Abstract:
A method for quickly and efficiently locating objects, such as images having fixed aspect ratios, within a predefined space, such as a printed page, is provided. The method comprises generating a binary tree containing a first image. The system generates a second tree, where the second tree modifies the first tree by inserting a second image at a location or position on the first tree. This iterative process of inserting images one at a time continues until the system generates a final tree including all images. In each iteration, the position in the binary tree where the system inserts each subsequent image can be either a leaf or a node. The system generates a series of candidate trees, one for each subsequent image inserted into each and every location in the preceding tree, and the candidate tree having a highest score indicates the selected location for the subsequent image and the new baseline, preferred binary tree.

Description:
CROSS-REFERENCE TO RELATED APPLICATIONS 
     This application also relates to the following co-pending applications:
         U.S. patent application Ser. No. 10/675,724, filed Sep. 30, 2003;   U.S. patent application Ser. No. 11/769,671, filed Jun. 27, 2007;   U.S. patent application Ser. No. 11/127,326, filed May 12, 2005;   U.S. patent application Ser. No. 11/128,543, filed May 12, 2005;   U.S. patent application Ser. No. 10/831,436, filed Apr. 23, 2004;   U.S. patent application Ser. No. 11/126,637, filed Apr. 15, 2005;   U.S. patent application Ser. No. 11/151,167, filed Jun. 10, 2005;   U.S. patent application Ser. No. 11/069,512, filed Mar. 1, 2005;   U.S. patent application Ser. No. 11/865,112, filed Oct. 1, 2007;   U.S. patent application Ser. No. 10/987,288, filed Nov. 12, 2004;   U.S. patent application Ser. No. 11/364,933, filed Mar. 1, 2006;   U.S. patent application Ser. No. 11/127,326, filed May 12, 2005;   U.S. patent application Ser. No. 11/128,5433, filed May 13, 2005; and   U.S. patent application Ser. No. 11/190,436, filed Jul. 27, 2005.       

     BACKGROUND OF THE INVENTION 
     1. Field of the Invention 
     The present invention relates generally to the field of computational placement of elements, and more specifically to efficiently placing or locating photographs or graphic images on a page. 
     2. Description of the Related Art 
     Computer software is currently available for a user to collect and display graphical images in a visually pleasing format. Such computer software develops what have been called photo albums, comprising a series of pages having images selected by the user and arranged in various manners. A photo album page, as the term is used herein, refers to multiple graphical images or pictures positioned on a page of fixed size. Graphical images or pictures as used herein refer to a software depiction of virtually anything, including text, such that the graphical image or picture can be considered to have a rectangular boundary. Examples of graphical files include .gif, .tiff, and .jpeg graphical representations, but can include virtually any image having a boundary. For example, an oval shape block of text may be considered a graphical image or picture having rectangular borders touching the top, bottom, left, and right side of the oval shape block, including an optional border. 
     In deciding how and where to place graphical images on a photo album page, software must address various environment specific issues. For example, the number of pictures on the page, the size of the pictures relative to each other, spatial distribution of pictures, available empty space, and the existence of captions all factor into the placement of the selected graphical images on the photo album page. 
     In previous software systems for arranging graphical images, arrangement frequently occurred “by hand.” In this process, the user opened a blank page document and imported digital graphical images. Software generated a “layout” on the photo album page by enabling the user to move images around the page, and possibly allowing resizing, so as to achieve a pleasing picture layout. The process of moving and resizing photos by hand can be tedious and time consuming. In response, developers have created automated software packages intended to at least partially automate the layout process. 
     Certain software packages automate the layout process by positioning images in rows and columns. By forcing images to fall into separate regions all of the same size and shape, layouts produced with this type of software package do not account for image aspect ratios, and graphical images may appear distorted when placed in the layout. This type of solution can lead to unused empty space on the page, which is visually unattractive and wastes available space. 
     Other software packages provide templates, where images are manually inserted into fixed template openings, or “holes.” Templates can be attractive and can make efficient use of space, but available templates are often unusable due to the failure of aspect ratios for template holes to correlate with aspect ratios of images. While the image can be cropped to provide an acceptable appearance and aspect ratio within a particular template hole, cropping is generally unsatisfactory, as it requires discarding part of the image. Also, while the image can be reduced in order to appear complete and uncropped through the template hole, such size reduction can be unsatisfactory because the image appears smaller and is therefore more difficult to see. Some software packages allow the user to create new templates, but the template creation process is typically tantamount to manual layout, and hence tedious and time consuming. 
     Certain generally available software packages have specific layout design issues. Kodak Memory Albums (“KMA”) exhibits tendencies that appear to automatically generate album page layouts without using templates. KMA does, however, leave empty space that could be occupied by simply enlarging a nearby image. 
     Canon PhotoRecord Gold (“CPG”) is another software package that provides automatic photo album page layout. In one mode, CPG appears to employ a method for creating templates that accommodate the desired number of images. However, image sizes appear to be ignored in this mode, which can result in image overlap. The image overlap is irregular and often excessive and thus generally unattractive. Alternately, the CPG user can move one image on the page, while the software shifts the other images around the page to accommodate the image being moved. Control of image position shifting appears to be haphazard and in some cases results in images being completely obscured. 
