Abstract:
System and method forms a lenticular viewing card having viewable depth or motion images by processing an original image into digital form and sampling and shifting the processed original image into at least two frames of images shifted perpendicular to the lenticular direction from each other by being sampled at different points. These frames of images are sliced and interlaced into a merged image that is printed and positioning into a viewing position with a lenticular lens sheet to permit a sequential viewing of the frames making up the merged image as a function of a user&#39;s viewing angle.

Description:
FIELD OF THE INVENTION 
     The invention relates generally to the field of lenticular imaging, and in particular to the creation of depth imagery (vertically orientated lenticular screens) and images with motion (horizontally orientated lenticular screens). More specifically, to a process for improving the clarity of view of elements forming the images. 
     BACKGROUND OF THE INVENTION 
     The history of lenticular imaging dates back to the early 1900&#39;s when Gabrielle Lipmann developed a process of integral photography, that when combined with a fisheye lens, offered a three-dimensional image to an observer. In 1925, J. S. Curwen patented a device (U.S. Pat. No. 1,475,430) involving two distinct images which changed from one to another, dependent upon the viewing angle presented to an observer. 
     While technology has advanced, the principal process remains similar. A lenticular image is comprised of a sequence of images that are interlaced to form a singular image where each individual image (or frame) is viewable at a different angle to the viewer when viewed through a lenticular lens sheet. These various images are termed views. 
     The current method of displaying an image, or portion thereof, which does not appear to change across a number of views; or throughout a depth or motion sequence, or a portion thereof, is accomplished by means of fixing the constant image to a constant coordinate location relative to the image area of each frame within the sequence from which the lenticular image is to be created. Fixing the image information in a constant location has always been assumed to provide the clearest and sharpest view of a stationary image 
     The conventional method, described above, displays the shortcomings of a lenticular imaging system, exhibiting a cutoff of detail where lenticule spacing exists, and a condensing of image information resulting in decreased clarity and legibility. 
     SUMMARY OF THE INVENTION 
     The present invention is directed to overcoming one or more of the problems set forth above. Briefly summarized, according to one aspect of the present invention, a unique method forms a lenticular image having either a viewable depth or a motion effect. The image is comprised of at least two frames of similar image source content where one or more images are sequentially displaced perpendicular to the lenticular direction; whereby the final image translation occurs at different portions of the source image. 
     Specifically there is provided a method for forming a lenticular image having viewable depth or motion effects, comprising the steps of: 
     a) interlacing at least two frames of similar image content with at least one frame sequentially displaced perpendicular to the lenticules; and 
     b) positioning a sheet of lenticular lenses so as to view the image content of the interlaced frames of similar image content. 
     Additionally, there is provided a system for forming a lenticular viewing card having viewable depth or motion images, comprising: 
     means for receiving and processing an original image in digital form; 
     means for sampling and shifting the processed original image from said receiving means into at least two frames of images shifted from each other by being sampled at different points; 
     means for slicing and interlacing the at least two frames of images into a merged image; and 
     means for writing the merged image whereby the positioning of a lenticular lens sheet into viewing position of the written merged image permits a sequential viewing of the at least two frames of images in the merged image as a function of a user&#39;s viewing angle. 
     These and other aspects, objects, features, and advantages of the present invention will be more clearly understood and appreciated from a review of the following detailed description of the preferred embodiments and appended claims, and by reference to the accompanying drawings. 
     ADVANTAGEOUS EFFECT OF THE INVENTION 
     The present invention has the following advantages: 
     The method produces a directional shift of an image (or portion thereof) between each section of a sequence or produces images of different pixel content. The process produces a sharper image of text or continuous tone or half tone color gray scale or binary objects to the viewer, creating increased legibility and clarity. Without the utilization of this method, a lenticular image may exhibit severe artifacts and a general lack of definition (i.e. fine detail). 
     The method renders control over both legibility (defined as ease of reading characters) and clarity (defined as overall image quality and the ability to see smooth edges specifically) of lenticular images and is a direct result of applying a shift or change in control to any individual element or in tandem with any or all other components (imagery, graphics, text, or other). 
     The method may eliminate the hidden image areas between the lenticules of the lenticular screen upon lamination of the lenticular screen to an image support layer. 
    
