Patent Application: US-66273110-A

Abstract:
a method to create a video sequence of a plurality of resultant images is disclosed . the video sequence is produced from images originating from a rolling shutter acquisition sensor .

Description:
different methods of correcting the rolling shutter presented above consider only the geometric aspect of image formation , either as a projection of a 3d scene on the 2d surface of the sensor either as a result of 2d - 2d transformation between successive frames . one of the features of the invention is to approach the problem from a different point of view , by considering the available image data in a 3d space where the 3 dimensions are given the 2 dimensions of the images ( abscissa and ordinate ) plus time . indeed , capturing a correct image of “ ccd ” type is equivalent to measure the intensity of light on the sensor plane at a fixed time t : it is therefore a vertical plane in this 3d space abscissa , ordinate , time ( x , y , t ) ( fig2 , perpendicular frame ). cmos imagers , meanwhile , capture a 2d image ( x , y ) as well , but each line corresponds to different moments in time . these time instants are distributed linearly between the start and the end of the acquisition of an image . lines acquired by a cmos sensor are distributed in space ( x , y , t ) along a tilted plane ( fig2 oblique frame ). our method is based on 2d image - to - image computations ( like the estimation of a homography or the calculation of optical flow ) to estimate the apparent motion of each pixel , then using the additional restriction of belonging to the tilted plane corresponding to an image acquired with rolling shutter to estimate the distortion that is to be compensated . one then reconstructs through simple geometric 3d calculations a vertical image corresponding to the corrected image . in the following , h is the height ( in pixels ) of the images taken by the camera and w its width . pixel indices start at 0 and end at h − 1 and w − 1 in each direction respectively . a reference image i 0 corresponding to the scene without distortion , and acquired at a given time interval starting at t 0 for a duration δt 0 ; an image i 1 deformed by the rolling shutter with acquisition starting at time t 1 for the duration δt 1 . this is illustrated by the fig1 in which an example of defects of skew effect type induced by a rolling shutter is shown . the camera moves horizontally from left to right , and the superimposed grid is the pixel grid . the acquisition of the image i 1 ( on the right in fig1 ) starts with the first line . the next line is acquired while the camera continues to move , resulting in a mismatch with the first line , and so on till the top of the image . the induced distortion is invisible on non - textured parts ( foreground , sky ). it is characteristic on the building : its vertical lines are now oblique . next , consider a given block p 0 of i 0 whose coordinates are ( x0 , y0 , t ( x 0 , y 0 )). the relative motion of the scene and the camera transforms p 0 into p 1 in i 1 with coordinates ( x1 , y1 , t ( x 1 , y 1 )). x1 and y1 are known by a first algorithm : for example , in the case of computing optical flow , x0 = x1 + u and y0 = y1 + v . the translation in equations of our intuition is as follows : in the case a sensor with rolling shutter , t ( x 1 , y 1 ) is not equal to the start of the acquisition of image i 1 . in other words , the vector joining p 0 and p 1 in the space - time volume considered is : p 0 ⁢ p 1 = ( x 1 - x 0 y 1 - y 0 t ⁡ ( x 1 , y 1 ) - t ⁡ ( x 0 , y 0 ) ) p 0 ⁢ p 1 = ( x 1 - x 0 y 1 - y 0 t 1 - t 0 = 1 framerate ) to compensate the effects of rolling shutter becomes forming an image i * corresponding to a moment t * constant throughout the image . selection of the reconstruction time t *. basically , the reconstruction time r can be selected arbitrarily . however , to obtain a better result , the reconstruction time t * should be selected according the following : in the case of the reference image is a previous acquired image : between the end of the acquisition of the current image and the end of the acquisition of the reference image , in the case of the reference image is a subsequent acquired image : between the beginning of the acquisition of the reference image and the beginning of the acquisition of the current image . hypothesis for instant line . we endorse the classical hypothesis of instant acquisition of each line , that is to say that all pixels belonging to the same line of the observed image &# 39 ; correspond to a same moment t ( line ). in addition , the electronic control sensor in the device spans the collection of the times t ( line ) linearly between all the lines of the image starting at the bottom , hence : without the hypothesis of immediacy , all calculations presented are valid , and one must then replace the formula giving the time by : t ⁡ ( x , y ) = y × w + x ( w - 1 ) ⁢ ( h - 1 ) ⁢ δ ⁢ ⁢ t + t start for an image of size w × h pixels ( width × height ) of coordinates belonging to [ 0 , w − 1 ]×[ 0 , h − 1 ]. suppose now that we want to reconstruct the image corresponding to the time t *. we introduce then a further hypothesis : we assume that the block p 0 moved in a straight line between the images