Image processing

The image processing indicates a discipline of the Mathématiques applied which studies the digital images and their transformations, with an aim of improving their quality or of extracting some from information.

It is thus about a subset of the Treatment of the signal dedicated to the images and the data derived like the Vidéo (in opposition to the parts of the treatment of the signal devoted to other types of data: its monodimensional and other signals in particular), while operating in the numerical field (in opposition to the techniques Analogical S of treatment of the signal, like the Photography or the traditional Television).

In the context of the artificial Vision, the image processing is placed after the stages of Acquisition and Numérisation, ensuring the transformations of images and the part of calculation making it possible to go towards a Interprétation of the treated images. This phase of interpretation besides is integrated more and more in the image processing, by calling in particular upon the Artificial intelligence to handle knowledge, mainly on information which one has in connection with what represent the treated images (knowledge of the field).

The comprehension of the image processing starts with the comprehension of what is an image. The mode and the conditions of acquisition and digitalization of the treated images largely condition the operations which will have to be carried out to extract from information. Indeed, of many parameters enter in account, the principal ones being:

the Resolution of acquisition and the mode of coding used at the time of digitalization, which determine the degree of accuracy of possible measurements of dimensions,
the optical adjustments used, (of which the development) which determine for example the clearness of the image,
the conditions of lighting, which determine part of the variability of the treated images,
the Bruit of the transmission chain of image.

Some typical examples of information which it is possible to obtain from an digital image:

the average Brightness
the average Contrast
the prevalent Color
the average rate of acuity (precise or fuzzy)
the rate of uniformity of the colors
the presence or the absence of certain objects

History

The image processing starts to be studied in the Années 1920 for the transmission of images by the underwater Câble energy of New York to London. Harry G. Bartholomew and Maynard D. McFarlane carry out the first digitalization of image with Data compression to send Fax from London to New York. The transfer time passes thus of more than one week to less than three hours. There is no really evolution thereafter until the period of post-war period.

The treatment of the signal takes importance towards the end of the Second world war with the arrival of the Radar. The oil prospection takes part also much in the development of the techniques of treatment of the signal.

The true rise of the image processing takes place only in the Années 1960 when the Ordinateur S start to be sufficiently powerful to work on images. A little later the redécouverte of the Transformée of fast Fourier (FFT) revolutionizes the field, while making possible handling of the contents frequential of the signals on computer. However, the essence of research still relates, at that time, to the improvement of the images and their compression.

In 1980, David Marr formalizes the first the Détection of contour S in a way precise (D. Marr and E. Hildreth: Theory off Edge Detection , Proc. R. London plowshare, B 207,187-217, 1980). During Years 1980, a true passion is done day for the image processing and especially for the comprehension of the image by expert systems. The ambitions were too much large, the failure was all the more cooking.

The Années 1990 are pilot constant improvement of the operators. The medical research becomes a very large applicant in image processing to improve the diagnoses made starting from the many techniques of Medical imagery, the technique queen being IRM. Advertizing executives, then the general public are familiarized with the final improvement of image thanks to the software Photoshop, and the image processing in an esthetic objective is spread with the appearance of other dedicated software (The Gimp, Paint Shop Pro). Lastly, the decade is completed on the passion for the multimode ondelettes and images.

Types of handled data

The delicatessen of image has mainly digital images, therefore sampled. He also has intermediate data of various natures: charts of areas, related lists of points, tables of measured values, etc

With regard to the images themselves, they are seen as functions of $\ mathbb Z \ times \ mathbb Z$ in $\ mathbb Z^n$ ( $\ mathbb Z$ represents the relative whole and $N$ the component count of the image, 1 for level of gray, 3 for RGB, more for the spectral images). The most used representation is a table with several dimensions (representing space dimensions of the image), in which the values have a semantics depending on the type of signal that they code (luminous intensity of the point, the distance to a point of reference, or the number of the area of membership for example).