    
     BRIEF DESCRIPTION OF THE DRAWINGS 
     FIG. 1 illustrates a simplified Prior Art structure that incorporates a lenticular sheet and permits the viewing of images by angular displacement of the lenticular sheet relative to a viewer; 
     FIG. 2 illustrates the current method of resampling at constant coordinate locations in the image area to form the image slices that are positioned behind each lenticule of the lenticular sheet of FIG. 1; 
     FIG. 3A illustrates the result of current sampling techniques before adhesion or printing to the back surface of a lenticular sheet; 
     FIG. 3B demonstrates the modified sampling process of the present invention before adhesion or printing to the back surface of a lenticular sheet; 
     FIG. 4 depicts an image of the letter “O” that is to be incorporated into a lenticular viewing structure; 
     FIG. 5 is a set of intensity profile curves taken from a scanning of the image of the letter “O” of FIG. 4; 
     FIG. 6 depicts the image of the letter “O” with P and Q dimensions; 
     FIG. 7 illustrates in block diagram form a system for receiving digitized imaging data and for driving a lenticular image writer to write the image represented by the imaging data; 
     FIG. 8 is a graphic representation of edge sharpening for images of the present invention; 
     FIG. 9 illustrates an edge pixel transition; 
     FIG. 10 illustrates the shifting of a sampling grid in accordance with the present invention; 
     FIG. 11 illustrates the shifting of a sampling position between views; and 
     FIG. 12 is a set of keyed graphs 1-4 representing the intensity values of, for example, the letter “O” at different lenticular viewing angles incorporating the teachings of the present invention; 
     FIG. 13 is a set of graphs representing the intensity values of the letter “O” using PRIOR ART; 
     FIG. 14 are position graphs illustrating the position of pixel elements with respect to adjacent lenticules; and 
     FIG. 15 represents a change in a viewer&#39;s viewing angle through a lenticular lens sheet to a sequence of views that have been shifted in accordance with the teachings of the present invention. 
    
