2D image mosaic building 2D3 - Ifremer

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Project Exocet/D page 8/16 In the RMR algorithm, the first stage consists in choosing a motion model. Then, the aim is to estimate the parameters of the model using the classic method of robust estimation in the domain of image and signal processing. This step is combined to a coarse-to-fine estimation using multi-resolution levels of images. 3.2.2. Algorithm description 3.2.2.1.Model of motion In the first step of the algorithm, a motion model is chosen. In the RMR algorithm, we consider the class of 2D polynomial motion models and we deal only with the 2D affine model which is not too complex but enough representative of a large part of motion transformations: ⎧u( X ) = a + a x + a y i 1 2 i 3 i ⎨ ⎩v( X ) = a + a x + a y i 4 5 i 6 i And with matrix notation, it can be stated as: ⎡u( X ) i ⎤ ( X ) = B( X ) A i ⎢ ⎥ = ⎣v( X ) i ⎦ V i Where A ( a a a a a a 1 2 3 4 5 6 T = ⎡1 x y 0 0 0 i i ⎤ And B = B( X ) = i i ⎢ ⎥ ⎣0 0 0 1 x y i i ⎦ ) For each point X , one can write the flow constraint equation linking spatial and temporal intensity gradients: ( X ) ∇I( X ) + I ( X ) = 0 V , I x i ⋅ i t i i ( X ) u( X ) I ( X ) v( X ) + I ( X ) = 0 i i + y i i t i where ( ) is the spatial gradient vector of the intensity, is the partial temporal i derivative of the intensity relative to time and is the vector field. X I ∇ ) ( t i X I ( ) i X V 3.2.2.2.Robust estimation The goal of robust estimation is to find the parameter vector Θ which best fits the model ( X , Θ) to the observations . y M i i t t In our case, Θ = ( A , 0) . The estimation of parameter Θ is achieved by a maximum likelihood estimator: Θˆ = argmin∑ ρ ( y − M( X , Θ)) where ρ is called the M-estimator and corresponds to the i i Θ maximum likelihood estimation. Deliverable N° 2D3 Report on image mosaic building DOP/CM/SM/PRAO/06.224 Grade : 1.0 27/09/2006
Project Exocet/D page 9/16 This estimation is performed at all the scales of a multi-resolution images pyramid so that at each scale the estimation is refined. 3.3. Metric conversion - camera self-calibration The displacement calculated by image processing is given in pixels. The aim of video mosaicing is to provide the mosaics with metric dimension in order to make quantitative measurements within the images. Thus, the displacement and the image size in pixels must be converted into meters (see Figure 3). h f l camera 1 pix L image plane seabed plane Figure 3: Link between one pixel and its real metric size on the seabed Thus we have the relationship: −1 −1 SizeOfAPixel( m ⋅ pix ) l( m ⋅ pix ) = ⋅ h( m) , f ( m) Given that SizeOfAPixel( m ⋅ pix −1 f ( m) ) = , we deduce that: α( pix) −1 h( m) l( mm ⋅ pix ) = , where α is an intrinsic parameter of the camera which has to be α( pix) estimated and h is the altitude of the camera. Since it is not always possible to deploy a calibration pattern on the seabed, an algorithm for camera self-calibration has been investigated [PES03]. The self-calibration algorithm allows us to determine the intrinsic and extrinsic parameters of a vertical camera mounted on an underwater vehicle. This method needs only a sequence of few images of the seabed and is based upon the determination of the epipolar geometry between two successive image of the sequence. The diagram below presents all the steps of the self-calibration method: Deliverable N° 2D3 Report on image mosaic building DOP/CM/SM/PRAO/06.224 Grade : 1.0 27/09/2006
Page 1 and 2: Underwater Systems Department A.G.
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Page 7: We can note that J ( x) = I( x −
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Page 15 and 16: 4.2. User interface Project Exocet/

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