     Another product called FotoFusion (“FF”) from LumaPix generates single-page collages of photos. FF has an autocollage feature that takes a list of input images and generates a layout of all the images on a single page, and provides an ability to generate various alternative layouts. In the layouts generated by the autocollage feature, little or no white space exists between the photos, and the photos fit together like bricks in a wall. However, the photos in the layout are cropped, and parts of the photos discarded, which is undesirable. 
     None of the presently available software designs allows the user to specify relative image size for multiple images while simultaneously retaining the entirety of the images presented. Specification of relative image size can be desirable when, for example, the user wants one image to be significantly larger than all the others on the page. Further, no presently available software design completely eliminates empty, unused space within the rectangular region occupied by images on the page, while simultaneously retaining the entirety of the images presented. This rectangular region may be described as the “convex hull” staked out by the images. 
     Certain floorplanning or layout tree structures have been employed in different contexts. For example, others have used layout tree structures for VLSI circuit layout and for general document layout. In VLSI circuit layout, however, the circuits can be fixed in size, but do not typically have fixed aspect ratios. Circuits can thus be altered independently in x and y dimensions without regard to maintaining a ratio between x and y. Floorplanning solutions tend to materially differ from image placement designs due to the aspect ratio maintenance requirements frequently associated with image placement designs. In general document layout, as opposed to image layout, aspect ratios are also considered variable. 
     In certain circumstances, repeated determination of multiple potential layouts may afford a user a variety of possible attractive layouts from which to choose. However, certain users may wish to rapidly obtain an efficient layout, requiring minimal effort and relatively rapid processing. 
     It would therefore be desirable to offer a relatively rapid and efficient software solution to placing graphical images on a page with a minimal amount of empty space and a maximum variety of layout designs, while at the same time refraining from cropping the images received and minimizing drawbacks associated with previous graphical placement software. 
     SUMMARY OF THE INVENTION 
     According to a first aspect of the present design, there is provided a method for arranging a set of objects within an area. The method comprises (a) initiating a binary tree and associating a first object with the binary tree, (b) selecting a subsequent object not included in the binary tree, (c) establishing at least one candidate tree, wherein each candidate tree comprises objects from the binary tree and the subsequent object, (d) computing a score for each candidate tree and selecting one candidate tree having a highest score associated with placement of the subsequent object, (e), repeating (b), (c), and (d) until the candidate tree includes the set of objects, and (f) arranging the objects within the area in accordance with the candidate tree. 
     According to a second aspect of the present design, there is provided a method for arranging a set of objects within an area. The method comprises establishing a tree structure, associating a first object with the tree structure to form a candidate tree, modifying the candidate tree to form at least one alternate candidate tree by associating a subsequent object with at least one available location on the candidate tree, computing scores for each alternate candidate tree with the subsequent object in each available location, selecting the alternate candidate tree having a best score, and designating the selected alternate candidate tree to be the candidate tree, repeating said modifying, computing, selecting and designating for all remaining subsequent objects, and arranging the set of objects within the area in accordance with the candidate tree. 
     According to a third aspect of the present design, there is provided a method for arranging a set of objects within an area. The method comprises establishing a candidate tree having having at least one node, and at least one leaf connected to one node, and at least one object associated with the candidate tree, modifying the candidate tree to form at least one alternate candidate tree by associating a subsequent object with at least one available location on the candidate tree, computing scores for each alternate candidate tree with the subsequent object in each available location, selecting the alternate candidate tree having a best score, and designating the selected alternate candidate tree to be the candidate tree, repeating said modifying, computing, selecting and designating for all remaining subsequent objects, and arranging the set of objects within the area in accordance with the candidate tree. 
     These and other objects and advantages of all aspects of the present invention will become apparent to those skilled in the art after having read the following detailed disclosure of the preferred embodiments illustrated in the following drawings. 
    
    
     
       DESCRIPTION OF THE DRAWINGS 
       The present invention is illustrated by way of example, and not by way of limitation, in the figures of the accompanying drawings in which: 
         FIG. 1  illustrates the concept of strict area layout for a predefined space such as a printed page; 
         FIG. 2  shows brick style layout of objects or images; 
         FIG. 3  illustrates the concepts of aspect ratio and relative area proportion; 
         FIG. 4  is a broad general flowchart for an embodiment of the complete photo album creation system showing inputs and outputs; 
         FIG. 5A  shows a sequential division of a predefined area, such as a page, into subareas; 
         FIG. 5B  is a divided predefined area and its corresponding binary tree structure; 
         FIG. 6  illustrates a detailed flowchart of an embodiment of the complete photo album creation system; 
         FIG. 7  is a flowchart illustrating forming a bounding box and is equivalent to element  604  of  FIG. 6 ; 
         FIG. 8  illustrates a flowchart representing block  701  of  FIG. 7 ; 
         FIG. 9  is a flowchart of block  702  of  FIG. 7 ; 
         FIG. 10  illustrates a broad conceptual flowchart of an embodiment of a photo album creation system according to the single pass design, including inputs and outputs thereof; 
         FIG. 11A  is the first part of a detailed flowchart of an embodiment of a photo album creation system according to the single pass design; 
         FIG. 11B  is the second part of a detailed flowchart of an embodiment of a photo album creation system according to the single pass design; 
         FIG. 12  shows sequential loading of images or objects according to the single pass design; 
         FIG. 13A  shows a tree having four associated images and a desire to insert new image  5 ; 
         FIG. 13B  illustrates locating a new image  5  beneath a new horizontal split node, and locating original images  1  and  4  as children of the new, horizontal split node; 
         FIG. 13C  illustrates locating a new image  5  beneath a new vertical split node and locating original images  1  and  4  as children of the new, vertical split node; 
         FIG. 14  is a flowchart of the normalization process according to the single pass design; 
         FIG. 15A  represents operation of element  605  of  FIG. 6 ; 
         FIG. 15B  illustrates the variables employed and the preloading of values available for use in performing element  605 , as represented by  FIGS. 15A ,  16 , and  17 ; 
         FIG. 16  shows operation of element  605  if the desired parent cut direction is vertical; and 
         FIG. 17  is a flowchart of element  605  operation if the desired parent cut is horizontal. 