    
     To facilitate understanding, identical reference numerals have been used, where possible, to designate identical elements that are common to the figures. 
     DETAILED DESCRIPTION OF THE INVENTION 
     Referring to FIG. 1, a simplified Prior Art arrangement of a lenticular image  10  is shown comprised of a support layer  14  on which are formed image slices, denoted generally as X and Y, which are in alignment with respective lenticular lens elements  12  that are part of a lenticular sheet  16 . In the Prior Art arrangement the horizontally orientated lenticular image contains only two views, X and Y of an object. The information for view X is placed along the upper half of the image area of each lenticule  12 . Likewise, information for view Y is based in the lower half of each lenticule  12 . When the object is viewed, view X is displayed to the observer at one viewing angle while view Y is displayed at another angle. In actual practice the number of slices per lenticule of the image containing the object to be viewed ranges from between 2 to more than 30. 
     A subject displayed in the lenticular image, which would not change in position between X and Y, would display the same information in both views within the image. This would be the case, for example, when an item of text were to be viewed (see, for example. Morton U.S. Pat. No. 5,276,478). 
     Referring to FIG. 2, in the present description the complete source image  20  is a number 1 which is meant to be viewed flat with no depth or motion within a lenticular image. Utilizing the teachings of the prior art, the same portion of the number 1 would be repeated under each of the lenticules for the number of slices that would be selected for forming, for example, the motion image. If there are more lines in each image in the sequence than there are lenticules, then in order to print it, the sequence image is subsampled. In FIG. 2 the number 1 is subsampled into 2 frames, and the final image would display segment lines  21 ,  23 , and  25  corresponding to one frame, and  22 ,  24 , and  26  corresponding to the other frame under lenticules  27 ,  28 , and  29 , respectively, in both view X and view Y. 
     In the prior art, finite details are lost due to sectioned subsampling and lenticular alignment. Arrows indicate where the subsampling would take place. Therefore, where the subsampling takes place is where portions of detail would be displayed in the final image and conversely, where the subsampling does not take place details are lost. Likewise, the alignment of the lenticular sheet over the interlaced image produces invisible image areas between the lenticules. 
     Incorporating a downward shift in the sampling of the numeral 1 (that is resampling starts at one line lower than for the image) for the second view, that is, instead of displaying lines  21 ,  23 , and  25  in both view X and Y, view X would display lines  21 ,  23 , and  25 , the view Y would display lines  22 ,  24 , and  26 . This results in a subjectively sharper image to the viewer. The shortcomings of the lenticular screen are also avoided when utilizing this technique. 
     In FIG. 3A the conventional (non-displaced sampling) will display the image as shown, while in FIG. 3B the improved technique, of utilizing, shifting sampling is shown. The methodology of this technique can be appreciated by reference to the single image  30  shown in FIG.  4  and the following: Image  30  comprising an “O” labeled  32  is designed to subtend N P  pixels by N L  lenticules where each lenticule comprises M views. Two adjacent lenticules are labeled  34  and  36  and will be discussed in the improvement description relating to FIG.  5 . The arrowed line&#39;s  38  and  40  represent sliced profiles of the pixel values that form the letter “O.” The lenticules may be horizontal for motion images and alternatively may be vertical for depth images. Other effects may involve the lenticules in a variety of directions. 
     FIG. 5 shows one way to represent a portion of the “O” image  32  as an image positioned under the lenticular lens contained in the image  30  in terms of sequential pixel intensity values that exist along the arrowed line  38  shown in FIG.  4 . An intensity profile  42 , for each of the M pixels under the lenticule  34 , takes on pixel intensity values corresponding to the intensity value shown as  44  while the background takes on the pixel intensity value shown as  46 . The span or width of the lenticule  34  in FIG. 4) is shown as  48 . Similarly the span or width of the lenticule  36  (in FIG. 4) is shown as  50 . An alternate way to represent this portion (along  38  of the letter “O”) is shown as the dashed intensity profile  52  which shifts the image edge to center it under the intended position of lenticule  34 , assuming that the lenticule  34  is correctly aligned with the image so that the pixel values of different frames under lenticule  34  representing the image “O”  32  are different. Another profile along line  38  is shown as the dotted profile  54  which provides smooth gray scale intensity values along the edges of the letter “O”. When pixels along path  38  are compared to pixels along path  40  (profiles  52  and  54 ) they generally have different pixel values for some of the M views under a specific lenticule whereas intensity profile  42  generally has the same pixel values along paths  38  and  40 . Furthermore, unless the edge of the object being represented is parallel with the lenticules, transitions between levels  46  and  44  will generally occur at the same point along paths  38  and  40  whereas transitions for profiles  42  and  52  will typically occur at different points along paths  38  and  40 . It will be appreciated that profile  42  corresponds to prior art whereas profiles of the type  52  and  54  are formed by this invention. This effect is the result of the processing which will be described later in relation to FIG. 7 in conjunction with FIGS. 6,  8 ,  9 , and  10 . 
