Patent Publication Number: US-9900580-B2

Title: Techniques for improved image disparity estimation

Description:
CROSS-REFERENCE TO RELATED APPLICATIONS 
     This application is a continuation of, claims the benefit of and priority to previously filed U.S. patent application Ser. No. 13/710,312 filed Dec. 10, 2012, entitled “TECHNIQUES FOR IMPROVED IMAGE DISPARITY ESTIMATION”, the subject matter of which is incorporated herein by reference in its entirety. 
    
    
     BACKGROUND 
     In the field of image acquisition and processing, it may be desirable to generate a composite image based on a set of images captured by a two-dimensional camera array. Generating such a composite image may involve combining some or all of the captured images. Combining the captured images may require an accurate determination of correspondences between positions and/or pixels within the respective captured images. Based on such correspondences, depths may be estimated for objects and/or features associated with those positions and/or pixels. The accuracy with which such correspondences may be determined may depend on the accuracy of one or more image disparity factors by which they are characterized. Accordingly, techniques for improved image disparity estimation may be desirable. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         FIG. 1  illustrates one embodiment of an apparatus and one embodiment of a first system. 
         FIG. 2A  illustrates one embodiment of a camera array. 
         FIG. 2B  illustrates a second embodiment of the camera array. 
         FIG. 3A  illustrates one embodiment of a captured image array 
         FIG. 3B  illustrates one embodiment of a first rectified image array. 
         FIG. 4  illustrates one embodiment of a second rectified image array. 
         FIG. 5  illustrates one embodiment of a third rectified image array. 
         FIG. 6  illustrates one embodiment of a fourth rectified image array. 
         FIG. 7  illustrates one embodiment of a first logic flow. 
         FIG. 8  illustrates one embodiment of a second logic flow. 
         FIG. 9  illustrates one embodiment of a third logic flow. 
         FIG. 10  illustrates one embodiment of a second system. 
         FIG. 11  illustrates one embodiment of a third system. 
         FIG. 12  illustrates one embodiment of a device. 
     
    
    