     
    
    
     DETAILED DESCRIPTION OF THE INVENTION 
     The present design includes two functions, a full function that creates a variety of image layouts that may be selected by the user and that depend in large part upon user input, and a “single pass” function that is less computationally intensive than the full function but produces a visually attractive layout in a shorter period of time based on fewer inputs from the user. 
     With respect to the both the full function and single pass function, two specific modes of layout operation are considered, namely “strict area” layout and “brick” layout. 
       FIG. 1  illustrates the strict area layout mode of operation. Strict area generally refers to an image being located strictly within a particular area or subarea of the page. Conceptually, the page may be divided into multiple subareas, such as the left and right halves of the page, and the strict area layout mode may center one image in the right half of the page and another image in the left half of the page. When using the strict area mode of operation, the user may provide a relative area proportion value with each image, used for purposes of dividing the page into areas. Use of a relative area proportion value enables the user to specify one image being one-third the area of a second image on the same page and one-quarter the area of a third image, where areas are divided according to this preference and images centered in each area so divided. Relative area proportion is a numeric value, and in the foregoing example, if all three images are originally of the same area, the first relative area proportion will be 1.0, the second 3.0, and the third 4.0. Relative area proportion is independent of the concept of aspect ratio, a subject discussed later. 
     Mathematically, the strict area mode of operation indicates that on a given page, the areas of the images satisfy: 
                 A   1       e   1       =         A   2       e   2       =     Λ   =       A   N       e   N                 
where N is the number of images on the page, {A i } are the actual image areas, and {e i } are the user specified relative image area proportions. Strict area layout controls relative image area proportions. If the user specifies that image A is to be three times the size of image B, the strict area layout mode directs image A to be three times the size of image B irrespective of the exact position or size of image A and image B on the page. Strict area layout may also be employed where the user specifies area constraints in a more casual way. For example, the user may specify that certain selected images should be larger than the other images on the same page (i.e., not larger by a precise multiplicative factor).
 
       FIG. 2  shows the alternate “brick layout” mode of operation. In  FIG. 2 , no white space exists between the images, which fit together like bricks in a wall. Brick style layout visually appears efficient, as no empty space exists within the “convex hull” staked out by the photos or images on the page. 
     While both the examples in  FIGS. 1 and 2  show pages containing images only, the present design allows the user to also print a caption or insert a block under each image regardless of layout style. The user may also specify a “gutter width” of empty space to separate images in either layout style. 
       FIG. 3  shows the concepts of aspect ratios, area, and relative area proportion for the present design. The aspect ratio is defined as the ratio of image height divided by image width. Box  301  has an aspect ratio of 2.0, while box  302  has an aspect ratio of 0.5 (one to two). The system seeks to maintain aspect ratios throughout operation. Each image occupies an area on the page. The “area” as used herein is an fixed attribute of a rendered image, which may measured for example in units of square inches. Assuming an 8.5 inch by 11.0 inch piece of paper, the page area is 93.5 square inches. A photo printed on that page with height 4.0 inches and width 6.0 inches has an area of 24.0 square inches. The “relative area proportion,” as used herein, is an image attribute used to compare areas of two images on the same page. As such, “relative area proportion” and “area” are related but different concepts, with the former being purely relative in nature and the latter being absolute and measurable. Layout  303  shows a page with a first image  304  having relative area proportion 1.0 and a second image  305  having relative area proportion 4.0. Since the relative area proportions differ by a factor of 4, so do the measurable areas of the two images in rendered output (e.g., on a printed page, on a representation of physical space, or on a computer display), regardless of the particular numerical values of their measurable areas. 
       FIG. 4  shows a flowchart for the complete photo album creation system  400 . Input to the photo album creation system  400  is a listing  401  of the images to be included in the album, where the listing  401  here comprises img0.jpg, img1.jpg, and img2.jpg on Page 1, followed by img3.jpg and img4.jpg on Page 2. Other listings may be provided depending on user desires. Such a listing may indicate the position of each page break. Alternately, the design may use time stamps or other available computer information to determine page breaks. For example, if several images were captured within a few seconds of one another, followed by a pause, followed by more images, the page break may be located between the two groups distinctly separated in time. Output from the photo album creation system  400  is a photo album output, such as a collection of pages in, for example, pdf, jpg, or other available format, typically graphical in nature. 
     Generally, the focus of the present design is to progress from a relatively loose layout configuration where the system broadly assigns graphic images to leaf nodes in a tree structure to a precise layout configuration consistent with the mode of layout operation specified by the user. 
