Bobkov A.V. - Image registration in the real time applications (779134), страница 21

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Properties of discrete spaceА) Parallel lines can have common pixelsВ) Intersected lines can have no common pixelsThe experiments show that this method could not process correctly evensimple images. However, additional research shows that it is possible to change thecomputation scheme, so that it will produce linear responses in parameter spaceinstead of sinus. We will return this scheme in the line segment matching methods.4.6.2. Method based on line pair comparisonThe key disadvantage of the previous method is the overstating of thequality functional value for the points of parameter space, so the quality functionalis calculated incorrectly.

To eliminate this problem it has been decided toaccumulate only those points of the translation parameter space where real curvescrossing exist.To do this, a whole line set is divided into pairs. Each pair contains a linefrom one frame and an appropriate line from another frame, if these lines seem tobe the same. To compare lines, information about line position, brightness,thickness and gradient direction is used. Each line may be included into severalpairs.When pairs are formed, appropriate translation parameters are calculated foreach two pairs and the value calculated is marked on the translation parameterspace, as before. A position of maximum value in the parameter space willtraditionally be considered as the desired translation parameters.The scheme of the translation parameter calculation is presented at Fig.4.3.97Fig.4.3.

A scheme of translation parameters calculationWhen line l1 converts into l1’ and l2 into l2’, a point C of l1 and l2 crossingtranslates into point D of l1’ and l2’ crossing. The CD vector is desired translationL.It is denoted ∆ρ=ρ2−ρ1, ∆ϕ=ϕ2−ϕ1.∠CEA = ∆ϕ as angles with perpendicular sides. Appropriately, ∠CBF= ∆ϕ.ADBC is a parallelogram, because its appropriate sides are parallel. So itsappropriate sides are equal: AD=CB and AC=DB.∆CFB is a right-angle triangle, so AD=CB=∆ρ2Cos∆ϕ; FB=∆ρ2Sin∆ϕ.Similarly DB=AC=∆ρ1Cos ∆ϕ; AE=∆ρ1Sin∆ϕ.Then DE=AD-AE=∆ρ2Cos∆ϕ–∆ρ1Sin∆ϕ.∆CED – is a right-angle triangle, so CD2=CE2+ED2; then distance L can befound as follows:L=∆ ρ 12 + ∆ ρ 22 − 2∆ ρ 1 ∆ ρ 2 Cos∆ ϕSin∆ ϕ(4.0)From the same reason:∠ECD=arctg(ED/EC)=arctg(Cos∆ϕ/Sin∆ϕ–∆ρ2/∆ρ1Sin∆ϕ);Appropriate angle of inclination can be found as follows:∆ρ2Cos∆ ϕarg( L ) = ϕ 1 + arctg (−)Sin∆ ϕ∆ ρ 1 Sin∆ ϕ(4.0)Our experiments show that the algorithm processes correctly both artificialand natural images.

The main disadvantage is relatively large computation time(maximum processing time of 128x128 256-grayscale image for Durontm750processor achieves 1.5 seconds – in comparison to 0.3...0.5 sec for other methodsthat are discussed below). But this is compensated by greater stability. Themethod is suitable for practical applications due to its reliability.984.7. SECONDARY FEATURE EXTRACTION METHODSThe basic idea of this approach is to combine lines into more complexobjects in order to use them for the registration.

A pair of matching objects on bothimages provides exact information about the transformation, which cannot beobtained from matching line pair. Furthermore, more complex object allows moreaccurate and reliable identification procedure to separate true matches. This causereduction of pairs to be taken into account and hence significantly decreasingamount of computations. However, the more complex object, the rare it can befound on the image, so this can cause fault of registration process when imagescontain little amount of required object.As a rule, this group of methods allows radical reduction of computationtime, but usually leads to less reliability.

These methods cannot be used by itself,but it can be used together with more reliable methods in order to increase itsperformance or accuracy.4.7.1. Corner comparisonThe calculation scheme is the same as on the pair comparison method, butdue to changing of comparison order a significant increasing of performance canbe achieved.At the first stage lists of corners of the base and current frame areconstructed. A corner is a line segments pair, which crosses under 30 o-120o angleand has a pair of neighbour ends. The amount of corners, extracted in such a wayis many times less than the appropriate amount of identical line pairs. Since theamount of comparisons (and appropriate computation time) depends on thesquared amount of objects compared, this leads to radical increasing ofperformance.The algorithm is able to process artificial images with high accuracy andspeed, but fails on certain aspects of natural images – for example, townlandscapes.

This kind of images contains a huge amount of little objects(buildings) and curves (streets) so it does not allow enough corners to be extractedfor reliable processing.99Fig.4.4. Scheme of corner comparison4.7.2. Stripe comparisonThe basic idea is the same. Lines are combined into more complex object –stripe, and then the stripes are used for frame comparison. The stripe can beconsidered as two parallel neighbour lines with opposite directed brightnessgradient. The idea of the method is to use stripes of one direction to determinetranslation in perpendicular direction that can be found exactly.

Then thistranslation can be used to calculate a common translation.At the first step a set of stripe are extracted. This is a fast procedure becauseonly the gradient direction information is used for each line.At the second step translations ∆ρi(γ) for each stripes set with orientation γare calculated.

Then doubtful values are eliminated: only values with qualitycriteria J(∆ρi) not less than C*Jmax(γ) remain, where C=0.5..1 is threshold leveland Jmax(γ) is maximum criteria value for stripes with orientation γ.At the third step, accumulated values of ∆ρ(γ) are used to calculatetranslation in according to formula (4.1) and (4.2). As before, amount ofappropriate values L of translation are accumulated in the parameter space, and theposition of maximum in parameter space considered as the desired translationparameters.The experiments show significant speed of calculation, but the accuracy wastoo low: about a half of the natural images were processed incorrectly. Thesituation becomes even worse when small geometric distortions (e.g. rotation) arepresent. Due to line extraction features, a stripe width will depend on the rotationangle, making it impossible to compare stripes exactly.100Fig.4.5.

Scheme of stripe comparison4.7.3. Comparison of line segment middlesThis method uses the middle point position of the appropriate line segmentsto determine the translation parameters. The pair of line segments from base andcurrent frame allows us to determine the whole translation vector L, not only itsprojection, which is orthogonal to the appropriate line direction. Therefore it ispossible to take this feature into account.The method works as follows. For each line segment of the current frame anidentical segment of the base frame is looked for (they must have approximatelyequal size and brightness).

For each of these pair the translation vector coordinates are calculated as translation of segments middle:x1 + x2 − x1 ' + x2 'Lx =22(4.0)Ly =y1 + y 2 y1' + y 2'−22(4.0)Then the traditional procedure is used: calculated values (Lx, Ly) areaccumulated in the translation parameter space, and position of maximum in thisspace considered as the desired translation parameters.The method is faster than the pair comparison due to calculation simplicity(compare formulas (4.1-4.2) and (4.3-4.4)). The experiments show that the methodhas both high performance and adequate accuracy.

However, a significantdrawback for this method was found. The maximum value is extremely low andequal to 2 in many cases. This feature reduces the method reliability. Althoughmost of the images were processed correctly, this effect can cause a seriousproblem. To reduce such a negative effect, a slide frame was used instead of puremaximum: maximum position is the position of slide frame, when sum of elements101inside the frame is maximal.

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