Acquisition of an image

The study of this stage passes inevitably by the system of acquisition which refers: the eye. One can use webcams, numerical cameras, industrial cameras, cameras infra-red… In medicine, one uses imageurs IRM, Mtoe, scanner X, echography Doppler, echography, Scintigraphie, etc

All these systems can be compared with sensors. It should not be forgotten that there is stage of an analogical/numerical conversion. It is often this stage which limits the resolution of the image.

One of the interesting characteristics of these sensors is the size of the smallest element (Pixel), but also the intercorrelation of two close elements: more this intercorrelation is weak, better is the image.

Operators of image processing

August 1st By analogy with the mathematical operators, one calls operators of image processing of the more or less complex treatments taking in entry an image or a whole of information relative to an image, and producing an image or a whole of information relating to the initial data.

One generally classifies the operators as various families, according to information which they accept in entry and which they provide in exit, and according to the transformations that they subject the data. Thus, for example, one distinguishes (this list is far from being exhaustive):

Operators image→image:

operators of modifications pixel to pixel (also called point-to-point operators): change of the dynamics of the image, binary operators pixel with pixel (and, or, xor, etc);
local operators (the pixels according to their vicinity treat): operators of blur, operators morphological (erosion, dilation, skeleton), operators of detection of contours;
operators in frequential space: operators of reduction of the noise, filters band pass (often used in first approach to improve the image, they are called then operators of preprocessing);
total operators: calculation of the distances.

Operators image→ensemble of information:

operators of segmentation in borders, areas;
operators of classification of pixels;
operators of calculation of parameters.

Operators together of informations→image

manufacturers of image starting from a chart of areas or a list of borders.

The following parts attempt to detail the various operators and their usual applications, then to present the way in which they are combined to build an application of image processing.

Point-to-point operators

This improvement can initially be used to facilitate the visualization of the image on a screen of computer. The capacities of vision of the human being being limited, it is essential to adapt the dynamics of the image to our vision.

One often speaks about Lookup Counts or LUTE , which one also finds in the FPGA. It is about the simplest operator that one can find since in each pixel of the image one modifies the level of gray using a function. Thus, to clear up an image, one applies the function log () to each level of gray. On the contrary to make darker one image a little too saturated, an exponential function is applied. One can notice that the thresholding is anything else only one particular table of posting, that which associates the black with all the levels lower than a certain threshold and the white than all the others. It is about a very simple operator and particularly used but who hiding place a great difficulty, to find the threshold adequate and in an automatic way!

These point-to-point operations, thus qualified because they works only on one pixel (and not on a vicinity), have a well limited effect. In the presence of noise they are not of any utility.

Local operators

It is then necessary to use more complex operators of treatment very often divided into two subcategories:

linear operators,
nonlinear filters.

The first subcategory includes/understands all the operators being able to express their result like a linear combination of the levels of gray of a vicinity of the image. These filters have spectral characteristics, one speaks thus about low-pass filter (the image becomes fuzzy) or about high-pass filter (contours arise).

The second subcategory includes/understands the field of mathematical morphology, as well as other treatments like the characteristic detectors of points, the operator of Di-Zenzo (detecting of contour generalized with the case color), the Retinex filter, as well as the homomorphic operators (those which work on the log of the image), but also all operators allowing to extract for example from information on texture the image (matrix of co-occurence, index fractal, length of beach…).

One is often accustomed to seeing a detector of contours applying after a low-pass linear filter… which makes the image fuzzy! Most of the time it is necessary to combine nonlinear filter and linear filter astutely in order to detect what one wishes while disregarding noise.

Once the eliminated noise and the image restored in order to compensate for the deformations introduced by the medium of transmission and the optics of acquisition, one can pass at the stage of segmentation which must make it possible to carry out a partition of the image in homogeneous related units.

There exist two main categories of segmentations:

the segmentation of area
the segmentation of contour; one is then confronted with a problem of representation of the result by simple primitives.