     For purposes of defining the terms used herein, a “tree” is a structure such as that shown on the right side of  FIG. 5B , where components of the tree correspond to features of the available page. The points in the tree that have branches emanating from them will be referred to as “nodes,” while the point in the tree that do not have branches emanating from them are referred to as “leaves.” The page may be divided sequentially such as in the manner shown in  FIG. 5A . Each division corresponds to one node in the tree. The representation on the left of  FIG. 5B  shows a page divided into six subareas, representing five divisions made from the original page. The representation on the right of  FIG. 5B  is a tree having six end points, or leaves  501 ,  502 ,  503 ,  504 ,  505 , and  506 , and five nodes,  507 ,  508 ,  509 ,  510 , and  511 . A tree used in the present design, such as tree  500 , therefore includes multiple leaves such as leaf  501 , multiple branches such as branch  512 , and multiple nodes such as node  507 . The present design builds different tree structures depending on the desires of the user and the images presented, where each resultant tree structure forms a layout, and multiple tree structures and layouts may be prepared. 
       FIG. 6  shows a detailed flowchart of the present design. The input to the design is a list of the images  601  that are intended by the user to appear on the page, and the output  611  is a layout specification, best_T, indicating a position and size for each image in the list of images  601 . The basic operation entails the system generating a number of candidate layouts, along with a score for each candidate layout, and then outputting a candidate layout having the highest score via the output  611 . 
     The preferred mode of operation is for the output best_T to provide one best layout having the highest score among all the candidate layouts. However, in a scenario where the user desires to examine multiple alternative layouts, the output best_T may represent a plurality of layouts. For example, five layout tree structures may be desired so that the user can choose among the five. In the multiple alternative layout scenario, best_T could represent a number of candidate layouts selected as having higher layout scores than any other layout computed. 
     Element  602  generates a layout tree structure T having N leaf nodes, while element 603 takes the tree structure so generated and assigns each image to a leaf in T. The system may assign leaves, branches, and nodes randomly, and may recall earlier trees attempted if the user ultimately decides to employ a different design and thus desires to revisit a previous tree. Element  603  may randomly assign images to leaves in the tree so created, which may also be done randomly and the choice retained if an alternate layout is desired. Taking  FIG. 5B  as an example, six images may be received, and a five node—six leaf tree employed. Alternately, the two bottom leaves, namely leaves  502  and  503 , could be located below leaf  501 ,  504 ,  505 , or  506 , making those leaves nodes, and node  511  into a leaf. 
     Element  602  may be implemented in different ways to generate a layout tree structure. The input required to element  602  is the number N of images. One way to generate the layout tree structure entails generating a binary tree structure with N leaves and (N−1) nodes, and subsequently assigning a cut direction to each node. Both the shape of the tree structure (i.e., the network of nodes and leaves), and the cut directions assigned to the nodes may be random. In the present aspect of the design, the system generates the tree structure deterministically while the cut directions are assigned randomly, effectively flipping a coin and assigning HORIZ (horizontal cut) in case of heads and VERTIC (vertical cut) in case of tails. The present implementation for element  603  is to generate a random one-to-one mapping between the images and the leaves of the tree. Elements  602  and  603  thus provide the general framework for candidate layouts. 
     Element  604  then characterizes a bounding box for the images in the subtree for each node in tree structure T. As used herein, the “subtree” of a node is defined as the node itself, taken along with all the branches, nodes and leaves that emanate from the node in the direction of the leaves, or emanate in a generally downward direction for the trees illustrated in the drawings herein. A bounding box is an area of space that bounds the image, as well as any associated caption or other material. In element  605 , the system assigns physical space on the page in accordance with the bounding box of each node in T. The result from element  605  is a candidate layout specified consistently with the selected mode of layout operation, or desired layout style (e.g., strict area layout or brick layout). Elements  604  and  605  are described in more detail below. 
     Decision  606  determines whether the candidate layout is the first candidate layout formed, and if so, element  608  moves T into a Best Tree (best_T) register or storage location. If the result of decision  606  is that the candidate layout was not the first candidate layout formed, decision  607  computes a score for T and a score for best T. If the score of T is greater than the score of best_T, step  608  moves T to the best_T position or register, and control then moves to decision  609 . On the other hand if the result of decision  607  is that the score of T is not greater than the score of best_T, control then moves to decision  609 . 
     The score may be computed in different ways. One way to compute a score is to assess the empty space on the page and the layout with the least blank space is the best layout. This scoring may be used for strict area layouts, since relative area proportions are already fixed in the case of strict area layout. Another way to compute the score is to seek the most uniform images on the page, accomplished by determining the ratio of the smallest image area on the page divided by the greatest image area on the page, and choose the greatest result. For scoring brick style layouts, scoring may be performed by determining a combination of empty space and image area uniformity so that neither criterion suffers excessively at the expense of optimizing the other. 
     Decision  609  determines whether the desired number of image-to-leaf assignments have been considered for the particular tree structure T. This desired number maybe determined by the user or other controlling entity, such as a remote automated program. In general, designating a greater number of image-to-leaf assignments increases the chance of finding a better layout. Desired number is highly dependent on the number of images desired for the specific page. If the number of images is low (e.g., two or three images), the desired number may be set low. If the number of images is great, the desired number may be high, e.g., 100 or more. With respect to the flowchart, if the result of decision  609  is negative, control passes back to element  603 , where the system generates a new image-to-leaf assignment, resulting in a new layout configuration. If the result of decision  609  is positive, control passes to decision  610 . 