i 0 and i 1 to arrive at block p 1 ; we can then reconstruct the image corrected i * corresponding to t *: it simply corresponds to the intersection between all vectors p 0 p 1 and the vertical plane defined by t = t *. note that in fact , the acquisition starts at the top of the sensor , but the optics reverses the image . hence , the scanning does begin at the bottom of the recorded image 1 . we construct the matrix of plücker l corresponding to the straight line ( p 0 p 1 ); 2 . the intersection between the straight line ( pp ) and the vertical plane π of normal vector ( 0 , 0 , 1 ) t corresponding to t = t * is given by the result of the multiplication lπ t . the detail of the calculations of a line - plane intersection in 3d is given at the end of the present section . finally , for each pixel p 1 of the deformed image i 1 , this procedure allows us to obtain its coordinates in the corrected image i * without rolling shutter effect . calculation of the intersection between a straight line and a 3d plan consider 2 points p 0 =( x 0 , y 0 , t ( x 0 , y 0 )) and p 1 =( x 1 , y 1 t ( x 1 , y 1 )). the line ( p 0 p 1 ) joining them can be expressed as a matrix of plücker l as per the following calculation done in projective coordinates : the vertical plane corresponding to the time t = constant is parameterized by the vector π t =( 0 , 0 , 1 , − t ). the intersection between the line ( p 0 p 1 ) and the plane defined by π t is given by lπ r . we then obtain : l ⁢ ⁢ ∏ t = ( 0 x 0 ⁢ y 1 - y 1 ⁢ x 0 x 0 ⁢ t ⁡ ( x 1 , y 1 ) - t ⁡ ( x 0 , y 0 ) ⁢ x 1 x 1 - x 0 x 1 ⁢ y 0 - y 0 ⁢ x 1 0 y 0 ⁢ t ⁡ ( x 1 , y 1 ) - t ⁡ ( x 0 , y 0 ) ⁢ y 1 y 0 - y 1 x 1 ⁢ t ⁡ ( x 0 , y 0 ) - t ⁡ ( x 1 , y 1 ) ⁢ x 0 y 1 ⁢ t ⁡ ( x 0 , y 0 ) - t ⁡ ( x 1 , y 1 ) ⁢ y 0 0 - t ⁡ ( x 1 , y 1 ) + t ⁡ ( x 0 , y 0 ) x 1 - x 0 y 1 - y 0 t ⁡ ( x 1 , y 1 ) - t ⁡ ( x 0 , y 0 ) 0 ) ⁢ ( 0 0 1 - t ) l ⁢ ∏ t = ( ( x 0 ⁢ t ⁡ ( x 1 , y 1 ) - t ⁡ ( x 0 , y 0 ) ⁢ x 1 ) - t ⁡ ( x 0 - x 1 ) t ′ - t ( y 0 ⁢ t ⁡ ( x 1 , y 1 ) - t ⁡ ( x 0 , y 0 ) ⁢ y 1 ) - t ⁡ ( y 0 - y 1 ) t ⁡ ( x 1 , y 1 ) - t ⁡ ( x 0 , y 0 ) t 1 ) the calculation done here is completely general : it is valid between 2 different images of an uncorrected video ( defined by their coordinates t ( x 0 , y 0 ), t ( x 1 , y 1 ) as long as the hypothesis of uniform rectilinear motion ( possibly independent ) for each pixel holds . there is no need for the hypothesis of instant line if one is able to also calculate accurately the times t and t ′ without it . important notes the calculations presented in this report are completely generic , requiring only the hypothesis of uniform straight motion for each pixel of an image . this is true most of the time given the very short durations considered ( video sequences usually have a framerate of 10 to 30 images per second ). for example , we can : correct sequences containing moving objects : provided that the association ( p 0 , p 1 ) is reliable , the correction made to each pixel is independent of that made to the other pixels surrounding it , hence allowing for different corrections when different motions are encountered in a single image ; correct sequences that do not meet the hypothesis of instantaneous acquisition for each line : it is sufficient to know the function associating the image coordinates ( x , y ) the time coordinate t , but the latter need not be obtained by equation 3 ( it is simply the most common case ). strong rolling shutter cases (“ jellocam ” effect ) can be corrected using the equations provided . in this specific case , the main difficulty lies in the evaluation of the point associations ( p 0 , p 1 ). if it is possible to express the data mapping between p 0 and p 1 by an homography h ( i . e . p 0 = hp 1 ), then we find a method similar to that described in the prior art but we are not limited anymore to translation movements and zooming at the level of the camera . if the data mapping is given by computing the optical flow , then we are able to correct the effects of jellocam that cannot be taken into account by the methods based on rigid transformations such as homographies . when a rolling shutter camera is used , individual frames are tilted in the space - time domain , while they are perpendicular to the time axis for global shutter and ccd cameras ( see fig2 ). the acquisition of the reference image starts at time t 0 for a duration of δt 0 seconds . the acquisition of the current image starts at time t 1 and lasts δt 1 seconds . both images have dimensions h by w pixels , where h is the height and w the width of the image respectively . furthermore , image coordinates start at 0 , hence the last row of the image is at the vertical coordinate h − 1 ( fig3 ). for this drawing we have chosen a reference frame anterior to the current image , but the converse is also possible and does not change the computations since all the computations involve the signed difference between each time , and not the actual time values . each block of the reference image is associated with its spatial coordinates ( x 0 , y 0 ) in the reference image and its motion vector ( u , v ). using these notations , the block has then the coordinates ( x 1 , y 1 ) ( x 0 + u , y 0 + v ) in the current image by definition of the motion vector . the