The directed segmentation contour knows many progress around the use of active Contours or the whole of levels. The introduction of probabilistic aspects (chain of Markov and fields of Markov) made it possible to work by reducing knowledge a priori necessary to obtain a satisfactory treatment.

In this stage one often finds part of classification of the pixels in classes. One tries to gather within the same unit, also called class, the pixels showing the same characteristic: level of gray included/understood in a certain interval or derived second the higher than a certain threshold.

Linear filters

General information

A linear filter transforms a whole of data input into a whole of output data according to a mathematical operation called convolution. When they are data digitized like in the case of the image processing, the relation between the values of the pixels of exit and that of the pixels of entry is described by a table of numbers, generally square, called matrix of convolution. The computing time is often reduced when one wants to separate a filter in two filters whose mutual convolution makes it possible to reconstitute it. This remark is used in particular to create a two dimension filter starting from two only one dimension filters (vectors) in the horizontal direction and the vertical direction.

Smoothing

Detection of contours

Morphological operators

Construction of an application of image processing

The objectives of the applications can be various natures:

to detect the presence of an object or its absence,
to calculate the characteristics of one or several elements of the image.

In all the cases, the idea is, on the basis of an initial image, to extract some from information. For that, one will use the operators with the manner of software bricks , by combining them and by connecting them. These techniques are the base of the systems of industrial Vision.

Recognition of objects

The recognition of objects is a branch of the artificial Vision and one of the pillars of the industrial Vision. It consists in identifying forms pre-described in a Digital image, and by extension in a flow Digital video. Attention not to confuse recognition of objects ( object recognition or shape recognition in English) and Pattern recognition ( pattern recognition in English). The first attempts to recognize geometrical forms in an image, whereas the second seeks to identify reasons in statistical data. Confusion comes owing to the fact that one often uses the pattern recognition as technique applied to the recognition of objects.

Some concrete examples of image processing

Control of presence/absence. On line productions, one checks at the end of the chain with a video camera the presence of a part in a more complex unit. For that very often it is enough to make a simple thresholding in a specific area.

Control of the level of maturation of the fruits on a chain of conditioning. It is a question of recognizing with the color and the texture of the fruit its degree of maturity and thus the category under which he will be packed then sold.

Construction and correction of geographical maps according to air satellite images or images. One readjusts according to topographic information the received images, then one puts them on the chart in correspondence with the information found in the image: transportation routes, ways and water levels, pieces agricultural…

Monitoring and evaluation of the agricultural production. It is possible to determine the degree of maturation of the cultures, the quantity of water necessary for the irrigation, the average output… One can thus establish forecasts on broad scale of harvest to come.

Recognition of the writing. The recognition of the manuscript writing progresses day in day. It is sufficiently operational so that the majority of the addresses, even handwritten, are recognized automatically on the postal mail.

Search for image by the contents. The objective of this technique is to seek, among a database of images, the images similar to an image example, or having certain characteristics, for example to seek all the images comprising a bicycle.

Glossary in bulk

zone of interest : in the development of a system of image processing, it is only seldom interesting to apply a operator of image processing to the totality of the image. Generally only part of the image must be treated. This zone is called zone of interest.
Retiming : technique consisting in finding a transformation geometrical allowing to pass from an image (known as source) to another image (known as target).
Squelettisation : allows to obtain the skeleton of a form (object of size lower than the initial object and which preserves topological information or geometrical compared to the object).
filter : another name of an operator taking an image in entry and producing an image.
pixel : contraction of “picture element”, smaller element of an digital image 2D.
voxel : deformation of pixel for the images 3D, “element volume”.
segmentation : operation which consists in extracting from an image of the geometrical primitives. The primitives most employed are the segments (contours) or surfaces (areas).
calibration : operation which corrects the defects of the sensors of images.
useful sheets of formulas in vision: sheets memorandum for the problems of numerical vision.

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