     In FIG. 6 the original source image  30  used to generate the image  32  of the “O” is comprised of P pixels by Q lines (or visa versa P lines by Q pixels if the scan lines run vertically on the page). The Image  30  is processed for inclusion as part of a lenticular image using the improvement of the present invention. Data representing the pixel amplitudes of the P pixels are provided as inputs to the processor o f FIG. 7 on line  56 . If Q is less than K*N L  where K falls in the range of 3 to 40 then it is necessary to increase the resolution in the Q direction. If the image  36  of the “O” is a binary image such as text, then edge position smoothing may be initially required in order to achieve good image quality. Within the processor of FIG. 7 the smoothing process is performed by edge position smoothing block  58  as shown in greater detail in FIG.  8 . The edge  88  corresponds to the edge of the incoming image on line  56  and represents a small region of the image. To smooth this edge involves increasing the resolution of the incoming image to values which are 4 to 40 or more times greater (depending on the number of views or frames over which the image is to subtend) for P and/or Q. This results in the output edge data appearing on line  60  having the smooth profile represented by profile  90  in FIG.  8 . This smooth profile avoids the pixelization of aliasing affects of the incoming image which might otherwise appear in the final image. The specific methodology for performing this function are well known and include converting edge  88  into a vector string and then repixelizing the vector string at the desired higher resolution. 
     Referring back to FIG. 7, it is next desirable to apply edge amplitude smoothing to the output edge data on line  60 . The edge amplitude smoothing function  62  of the processor improves the clarity of images, especially binary images, by smoothing the amplitude of the edge of an image to provide the greatest image clarity. This produces a continuous tone image from a binary image by applying a filtering function to the binary data using a convolution kernel so as to produce two dimensional smooth gray scale images. The action is shown typically in FIG. 9 where a binary step edge  92  is transformed to a gradually changing transition in signal intensity value  94 . This process can also result in greater pixel amplitude resolution enabling the process to produce different pixel values for successive frames. 
     If the original source image  30  of FIG. 6 is represented in a non-pixelized format such as Postscript or a vector representation, then the imaging data enters the processor on line  64  of FIG. 7 at the input to the rendering process  66 . The rendering process takes the vectors and represents them as pixels at the required resolution as previously discussed. 
     In the case of continuous tone source images, the intensity profile (of which is represented in FIG.  8 ), representing the image data is entered on line  56  and is processed by the scaling function  68  to increase its resolution so as to have sufficient image content for the subsequent shifting and sampling process  70 . This function can also be used for binary or discrete tone level images though not with the effectiveness of functions  58  and  62 . Scaling is generally performed using nearest neighbor, linear, or cubic interpolation which are standard image processing sizing techniques, or sizing techniques as might be found in Adobe Photoshop and similar software. 
     Pixel data on line  60  is generally directed to the edge amplitude smoothing function  62  however, it can also be directed directly to the shifting and sampling function  70  on line  72  if it is only desired to shift and sample binary image data. This path may however result in lower image quality. Also if the data on line  56  has sufficient resolution, it may also be passed directly to the shifting and sampling function  70  on line  57 . 
     The edge amplitude smoothing function  62  may be used to improve the clarity of images, especially binary images, by smoothing the amplitude of the edge of the image. The amount of smoothing that gives the best clarity is a function of M, N L , P, Q, K, and the overall resolution sharpness of the lenticular imaging system. It is often influenced also by the shifting and sampling function  70  and can be best assessed experimentally by changing values to provide the best image. 
     It should be appreciated that the choice of input  55 ,  60 , or  74  depends on the characteristics of the incoming signal and the desired clarity improving approach which is best determined experimentally. Input line  55  is used when the resolution of the input data on input line  56  is sufficient to satisfy the K criterion mentioned above. Input  60  is used when edge position smoothing is initially required, and input  74  is used when the input signal on line  64  is in vector or postscript format. 