positions of the block are augmented to also include the acquisition time of the time and become ( x 0 , y 0 , t ( y 0 )) and ( x 1 , y 1 , t ( y 1 )) in the reference and current image respectively ( see fig3 ). we make the hypothesis that all lines are sampled regularly during an image acquisition , and that the reading of a line is almost instantaneous . under these assumptions , one can compute : we then consider the selected reconstruction time and give the formula to infer the resultant image from the reference and current image . we make the assumption that the light ray trajectories are straight lines . hence , for each block , its position in the resultant image is given by the intersection of the plane of constant time t * and its trajectory . using plücker matrices and homogeneous coordinates to represent the block trajectory and this plane , the coordinates of the given block in the resultant image are given by the following matrix product : finally , by calculating this product and then inverting the homogeneous coordinates , the position of the given block in the resultant image coordinate system are : 1 t ⁡ ( y 1 ) - t ⁡ ( y 0 ) ⁢ ( x 0 ⁡ ( t ⁡ ( y 1 ) - t * ) - x 1 ⁡ ( t ⁡ ( y 0 ) - t * ) ) 1 t ⁡ ( y 1 ) - t ⁡ ( y 0 ) ⁢ ( y 0 ⁡ ( t ⁡ ( y 1 ) - t * ) - y 1 ⁡ ( t ⁡ ( y 0 ) - t * ) ) note that we never make the assumption that the reference time had to be anterior to the correction time , nor did we make the assumption that the two frames i 0 and i 1 were consecutive . actually , all the derived calculations rely on the signed difference between the different times . hence , actual values are not used and the presented results are generic . the diagram of the fig4 summarizes the process of producing a corrected image belonging to the resultant video sequence . the corrected image creation process is given 2 images acquired by a rolling shutter cmos imaging sensor , along with the times and duration used to acquire the images . one of the images is a reference image , the other is the current image that will be transformed to produce the corrected image . for each block of the current image the corresponding block inside the reference image is found , hence computing a motion vector for each block of the current image . this motion vector , along with the current and reference block position and the times and duration associated with the two images are used to compute the amount and direction of the correction that should be applied to the current block . finally , given all the individual block positions , a corrected image is formed . this corrected image is similar to an image acquired by a ccd imaging sensor , i . e . it corresponds to a single time t * and is not affected by the rolling shutter technology . the diagram of the fig5 describes the application of the proposed invention inside an imaging device such as an hand held camera . rays of light go through a lens and are measured using a cmos rolling shutter imaging sensor . pixels values are stored in frame memory . the device keeps in memory two images , namely the reference image and the current image , corresponding to two different periods in time , along with the acquisition start time and acquisition duration used . then , a dedicated module computes for each block of the current image the corresponding block in the reference image , hence computing a two dimensional motion vector for each block of the current image . this motion information is used , along with the acquisition start time and acquisition duration associated with each image to compute the corrections required to remove the rolling shutter effects . then , a ccd - like image , namely the corrected image , is computed after gathering the corrected positions for each block of the current image . this corrected image corresponds to a single time instant , as if it was acquired using a ccd imaging sensor . this corrected image is transferred to a frame encoding module to transform it into a format more suitable for digital storage , and finally written to a digital mass media . the frame encoder does not need to recompute the block motions since they have been computed beforehand . hence , the motion estimator module can be shared by the frame correction and frame encoding processes . the correction method of geometric artifacts of rolling shutter proposed is generic and independent of the targeted application . consequently , the proposed method is suitable for any product that has to process the videos taken by a cmos sensor . as these sensors become common even for high - end cameras , the concerned imagers are very varied . the method will be implemented into the processor of these cameras in order to produce the video sequence . most of the computing time is actually devoted to the calculation of pixel to pixel correspondence . but methods for estimating these real - time already exist . one can imagine , for example , operate the computation of optical flow directed to the mpeg compression of a camera , or well add a point detector of quick interest . thus , applications integrated within the cameras ( e . g . webcam , or by dedicated hardware in a camcorder ) are easily possible for our correction system . 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