     At decision  610 , the system determines whether the desired number of layout tree structures have been considered, where desired number may be determined by the user or other controlling entity. The layout tree structure significantly effects the resulting layout. Therefore, a greater number of layout tree structures increases the chance of the user finding a better layout. If the result of decision  610  is positive, best_T results at output  611 . If negative, the system repeats element  602  by generating a new layout tree structure T having N leaf nodes. 
     In element  604 , for each node and leaf in the layout tree structure, the system characterizes a bounding box enclosing images in the subtree rooted there. The system computes an aspect ratio, denoted “a,” and a relative area proportion, denoted “e.” From these parameters, the system characterizes or defines a bounding box. For example, an aspect ratio of 4:3 may be characterized as an “a” of 1.3333, and the relative area proportion may be 1.0 for a first image and, for example, 2.5 for a second image, indicating the second image is desired to be 2.5 times as large as the first image. An “a” of 1.3333 and an “e” of 2.5 thus defines a bounding box that may be manipulated and positioned. 
     Characterization of a bounding box for any node requires a priori characterization of the bounding boxes for its two children, as will be discussed. Due to this a priori bounding box characterization requirement, element  604  in  FIG. 6  operates to, in a sense, work “up” the tree, from a lowest leaf node up through nodes to the top, or root, of the tree. 
     For leaves, the bounding box characterization of element  604  is straightforward, in that the aspect ratio is equal to the aspect ratio of the photo assigned to the leaf. For strict area style layout, the user may provide the relative area proportion. Alternatively, the system may determine relative area proportions for the leaves in a random or dynamic fashion. For brick style layout, the initial numerical values of the relative area proportions are immaterial and the user or system may assign any positive value. 
     For nodes, the system forms a bounding box according to the flowchart in  FIG. 7 . Input is either a strict area style indication or a brick style indication, typically specified by the user. For block  701 , executed when the system provides a brick style indication, the system adjusts the relative area proportions of one child of the node and all its children depending on the type of cut desired. If the current node has a horizontal cut, adjustment is made so that the widths of the bounding boxes of the two children are equal. If the current node has a vertical cut, adjustment is made so that the heights of the bounding boxes of the two children are equal. At block  702 , performed for both strict area style and brick style, the system computes relative area proportion and aspect ratio for the current node as a function of relative area proportions and aspect ratios of its two children. 
     In operation, if the current node provides a vertical cut, block  701  adjusts the right child so that the rectangle containing the images in the subtree of the right child will have the same height as the rectangle containing the images in the subtree of the left child. Similarly, if the current node provides a horizontal cut, block  701  adjusts the right child to have the same width as the left child. 
     The decision to adjust the right child in operation, as opposed to adjusting the left child, is neutral, or a “don&#39;t care.” That is, alternately, block  701  could adjust the left child and all of its children to have the same height or width as the right child. Either method may be implemented, as the system is setting relative area proportions which may be altered at this point. 
     Specifically, in block  701 , the system multiplies the relative area proportions of the right child and all its children by the following factor: 
             factor   =     {               (       e   1     ·     a   1       )     ÷     (       a   r     ·     e   r       )       ,     if   ⁢           ⁢   cut   ⁢           ⁢   direction   ⁢           ⁢   is   ⁢           ⁢   vertical                     (       e   1     ·     a   r       )     ÷     (       a   1     ·     e   r       )       ,     if   ⁢           ⁢   cut   ⁢           ⁢   direction   ⁢           ⁢   is   ⁢           ⁢   horizontal                     
where e 1  and a 1  are the relative area proportion and the aspect ratio, respectively, of the left child of the current node, and e r  and a r  are the relative area proportion and the aspect ratio, respectively, of the right child.
 
       FIG. 8  illustrates a flowchart representing block  701  of  FIG. 7 , while  FIG. 9  is a flowchart of block  702  of  FIG. 7 . From  FIG. 8 , element  801  obtains left and right children relative area proportions and aspect ratios. Depending on whether a horizontal cut, in this example, is desired at decision  802 , the system computesfactor according to element  803  or  804 . Withfactor computed, the system at element  805  multiplies relative area proportion for the right child and all its children by thefactor so computed. From  FIG. 9 , again element  901  obtains left and right children relative area proportions and aspect ratios. Again, in this example the system makes a decision  902  as to whether this is a horizontal cut (the decision may alternately be whether this is a vertical cut). If the present cut is horizontal, the system determines in decision  903  whether right child relative area proportion divided by right child aspect ratio exceeds left child relative area proportion divided by left child aspect ratio. If so, aspect ratio and relative area proportion for the current node are as computed in element  905 . Otherwise, they are as computed in element  904 . If the present cut is not horizontal, the system determines in decision  906  whether right child relative area proportion multiplied by right child aspect ratio exceeds left child relative area proportion multiplied by left child aspect ratio. If so, aspect ratio and relative area proportion for the current node are as computed in element  908 . Otherwise, they are as computed in element  907 . The result is thus an aspect ratio and relative area proportion for the current node. 