     The output of function block  62  passes to a scaling function  68  which scales the final image by resampling the image so that the output format on line  76  has N P  pixels across the image in the direction along the lenticules and a resolution. N P  is typically in the range of K 1 *M*N L  where K 1  is in the range of 0.5 to 16 or even higher. In the preferred embodiment K 1 =8. One factor in choosing K is so that the shifting and sampling function  70  has sufficient resolution to sample the image at small shifts and then having sampled provide a final image that is passed through a merge function  78  to a lenticular image writer  80  with the desired size in the written image by function  68 . In the desired final size each frame typically corresponds to N P  pixels by N L  lenticules corresponding to the size of the region in the final image to be subtended by source image  30 . 
     Merge function  78  receives M (1 through M) frames on each of lines  82 ,  84 , and  86 . The frames on line  82  correspond to the image on line  56  while the views on lines  84  and  86  correspond to other elements of the final image such as areas of text, areas of motion, areas of depth, or other graphics, or image content areas. The merge function  78  first merges using overlay and other image layering techniques to each of the respective views so that all of frame 1 components on lines  82 ,  84 , and  86  are merged into a single frame one. Then all frame 2 components are merged and so on, so as to make M separate frames. Function  78  then interleaves those frames into M interleaved slices under each lenticule as shown in FIGS. 1 and 15 (in FIG. 1, x corresponds to frame 1 and y corresponds to frame 2). Thus, other interleaved images on lines  84 ,  86 , etc. may correspond to digital data representing other components of the final lenticular image. These may include, for example, data generated from distinctly different views in either space or time of the same scene or may correspond to merge data from different scenes. 
     Thus, this merging process generally involves setting the relationship with other merged data such that some components are assigned specific views, other components are assigned specific positions in the final image and others are assigned specific layers of the image. 
     Whatever the source, most often the other components to be merged are interleaved in such a way that they correspond to the image required to represent different views behind each lenticule as demonstrated in FIG.  1  and also in U.S. Pat. No. 5,276,478. Notice in this prior art process multiple different images from the same scene are generally involved whereas in the current process multiple and different frames, which may appear to be the same views, under a given lenticule are derived from the same view or image. 
     The goal of the shifting and sampling process  70  is to sample the high resolution image in a grid which is oriented in both the direction at right angles to the lenticules and normal to the lenticules as shown in FIG.  10 . In FIG. 10, the grid has a pitch X 2  in the x direction and Y 2  in the y. The sampling grid is shifted by X 1  in the x direction and Y 1  in the y direction between the sampling process for each of the lenticule views. This shift may be in one or both directions (usually the y direction) and may be constant, variable, or random between consecutive views. The shifting occurs so as to provide an increase of image quality and the best pattern is arrived at by testing at various amounts of shift to satisfy a viewer&#39;s preference. This shift is also a function of lenticule pitch, viewing distance, the intrinsic overall resolution of the image on line  76 , and the detail desired to be reproduced. Points  96  to  102  and similar points represent a first sampling position for a first view or frame. Points  104  to  110  and similar points represent a second sampling position for a second view or frame. The sampled image  112  may be a black and white or color discrete level image or may be a black and white or color continuous tone image. Often it is advantageous in the case of text images, for example, to make the image continuous tone by filtering it with a continuous tone filtering function 
     FIG. 11 illustrates the shift between the same sampling points between the sampling for one frame and then for another frame so that the sampling occurs at different positions. Where an identical position is used on different frames that identical position is said to constitute one view, and two frames are said to have the same view. In fact, however, it may appear that even when the frames are different (that is having different value pixels), they may continue to appear to comprise a single view. Thus, for example, in a lenticular image having 24 frames, these 24 frames may appear as 3 views occupying the entire image area and each view comprising a different scene and each scene spanning 8 frames. However, each of the 24 frames may be different in detail (that is to say having different pixel values) and these 8 different frames corresponding to one scene may each be produced as described in this invention thereby 3 scenes producing 3 scenes each of 8 frames with higher image quality. 
     Furthermore when examining differences between frames by overlaying consecutive views, FIG. 12 shows a sample resulting from the shifting and sampling process  70 . It should be appreciated that the views or frames shown in FIG. 12 may also be shifted in relationship to each other due to the shifting action of  70 . 
     FIG. 13 represents the prior art approach where shifting of the sampling points between views or frames does not take place. 