     DETAILED DESCRIPTION 
     Various embodiments may be generally directed to techniques for improved image disparity estimation. In one embodiment, for example, an apparatus may comprise a processor circuit and an imaging management module, and the imaging management module may be operable by the processor circuit to determine a measured horizontal disparity factor and a measured vertical disparity factor for a rectified image array, determine a composite horizontal disparity factor for the rectified image array based on the measured horizontal disparity factor and an implied horizontal disparity factor, and determine a composite vertical disparity factor for the rectified image array based on the measured vertical disparity factor and an implied vertical disparity factor. In this manner, the various rectified images of the rectified image array may be more accurately combined. Other embodiments may be described and claimed. 
     Various embodiments may comprise one or more elements. An element may comprise any structure arranged to perform certain operations. Each element may be implemented as hardware, software, or any combination thereof, as desired for a given set of design parameters or performance constraints. Although an embodiment may be described with a limited number of elements in a certain topology by way of example, the embodiment may include more or less elements in alternate topologies as desired for a given implementation. It is worthy to note that any reference to “one embodiment” or “an embodiment” means that a particular feature, structure, or characteristic described in connection with the embodiment is included in at least one embodiment. The appearances of the phrases “in one embodiment,” “in some embodiments,” and “in various embodiments” in various places in the specification are not necessarily all referring to the same embodiment. 
       FIG. 1  illustrates a block diagram of an apparatus  100 . As shown in  FIG. 1 , apparatus  100  comprises multiple elements including a processor circuit  102 , a memory unit  104 , and an imaging management module  106 . The embodiments, however, are not limited to the type, number, or arrangement of elements shown in this figure. 
     In various embodiments, apparatus  100  may comprise processor circuit  102 . Processor circuit  102  may be implemented using any processor or logic device, such as a complex instruction set computer (CISC) microprocessor, a reduced instruction set computing (RISC) microprocessor, a very long instruction word (VLIW) microprocessor, an x86 instruction set compatible processor, a processor implementing a combination of instruction sets, a multi-core processor such as a dual-core processor or dual-core mobile processor, or any other microprocessor or central processing unit (CPU). Processor circuit  102  may also be implemented as a dedicated processor, such as a controller, a microcontroller, an embedded processor, a chip multiprocessor (CMP), a co-processor, a digital signal processor (DSP), a network processor, a media processor, an input/output (I/O) processor, a media access control (MAC) processor, a radio baseband processor, an application specific integrated circuit (ASIC), a field programmable gate array (FPGA), a programmable logic device (PLD), and so forth. In one embodiment, for example, processor circuit  102  may be implemented as a general purpose processor, such as a processor made by Intel® Corporation, Santa Clara, Calif. The embodiments are not limited in this context. 
     In some embodiments, apparatus  100  may comprise or be arranged to communicatively couple with a memory unit  104 . Memory unit  104  may be implemented using any machine-readable or computer-readable media capable of storing data, including both volatile and non-volatile memory. For example, memory unit  104  may include read-only memory (ROM), random-access memory (RAM), dynamic RAM (DRAM), Double-Data-Rate DRAM (DDRAM), synchronous DRAM (SDRAM), static RAM (SRAM), programmable ROM (PROM), erasable programmable ROM (EPROM), electrically erasable programmable ROM (EEPROM), flash memory, polymer memory such as ferroelectric polymer memory, ovonic memory, phase change or ferroelectric memory, silicon-oxide-nitride-oxide-silicon (SONOS) memory, magnetic or optical cards, or any other type of media suitable for storing information. It is worthy of note that some portion or all of memory unit  104  may be included on the same integrated circuit as processor circuit  102 , or alternatively some portion or all of memory unit  104  may be disposed on an integrated circuit or other medium, for example a hard disk drive, that is external to the integrated circuit of processor circuit  102 . Although memory unit  104  is comprised within apparatus  100  in  FIG. 1 , memory unit  104  may be external to apparatus  100  in some embodiments. The embodiments are not limited in this context. 
     In various embodiments, apparatus  100  may comprise an imaging management module  106 . Imaging management module  106  may comprise logic, algorithms, and/or instructions operative to capture, process, edit, compress, store, print, and/or display one or more images. In some embodiments, imaging management module  106  may comprise programming routines, functions, and/or processes implemented as software within an imaging application or operating system. In various other embodiments, imaging management module  106  may be implemented as a standalone chip or integrated circuit, or as circuitry comprised within processor circuit  102  or within a graphics chip or other integrated circuit or chip. The embodiments are not limited in this respect. 
       FIG. 1  also illustrates a block diagram of a system  140 . System  140  may comprise any of the aforementioned elements of apparatus  100 . System  140  may further comprise a display  142 . Display  142  may comprise any display device capable of displaying information received from processor circuit  102 . Examples for display  142  may include a television, a monitor, a projector, and a computer screen. In one embodiment, for example, display  142  may be implemented by a liquid crystal display (LCD), light emitting diode (LED) or other type of suitable visual interface. Display  142  may comprise, for example, a touch-sensitive color display screen. In various implementations, display  142  may comprise one or more thin-film transistors (TFT) LCD including embedded transistors. In various embodiments, display  142  may be arranged to display a graphical user interface operable to directly or indirectly control imaging management module  106 . For example, in some embodiments, display  142  may be arranged to display a graphical user interface generated by an imaging application implementing imaging management module  106 . In such embodiments, the graphical user interface may enable operation of imaging management module  106  to capture, process, edit, compress, store, print, and/or display one or more images. The embodiments, however, are not limited to these examples. 
