Bobkov A.V. - Image registration in the real time applications, страница 5

The homothetic groupincludes motion group and uniform scale transformation. The motion groupincludes rotation and parallel shift. The parallel shift transformation also forms agroup.When the space transformation cannot be described by uniform globaltransformation or if the transformation model is unknown, other methods oftransformation description must be used.1.2.2.1.2. Local transformationThe local transformation, or elastic transformation is described like a globaltransformation, but the transformation parameters are determined for a local areas.These parameters can either be determined on separate control points andinterpolated to a whole area, or they can be a constant in the local areas.1.2.2.1.3.

Optical flowThe optical flow or translation field is a set of displacement vectors for eachpixel. When scenes contain moving objects, analysis is necessarily more complexthan for scenes where everything is stationary, since temporal variations inintensity have to be taken into account. However it is possible to segment movingobjects by virtue of their motion: image differencing over successive pairs offrames should permit this to be achieved.The optical flow can be considered as a discrete or continuous function thatmust be optimised. Limitations to this function are obtained from prioryconsiderations. The optical flow is used in the cases when the globaltransformation is absent, and pixel translations are small.

In this case a globaltransformation g(X) can be written via an optic flow u(X) in a following way:g(X)=X + u(X)The problem that requires an image registration applies significantlimitations to a geometric transformation. For example, medical applications usethree-dimensional affine transformations or continuous optic flows. Thestereovision tasks use an optical flow with a single component that oriented amongthe epipolar lines.On the other side, the limitations of space transform can be increased byintroduction of simplifying assumptions.

For example, in air and space20photographic images registration tasks the affine transformation is often used, andprojective components and local distortions are neglected. Stereovision tasks alsosuppose that global transformation is absent, and the equations of epipolar lines areknown. Due to those simplifying assumption, the image registration task can besolved approximately and applied to the requirements to image obtaining devices.Another and more widely used form is a limitation to a transformationcoefficient value, i.e.

only a part of the search space is taken into account. Anexample of parameter limitation is a limitation of scale. When the scale issignificantly different from the one in question, it is required to define itsapproximate value.The development of more universal methods remains a research challenge.1.2.2.2. Image representationThere are two common approaches to image element selection: area-basedand detail-based methods.Area-based methods are also known as correlation-like methods or templatematching. They use the image pixel as a typical element.

The main information ispixel brightness, and the task is reduced to a minimisation of a target functiondescribed by equation (1.2).Detail-based methods use contour pixels, structural or geometric elements,texture spots or even whole objects. Each image element gives a control point withappropriate co-ordinates. The task is to find a correspondence between controlpoints, i.e. to minimise a target function described by equation (1.4).Both approaches have their own advantages and disadvantages. There aredifferent points of view, as to which approach is the more promising – see [Brown,1992] for more details.Area-based methods are more common. They apply no restrictions to imagecontent and allow one to obtain more accurate and reliable matching, since thewhole information from the image can be used.

But these methods cannot separatethe invariant information from the information which is changing from image toimage. So they are computationally extensive, and they are unsuitable for thesearching of global transformation with large number of parameters.The detail-based methods require a lesser amount of computations since thesource data size is significantly reduced. Furthermore, since the structural elementsdo not use brightness values directly, these methods are less sensitive to change inlightning conditions, and make them more reliable in several applications. But thedetail extraction itself is a complex task.

For example, the accuracy of detaildetection can be lower than the accuracy of control point selection. The amount ofstructural elements and the accuracy of appropriate control points are usuallylimited. That is why details cannot provide information about local translations,and global transformation can be determined inaccurately.An important feature in the detail-based method is the building of anadequate image description.

The process of description building must separate21relevant information, which represent spatial relations between scene physicalobjects and do not depend on survey conditions. So the detail-based methods playan important role on image interpretation and understanding. The effectiveness ofdetail-based methods can serve as criterion of model adequacy.In several cases a mixed approach can be used in order to combine theadvantages of detail-based and area-based methods. The first step is fast, reliable,but inaccurate matching by the detail-based method and the second step is to usethe area-based method to define a more exact position. There is a method that usesa multi-layer image registration system that uses different presentation of theimage with increasing levels of abstraction. They can use different element sets foreach level.

That is, for example, an areas of pixels with the same characteristics,groups of contour pixels and different structural elements. But the theory of such ahierarchical system is practically absent to this day.1.2.2.2.1. Image representation methods – an overviewThe first stage of image analysis is obtaining its numeric representation.Depending of the image representation, the image analysis methods used can havedifferent principles, different abilities and different characteristics. In Leavers[Leavers, 1992] the requirements for good image representation are reviewed. Agood representation must have the following characteristics:1. Decomposition is the ability to represent an image as a free combination ofsimple elements. The set of these components must be able to describe anyimage that can appear in a given application.2.

Accessibility – a representation must be computationally realistic. The imagedescription must be easily obtained and easily processed.3. Invariance – insensitivity to change in observing conditions – to the imagegeometric distortion and changes in illumination.4. Geometric and spatial relations. One shape must have only one representation,and vice versa – one description must correspond to only one shape.5. Similarity. Representation must describe both similarities and differences ofobjects.6.

Saliency. Primary characteristics must bring essential information about theobject while others must describe the detail description.7. Stability to noise and incomplete data.The simplest and most widely used image representation is a rectangulararray, each cell of which contains a brightness value of an appropriate object point.The array is called a raster image, and each cell is called a pixel. Such a form ofimage is usually obtained from a video camera or another source, and then it isused for further processing and obtaining a more compact description.

The rasterimage contains a maximum amount of information about a visual object. This ismain advantage, but also a main problem of raster representation: it is practicallyimpossible to process such a lot of information in real time. So a more compact butless full and less accurate presentation must be used instead.22Methods of flat shape representation can be classified in several ways.

Onemethod of classifications has been proposed by Loncaric [Sven Loncaric, 1997]. Ittakes into account:- Using full information about an object or about its boundary only:boundary, (external) representations and representation of the whole shape (regionbased, global, or internal representation).- A form of representation: a set of numbers (scalars, vectors, matrices etc.)or a set of geometric features.- A level of information preserving. Information-preserving presentationprovides a way to reconstruct (completely or partially) an original shape of anobject, while non-preserving representation characterises the shape but does notprovide information to restore it.1.2.2.2.2. Boundary representationBoundary representation describes only the shape of the objects on theimage regardless of colour, brightness or texture. This provides less informationabout object but makes the representation insensitive to changes in visibility andillumination conditions.

The boundary representation is suitable to describe objectcontours, coastal lines, roads and general line segments. To obtain a boundaryrepresentation, contour pixel detection is required.Edge pixels. The simplest boundary representation is a set of edge pixels.Edge pixels are usually less than 30% of the whole image pixels, and carry themost significant information in comparison to non-edge pixels (inside the object orbelonging to background).

So the use of edge pixels provides significant growth inprocessing performance while it represents an original image without significantloss of information. Edge pixels can be also binarized in order to provide a morecompact description and change the algebraic operations to a faster logicaloperation, or information can be supplemented by edge orientation information formore exact edge pixel comparison etc. Nevertheless, such a representation hassignificant disadvantages: it still is a large description, that is sensitive to noise andto geometric distortions.