     Referring back to FIG. 7, it has already been pointed out that a resolution of K times the lenticule pitch is required on line  76  where K is many times the lenticule pitch so as to have sufficient resolution in the image to be sampled as to have sampled viewers which accurately represent the image when sampled at a specific position. The shifting and sampling process  70  generally must produce the interlaced image slices positioned behind the lenticules which has M pixels across each lenticule thus having a resolution or right angles to the lenticule of M*N L . The term “generally” is used because it is also possible to create lenticular images where the number of views or frames does not correspond to the number of pixels or lines at right angles to the lenticule because the number of pixels or lines laid down by the printer does not match in an exact or integer manner to the lenticular material and as a result the image is scaled in the dotted line function, non-integer scan line scaler  87 . In this case the goal of the scaling is simply to ensure that M views span the lenticules (see U.S. Pat. No. 5,276,478 by Morton). This scaling, when applied, can also occur before merging provided all the imaging components are appropriately scaled to match the final desired size. 
     The effect of shifting and sampling can also be achieved as shown in FIG. 14 by taking input image data  114  representing amplitude data and generating a new image signal by sampling the amplitude of incoming data  114  at predetermined points and using the data to mike a signal of M pixels across each lenticule whose amplitude corresponds to the amplitude of the incoming signal at the predetermined input points. Depicted is a sampling for M=5 along a single direction where the sampling points are closer than the distance represented by the spacing of one lenticule. The input signal  114  is sampled at points  116  to  124  and regenerates a signal  126  where there are 5 equi-spaced samples across distance  128  corresponding to one lenticule. Note that because the, sample spacings are not necessarily equi-spaced the resulting signal can be discontinuous. 
     Again referring back to FIG. 7, lenticular image writer  80  next writes the image slices corresponding to, for example, image  20  or  32 , onto the image layer. The image writer may be capable of writing either continuous tone, half tone, or binary images. Generally speaking, if the output resolution of the image is N P  pixels by N L  lenticules where (each lenticule comprises M views then the image on line  82  must be N P  pixels by N L *M. This also means there must be N P  pixels across the image generated by the scaling function  68  and passing down line  76  or along line  84  depending upon which input has been chosen which in turn is dependent on whether the input is vector or pixel based. 
     Another alternative to uniformly shifting the image in the direction of right angles to the lenticules is to shift the image in random steps at right angles to the lenticules, each step being either in the same direction of random amplitude or some steps being forward and other steps being in reverse. The advantage of this approach is that there is no net motion, but the various frames contain, in the same manner as already described, a high resolution image which is correct for that particular sub-lenticule position or for that particular position with respect to the lenticule. 
     The random motion of text can be achieved either while moving the apparent position of the text in a constant velocity or keeping the apparent position substantially stationary. The latter can be achieved by having random motion where the sum of the motions over the full range of views is zero. Moving the apparent position can be achieved by providing random motion and introducing a drift associated with the random motion, that is, the sum of the individual motions is still moving in a constant direction. It will also be appreciated that the random motion may be exclusively at right angles to the lenticules or may have a component which is parallel to the lenticular direction. 
     Another embodiment of the invention is to compensate for the loss of intensity in areas containing fine text due its narrow width. This problem arises because when fine text which has thin strokes or a narrow structure, as seen through the lenticules, does not have the same contrast as course text of thick strokes or a wide structure. To compensate for this, the intensity or contrast of the fine text can be increased so that the resulting impact is that thin text and thick text have the same apparent intensity. If the full available dynamic range of intensity is used for the thin text, then it is advantageous to reduce the intensity or contrast of the coarse text. In other words, if the intensity or contrast of the thin text has reached its maximum limit of dynamic range for driving the printing device, then to compensate the intensity of the coarser text is reduced so that the overall appearance is matched. 
     In FIG. 15 as the viewer  130  passes across the front of the lenticular image  132 , what he sees will correspond to the overlaid sequence of views or frames corresponding to that represented by the set of graphs in FIG.  12 . FIG. 12 corresponds to the overlaid sequence cf views or frames, the lenticules by the viewer, across in front of the lenticular image  132 . 
     Use of the invention is advantageous for both continuous tone images, text, and graphic elements. 
     It will also be appreciated for all the above that while this description has sometimes focused primarily on motion at right angles to the long axis of the lenticular lens element that motion can also be provided in directions which have a component along the lenticules long axis. 
     The invention has been described with reference to a preferred embodiment; However, it will be appreciated that variations and modifications can be effected by a person of ordinary skill in the art without departing from the scope of the invention. 
     