     A simple example follows. In the case of strict area style layout, the user may have specified for two images A and B an e 1  of 1.0 and an a 1  of 4.0 for image A and an e r  of 2.0 and an a r  of 2.0 for image B. Thus for the node having image A and image B as its children, from  FIG. 9 , with a horizontal cut desired, decision  903  computes whether 2.0/2.0 is greater than 1.0/4.0, and 1.0 is greater than 0.25. Thus a is equal to (2.0+2.0)/1.0, or 4.0, and e is equal to (2.0+2.0)*1.0, or 4.0. Thus the node containing images A and B has a bounding box defined by an aspect ratio of 4.0 and a relative area proportion of 4.0. 
     Thus, from element  605 , the system allocates a rectangular region of space on the page for the images associated with each node in the layout tree structure contained in the subtree rooted at the node. A rectangular region of space refers not only the height and width of the region, but also the region&#39;s absolute position relative to the borders of the page. In allocating space for any node that is not the root node, the system takes into consideration that it already allocated space for that node&#39;s parent. Conceptually, element  605  thus operates by working from “top to bottom” of the tree structure, starting at the root node and finishing at the leaf nodes. The regions of space allocated in step  605  are different than the bounding boxes determined in step  604 . The main difference is that regions of space reflect actual physical area in rendered output pages, which is measurable in distance units such as square inches or square millimeters; while bounding boxes are expressed using relative notions of area occupied. 
     In operation, element  605  causes the system to first assign the region of space of the entire page to the root node. This “entire page” may represent a complete face of a physical page, or only the useable portion of a physical page. For example, the entire page may not include space previously dedicated for margins, headers and footers. The system therefore assigns the height and width of the region of space to the root node, and further assigns spatial location coordinates indicating the left and bottom position of the region of space. Other spatial location coordinates could be used, such as the center of the region of space, or the top right-hand corner of the region of space. The region of space may further be assigned to a conceptual representation of a region. 
     With the height and width of the region of space assigned, the system then computes the aspect ratio and the area of the region of space. Generally, the aspect ratio of the bounding box of the root node as determined in element  604  may not equal the aspect ratio of the page. 
     Subsequently, the system steps through the nodes and eventually the leaves. At a node, the system takes the space allocated to the node, divides the space into non-overlapping subsets, and then assigns the subsets to the children of the node. Ways of dividing and assigning may vary depending upon the desired layout style. Element  605  operates as shown in  FIG. 15A , whether brick style or strict area style is employed. From  FIG. 15A , element  1501  indicates that for each node, the system divides the region of space between its two children, be they children nodes or leaves. Element  1502  states that for each leaf, the system determines the image size and position based on the region of space assigned to the leaf.  FIG. 15B  illustrates the variables used in element  605 , including the loading of variables performed in element  605 . The system initially sets the current node to be the parent. From element  1551 , the system defines and loads certain parent “region of space” variables. These variables are filled if the root node is the node evaluated, or these values may have been computed previously if the node evaluated is not the root node. parent_rs_ht represents the height of the parent region of space, and parent_rs_wd the width of the parent region of space. The bottom and left of the parent region of space are also designated, but other measures may be employed, such as top and/or right of the parent region of space. The system computes the parent region of space aspect ratio parent_rs_a, representing the parent region of space height divided by the parent region of space width. From element  604 , the system in element  1552  loads the relative area proportion of the bounding box of the left child of the parent into left_bb_e, the aspect ratio of the bounding box of the left child of the parent left_bb_a, and the right child counterparts of these values. The system in element  1552  also loads the aspect ratio of the bounding box of the parent into parent_bb_a. Finally, element  1553  computes right child and left child products and ratios. In decision  1554 , the system determines whether a vertical or horizontal cut is desired. If a vertical cut, the system progresses to the flowchart of  FIG. 16 , while a horizontal cut causes the system to progress to the flowchart of  FIG. 17 . 
     From  FIG. 16 , decision  1601  determines whether the parent region of space ratio parent_rs_a is greater than the aspect ratio of the bounding box of the parent, parent_bb_a. If so, operation progresses to element  1602 , which computes widths and heights of right and left regions of space as shown. From element  1602 , operation passes to element  1604 , computes bottom positions for the left and right children regions of space, right_rs_bt and left_rs_bt. Operation progresses to element  1605 , which computes a gap between the left and right children, and the left positions of the left and right children, left_rs_lf and right_rs_lf. 
     If the parent region of space ratio parent rs_a is not greater than the aspect ratio of the bounding box of the parent as determined in decision  1601 , the system determines in decision  1603  whether the right child producer as computed in element  1553  exceeds the left child product computed in element  1553 . If the right child product, right_prod, exceeds the left child product, left_prod, operation proceeds to element  1606 , which computes right and left child region of space heights, right_rs_ht and left_rs_ht. If decision  1603  determines that the right child product as computed in element  1553  is not greater than the left child product computed in element  1553 , the system computes right and left child region of space height, right_rs_ht and left_rs_ht, in element  1607 . Element  1607  thus computes the same variables using different computations than shown in element  1606 . From element  1606  or element  1607 , operation progresses to element  1608 , which computes left and right child region of space widths, left_rs_wd and right_rs_wd. Operation then progresses to elements  1604  and  1605  as shown to compute gap size and positions of the left and right children on the page. 
