2D image mosaic building 2D3 - Ifremer

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3.1.2. Algorithm description 3.1.2.1.Detection of point features Project Exocet/D page 6/16 According to the KLT algorithm, a feature is selected if it is easily “trackable” through an image stream. So, the features consist of windows of several pixel side, which are locally textured. More precisely, a window is selected if its mean gradient is high enough and without any particular direction. Mathematically saying, we consider the gradient vector within a window of typically 7x7 pixels: ⎡g x ⎤ g = ⎢ ⎥ ⎣ gy ⎦ We note Z the following matrix: 2 ⎡ g x Z = ∫∫ ⎢ W ⎢⎣ g g x y g g ⎤ x y ⎥ ⋅ω ⋅ dA 2 gy ⎥⎦ Where: • g is the image intensity gradient along the x-axis, x • g is the image intensity gradient along the y-axis, y • W is the computation window, • ω is a weigh function, • dA is the area of the computation window. This method relies on the fact that the Z-matrix eigenvalues are directly linked to the texture of the area they are computed in. If we try to give a simple meaning of the eigenvalues, we can say that two small eigenvalues represent a non-textured area whereas a high eigenvalue and a small one are characteristic of an area with one specific direction. In our case, only the textured but with no particular direction windows must be selected, that’s to say we are interested in areas having both high eigenvalues. So, within an image, small areas (7x7 pixels, for instance) will be selected only if both eigenvalues are greater than a given threshold. 3.1.2.2.Tracking of features The features that have been selected in the first part of the algorithm are then tracked through the video stream or the image sequence. The displacement between two successive images is supposed to be quite small since the camera moves slowly. So, nearly all the points of an image I are also in the next image J and they are linked by a translation vector d . Now, let’s give the relationship linking two images between two moments. Let be I ( x ξ, y −η, t ) I x, y, t + τ the image at t + τ . − the image at t and ( ) Put J ( x ) = I( x, y, t + τ ) and I ( x − d) = I( x − ξ, y −η, t ) where = ( ξ, η) vector of the point x = ( x, y ) between two time steps t and t + τ . Deliverable N° 2D3 Report on image mosaic building DOP/CM/SM/PRAO/06.224 d is the displacement Grade : 1.0 27/09/2006
We can note that J ( x) = I( x − d) + n( x) where ( x) For each window W , d is obtained by minimizing [ ( ) ] That leads to solve the following equation: Gd = e With: t G = ∫∫ gg ⋅ω ⋅ dA e ∫∫ W = W ( − J ) I ⋅ g ⋅ω ⋅ dA Project Exocet/D page 7/16 n represents the noise. ∫∫ W 2 n x ⋅ω ⋅ dA . This equation is solved for each selected window. So, for each window selected in the first image, we can compute the local displacement between the first image and the second one. The steps of point detection and tracking of the KLT algorithm are illustrated in Figure 2. Figure 2: Detection and tracking of points in a sequence of coral reef 3.1.2.3.Global displacement computation by least square method When the points are matched between two successive images, a global displacement is computed in order to register the images. The displacement is modelled as a 4-parameter rigid global 2D transformation, that’s to say a transformation composed of a translation, a rotation and a scale factor. This global displacement is computed by the iterative least square method. Each iteration enables to refine the result. Besides, this method is completed by an acceptance criterion which is used to validate the matches and to strike off the false matches in order to make the computation more robust. 3.2. RMR algorithm 3.2.1. Principle The second method we have investigated to build mosaics is the Robust Multi-Resolution (RMR) method which is based upon the estimation of the optical flow [ODO95]. The advantage of this method is that the motion is estimated from the whole image. Deliverable N° 2D3 Report on image mosaic building DOP/CM/SM/PRAO/06.224 Grade : 1.0 27/09/2006
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