       
         
               
             
               
               
               
             
           
               
                   
               
               
                 PARTS LIST: 
               
               
                   
               
             
             
               
                   
               
             
          
           
               
                   
                 10 
                 lenticular image 
               
               
                   
                 12 
                 lenticular lens elements 
               
               
                   
                 14 
                 support layer 
               
               
                   
                 16 
                 lenticular sheet 
               
               
                   
                 20 
                 complete source image 
               
               
                   
                 21 
                 segment line 
               
               
                   
                 22 
                 segment line 
               
               
                   
                 23 
                 segment line 
               
               
                   
                 24 
                 segment line 
               
               
                   
                 25 
                 segment line 
               
               
                   
                 26 
                 segment line 
               
               
                   
                 27 
                 lenticule 
               
               
                   
                 28 
                 lenticule 
               
               
                   
                 29 
                 lenticule 
               
               
                   
                 30 
                 single image (original source image) 
               
               
                   
                 32 
                 letter “O” 
               
               
                   
                 34 
                 lenticule 
               
               
                   
                 36 
                 lenticule 
               
               
                   
                 38 
                 arrowed line (sliced profile) 
               
               
                   
                 40 
                 arrowed line (sliced profile) 
               
               
                   
                 42 
                 intensity profile 
               
               
                   
                 44 
                 intensity value 
               
               
                   
                 46 
                 intensity value 
               
               
                   
                 48 
                 span/width of lenticule 34 
               
               
                   
                 50 
                 span/width of lenticule 36 
               
               
                   
                 52 
                 alternate intensity profile 
               
               
                   
                 54 
                 alternate intensity profile 
               
               
                   
                 55 
                 input 
               
               
                   
                 56 
                 line 
               
               
                   
                 57 
                 line 
               
               
                   
                 58 
                 edge position smoothing block 
               
               
                   
                 60 
                 line (input) 
               
               
                   
                 62 
                 edge amplitude smoothing function 
               
               
                   
                 64 
                 line 
               
               
                   
                 66 
                 rendering process 
               
               
                   
                 68 
                 scaling function 
               
               
                   
                 70 
                 shifting and sampling process 
               
               
                   
                 72 
                 line 
               
               
                   
                 74 
                 input 
               
               
                   
                 76 
                 line 
               
               
                   
                 78 
                 merge function 
               
               
                   
                 80 
                 lenticular image writer 
               
               
                   
                 82 
                 line 
               
               
                   
                 84 
                 line 
               
               
                   
                 86 
                 line 
               
               
                   
                 87 
                 non-integer scan line scaler 
               
               
                   
                 88 
                 edge 
               
               
                   
                 90 
                 profile 
               
               
                   
                 92 
                 edge 
               
               
                   
                 94 
                 signal intensity value 
               
               
                   
                 96 
                 point 
               
               
                   
                 98 
                 point 
               
               
                   
                 100  
                 point 
               
               
                   
                 102  
                 point 
               
               
                   
                 104  
                 point 
               
               
                   
                 106  
                 point 
               
               
                   
                 108  
                 point 
               
               
                   
                 110  
                 point 
               
               
                   
                 112  
                 sampled image 
               
               
                   
                 114  
                 input image data 
               
               
                   
                 116  
                 sample point 
               
               
                   
                 118  
                 sample point 
               
               
                   
                 120  
                 sample point 
               
               
                   
                 122  
                 sample point 
               
               
                   
                 124  
                 sample point 
               
               
                   
                 126  
                 signal 
               
               
                   
                 128  
                 distance 
               
               
                   
                 130  
                 viewer 
               
               
                   
                 132  
                 lenticular image