     In the event the parent cut direction is horizontal in decision  1504 , operation progresses to  FIG. 17  and specifically decision  1701 . Decision  1701  determines whether the parent region of space ratio parent_rs_a is greater than the aspect ratio of the bounding box of the parent, parent_bb_a. If not, operation progresses to element  1702 , which computes widths and heights of right and left regions of space as shown. From element  1702 , operation passes to element  1704 , computes left side positions for the left and right children regions of space, right_rs_lf and left_rs_lf. Operation progresses to element  1705 , which computes a gap between the left and right children, and the bottom positions of the left and right children, left_rs_bt and right_rs_bt. 
     If the parent region of space ratio parent_rs_a is greater than the aspect ratio of the bounding box of the parent as determined in decision  1701 , the system determines in decision  1703  whether the right child ratio as computed in element  1553  exceeds the left child ratio computed in element  1553 . If the right child ratio, right_ratio, exceeds the left child ratio, left_ratio, operation proceeds to element  1706 , which computes right and left child region of space width, right_rs_wd and left_rs_wd. If decision  1703  determines that the right child product as computed in element  1553  is not greater than the left child product computed in element  1553 , the system computes right and left child region of space width, right_rs_wd and left_rs_wd, in element  1707 . Element  1707  thus computes the same variables using different computations than shown in element  1706 . From element  1706  or element  1707 , operation progresses to element  1708 , which computes left and right child region of space heights, left_rs_ht and right_rs_ht. Operation then progresses to elements  1704  and  1705  to compute left and bottom positions for the left and right children as well as the gap between children. 
     Different ways of performing this computation and determination as element  605  may be employed while still within the scope of the present design. The system thus proceeds through leaf nodes, and determines a position and size for the image assigned to each leaf node. The system allocates a region of space to all leaf nodes having an aspect ratio equal to that of the image assigned to a particular leaf node. The system may position the image to be as large as possible within the available region of space. Alternatively, the system may position the image to be smaller than this largest possible size for the purpose of providing space between the images, thereby improving layout appearance in certain circumstances. As an example of this alternative, the system may designate each image to have height and width equal to 0.95 of the largest possible height and width allowable within the available region of space. (Still other methods could be used to locate white space between neighboring images.) This generally concludes operation of element  605 . 
     Finally, returning to  FIG. 6 , any of a number of scoring functions may be appropriate for element  607 . In strict area layout mode, where image relative area proportions are fixed, the system may use the fraction of the page occupied by the image(s). Scoring in this manner enables images to be as large as possible while simultaneously respecting the user specified relative area proportions. In brick layout mode, the user does not set the relative image area proportions, but rather relative image area proportions are dictated by the general configuration, such as the layout tree structure and the assignment of images to particular leaf nodes. In this case, the system may employ a more complex scoring function that encourages the images to be large and of relatively consistent area. Scoring may thus vary depending on desired performance and circumstances. 
     Single Pass Operation 
     In order to speed up the layout process, the foregoing arrangement and design may be modified to assemble a layout based on user input in a single pass, without the processing required from the flowchart of  FIG. 6  from the foregoing description. 
     While the present design could be used to generate layouts in any style, including the strict area style, brick style layouts may be advantageously employed in the present single pass design. 
       FIG. 10  shows a photo album creation system according to the present single pass design. According to  FIG. 10 , the user supplies a set of images, rather than the set of images, layout style, proportions, and so forth. As with the foregoing description, the system could take images from various sources, including a folder on the user&#39;s computer, a digital camera memory card, an online photo sharing website, or other similar image source. 
     The user further specifies the location of page breaks. However, it is unnecessary for the user to explicitly specify page breaks. For example, the user may specify that each page should have no more than five images. Alternately, the system may provide a maximum number of images per page, such as four, or may randomly or semi-randomly set page breaks, such as setting a random number between three and seven images per page. Other page break provisions may be provided. 
       FIG. 11  shows the single pass automatic layout design. The system takes the images  1001  specified and adds each image to the layout one at a time. The system writes the layout in the form of a binary tree structure such as the binary tree structure illustrated in the right half of  FIG. 5B . The system adds each image to the layout by inserting the image into the layout tree structure. The system may insert the image at any of multiple locations within a layout tree structure. The present design places the image in all available tree structure locations and selects the location yielding a layout having a highest score. Selection of the highest score layout location is represented in elements  1110  and  1114  of  FIG. 11 . The result of the single pass photo album generation system  1000  is a photo album output in a particular format, such as pdf. 
     Specifically, from  FIG. 11A , continued on  FIG. 11B , element  1101  initializes the layout tree T with one leaf including the first image. Element  1102  normalizes T, where normalizing in this context means operating according to the flowchart of  FIG. 14 , discussed below. Element  1103  moves T into the best_T slot. Element  1104  evaluates whether no further images are available, i.e. if this is the only image. If this is the only image, best_T is the T entered in element  1104 , and the operation ceases. If further images are available at element  1104 , element  1105  gets the next image, while element  1106  evaluates the first location in the tree T. The term “location” as used herein may be defined as either a leaf or a node. Element  1107  creates T′ as an augmented copy of T, where the augmentation is to add a new node in the place of the location, and with one child of the new node being the subtree of T whose root is the location of T, and with the other child of the new node being the image. In T′, a predetermined cut, such as a horizontal cut, is made at the new node. Element  1108  normalizes T′. Decision  1109  determines whether the location is the first location. If this is the first location, T′ is shifted into best_T at element  1111  and operation progresses to element  1112 . If this is not the first location, element  1110  computes a score for the newly fashioned T′ and a score for best_T, where scoring may be performed in the various aforementioned ways or in the manner described below. Element  1110  evaluates whether the resultant score for T′ is greater than, or the tree is better than, the resultant score for best_T, indicating an improved layout. If the score of T′ is greater than the score of best_T, then T′ moves into the best_T position or register and operation moves to element  1112 . If the score of T′ is not greater than the score of best_T, operation progresses to element  1112 . 
