) Triangular inequalities

Distances between two points (I,j) and (h,k) can be defined in several forms. Here we introduce European distance, "city block" distance, "checkerboard" distance.

European Distance:

The distance between two points can also be expressed as the minimum number of basic steps required to move from the starting point to the destination on the digital raster. If only horizontal and vertical movement is allowed, the distance is D4. D4 is also known as the "city block" distance.

d4[(I,j), (h,k)]=|i-h|+|j-k|

In a digital raster, you get D8 if you allow the movement of the diagonal direction. Called the "checkerboard" distance. d8[(I,j), (h,k)]=max{|i-h|,|j-k|}

Pixel adjacency: Any two pixels are called 4-adjacency (4-neighbors) if the distance between them is d4=1. 8-adjacency refers to the distance between two pixels d8=1.

An important set of pixels that are adjacent to each other, called a region. If there is a path between two pixels, then these pixels are connected. If there is no hole in the area, it is called a simple connected area, and the area with holes is called re-connected.

Edge: Is the local property of a pixel and its immediate neighborhood, which is a vector of size and direction. The edge tells us how fast the image brightness changes within a small neighborhood of a pixel. Edge Computing is an image with many luminance levels, the way the edge is computed is the gradient of the image function, the direction of the edge is perpendicular to the gradient, and the gradient direction points to the direction of the function growth.

The shape of the area can be described qualitatively with or with convexity. If any two points in the area are connected to a line and the line is completely in the area, we call the area convex. Convexity divides all regions into two equivalence classes: convex and non-convex.

2.3.2 Histogram

The luminance histogram of the image HF (z) gives the frequency at which the brightness value z appears in the image. The histogram of digital image generally has a lot of minimum and maximum value, which can be smoothed by local histogram. If the local average of the adjacent histogram elements can be used, the new histogram is calculated as follows:

where k is a constant that represents the size of the neighborhood used by smoothing.

2.3.3 Entropy (Entrony)

If we know the probability density p, we can estimate the information of the image with the entropy H.

Assuming that the possible result of discrete random variable x (also known as State) is X1,..., xn, set P (XK) is the probability of XK (k=1,..., N), the entropy is defined as

Visual perception of 2.3.4 images

In fact, the perceptual sensitivity of a person is roughly related to the light logarithmic relationship of the input signal, in which case the response of the composite excitation can be regarded as linear, after an initial logarithmic transformation.

Contrast Ratio (contrast)

Contrast is a local variation of brightness, defined as the ratio of the average of the object's luminance to the background brightness. The apparent brightness depends largely on the brightness of the local background, which is called the conditional contrast.

Sensitivity (acuity)

Sharpness is the ability to perceive image details.

Noise in the 2.3.5 image

The actual image is often degraded by the influence of some random error, called noise. Noise is generally characterized by its probabilistic characteristics. The ideal noise is called white noise. A special case is Gaussian noise.

When the image is transmitted through the channel, the noise is generally not related to the image signal, which is independent of the signal degradation is called additive noise. Model is f (x, Y) =g (x, y) +v (x, y)

Multiplicative noise: F=GV

Quantization noise: Occurs when the quantization level is insufficient.

Impact Noise: Refers to an image is destroyed by individual noise pixels, the luminance of these pixels is significantly different from its neighborhood. Pepper salt noise refers to saturated impact noise, when the image is destroyed by some white or black pixels. Pepper salt noise will degrade the two value image.

Image processing, analysis and machine Vision reading notes-------Chapter II image and its expression and properties