     From  FIG. 11B , element  1112  shifts T plus the new node into T′, with a different predetermined cut at the location as opposed to the cut of element  1107 . The system normalizes T′ at element  1113 , and again determines scores for T′ and best_T at element  1114 . Element  1114  may use the same or different scoring method as element  1110 , and again if the score of T′ is greater than the score of best_T, the system moves modified tree T′ into best_T, and operation then progresses to element  1116 . If element  1110  indicates the score of T′ is not greater than the score of best_T, operation progresses directly to element  1116 . Element  1116  determines whether no further locations are available in T. If no further locations are available in T, operation progresses to element  1118 . If further nodes are available in T, element  1117  evaluates the next node in T and operation progresses to element  1107  and proceeds as previously discussed. If no further nodes are available in tree T, element  1118  determines whether the page has no more images available for processing. If no more images are available, best_T moves into T in element  1119 , and the next image obtained using element  1105 . If no further images are available, best_T is the tree made available for image layout. 
     Successive insertions of images according to this design are shown in  FIG. 12 . Insertion of each image into an existing layout tree structure operates as follows. For a tree T having N images, the system may seek to add the (N+1)-st image. The system inserts the image at a particular location of T in three steps. First, the system removes the subtree rooted at the location, replacing it with a new, node having either horizontal or vertical orientation.  FIG. 13A  shows a tree  1301  having four associated images and a desire to insert new image  5 . The existing image layout without image  5  is shown as layout  1302 .  FIG. 13B  shows replacement of the subtree  1303  with a new node  1304 . Second, the system may position the new image as a child of the new node.  FIG. 13B  shows the new image  5  placed as a child of the new node  1304 . Finally, the system positions the subtree of T rooted at the original location as the other child of the new node. From  FIG. 13B , the system locates the new image, image  5 , next to the subtree of T rooted at the original node, and locates the original images, here images  1  and  4 , as children of the new node  1304  because they are included in the subtree  1303 . This tree phase process is further illustrated in  FIG. 13C . In  FIG. 13C , the system inserts the new image at the new “V” node  1305 . 
     Thus, in operation, the system assumes that the original layout, such as that shown in  FIG. 13A , has an aspect ratio equal to the aspect of the page. In both the trial layouts of  FIGS. 13B and 13C , shown on the page as layouts  1306  and  1307 , respectively, the system scales the layout to fit inside a the page. The two trial layouts have a different aspect ratio than the original layout, and all the images in the layout adjust to the new image. The system adjusts existing images in size and not aspect ratio. 
     Normalization of a layout is shown in  FIG. 14 . In essence, normalization makes the tree layout structure generally consistent with the desired style, such as brick style, and is substantially similar to elements  604  and  605  of  FIG. 6  above. From  FIG. 14 , element  1401  states that for each node in T, the system characterizes a bounding box of the images in the subtree rooted therein. Element  1402  operates by, for each node in T, assigning physical space on the page in accordance with its bounding box. Thus irregularly shaped images, images with captions, and so forth, may be uniformly defined and positioned in a visually acceptable format. Operation of elements  1401  and  1402  are similar or identical to operation of elements  604  and  605 . 
     Once the system has normalized the layout, the layout is scored in element  1110  and subsequently in element  1114 . The scoring function may have significant effects on the visual quality of the layout. One scoring function includes two terms, alpha and consistency. Alpha measures how well the aspect ratio of the page agrees with the aspect ratio of the bounding box for the images, a numeric value which may be between, for example, 0 and 1. Consistency may be computed as the area of the smallest photo on the page, divided by the area of the largest photo on the page. For both terms, a value of, for example, 1.0 represents an ideal, and a value of, for example, 0.0 represents the worst available alpha or consistency. 
     The scoring function may compute and initial score, such as for example ((1.5*alpha)+consistency). Other initial scores may be computed. This initial score may be penalized for values of alpha and/or consistency that are below thresholds, and the system may compare resultant scores for different parameters as specified above. 
     The foregoing description affords the ability to develop a visually pleasing layout without computing multiple layouts while affording the user the ability to provide certain inputs. 
     It will be appreciated to those of skill in the art that the present design may be applied to other systems that perform efficient placement functions, such as floorplanning for certain types of objects or items, including scalable items that can vary in size and possibly maintain a fixed aspect ratio. In particular, it will be appreciated that various types of optimal or enhanced placement functions may be addressed by the functionality and associated aspects described herein. 
     Although there has been hereinabove described a method and for performing efficient image placement on a surface such as a sheet of paper, for the purpose of illustrating the manner in which the invention may be used to advantage, it should be appreciated that the invention is not limited thereto. Accordingly, any and all modifications, variations, or equivalent arrangements which may occur to those skilled in the art, should be considered to be within the scope of the present invention as defined in the appended claims.