     In some embodiments, apparatus  100  and/or system  140  may be configurable to communicatively couple with a camera array  150 . Camera array  150  may comprise a plurality of cameras  150 - n . It is worthy of note that “n” and similar designators as used herein are intended to be variables representing any positive integer. Thus, for example, if an implementation sets a value for n=4, then a complete set of cameras  150 - n  may include cameras  150 - 1 ,  150 - 2 ,  150 - 3 , and  150 - 4 . It is worthy of note that although camera array  150  is illustrated as being external to apparatus  100  and system  140  in  FIG. 1 , in some embodiments, camera array  150  may be comprised within apparatus  100  and/or system  140 . The embodiments are not limited in this context. 
     In various embodiments, camera array  150  may comprise a two-dimensional (2D) camera array. A 2D camera array may comprise a camera array in which the optical centers of the cameras therein are situated in—or approximately situated in—a common plane in three-dimensional space, and arranged in—or approximately arranged in—multiple rows and columns within their common plane. It is worthy of note that because the optical centers of the cameras within a 2D camera array may be situated approximately on—but not necessarily precisely on—the common plane, the actual arrangement of optical centers in a particular 2D camera array may be three-dimensional. The embodiments are not limited in this context. 
     An example of a camera array  200  is illustrated in  FIG. 2A . As shown in  FIG. 2A , camera array  200  comprises nine cameras, labeled  202 - 1  to  202 - 9 , oriented as illustrated by the dashed arrows included therein. Each camera  202 - n  in camera array  200  comprises a respective optical center  204 - n . For example, camera  202 - 1  comprises an optical center  204 - 1 . The embodiments are not limited to this example. 
       FIG. 2B  demonstrates that camera array  200  of  FIG. 2A  may comprise a 2D camera array. Included in  FIG. 2B  are the optical centers  204 - n  of the cameras  202 - n  in camera array  200  of  FIG. 2A . As shown in  FIG. 2B , these optical centers  204 - n  are situated in—or approximately in—a common plane  210 , and reside—or approximately reside—in respective rows R 1 , R 2 , and R 3  and columns C 1 , C 2 , and C 3  within common plane  210 . For example, optical centers  204 - 1 ,  204 - 4 , and  204 - 7  all reside or approximately reside in column C 1 , and optical centers  204 - 7 ,  204 - 8 , and  204 - 9  all reside or approximately reside in row R 3 . The embodiments are not limited to these examples. It is worthy of note that although nine cameras  202 - n  arranged in three rows and three columns are featured in the example 2D camera array of  FIGS. 2A and 2B , 2D camera arrays comprising lesser or greater numbers of cameras and corresponding optical centers, rows, and columns are both possible and contemplated, and the embodiments are not limited in this context. 
     Returning to  FIG. 1 , in operation, a camera array  150  such as the 2D camera array  200  illustrated in  FIGS. 2A and 2B  may capture a plurality of captured images  152 - p , which may be regarded as comprising a captured image array  152 . A captured image array  152  comprising captured images  152 - p  captured by a 2D camera array  150  may be termed a 2D captured image array. In some embodiments, captured image array  152  may comprise a number of captured images  152 - p  that is equal to the number of cameras  150 - n  in the camera array  150 , and each of the captured images  152 - p  may comprise an image captured by a corresponding one of the cameras  150 - n . In various embodiments, there may be potential benefits associated with generating one or more composite images  160 - z  based on the various captured images  152 - p  in captured image array  152 . For example, in some embodiments, combining information comprised within the various captured images  152 - p  may be enable the generation of one or more composite images  160 - z  having desired and/or improved characteristics with respect to the various captured images  152 - p . In an example embodiment, information it may be possible to generate a composite image  160 - z  having a greater level of clarity, detail, or focus than any or all of the captured images  152 - p , by combining information comprised within the various captured images  152 - p . As such, in various embodiments, apparatus  100  and/or system  140 , and/or one or more elements external to apparatus  100  and/or system  140 , may be operative to generate one or more composite images  160 - z  by combining information comprised within the various captured images  152 - p  in captured image array  152 . 
     In some embodiments, in order to facilitate combining information comprised within the various captured images  152 - p  in captured image array  152 , apparatus  100  and/or system  140 , and/or one or more elements external to apparatus  100  and/or system  140 , may be operative to determine one or more positional correspondence relationships  156 - r  for the captured images  152 - p . Each positional correspondence relationship  156 - r  may identify a set of positions within the captured images  152 - p  that correspond to each other. A position within a first captured image  152 - p  and a position within a second captured image  152 - p  may be said to correspond to each other when the two positions comprise visual information describing the same—or approximately the same—point in three-dimensional space, such as a point on an object, surface, person, landscape, or other physical entity or visual effect captured by the camera array  150 . For example, if camera array  150  is used to capture a set of captured images  152 - p  of a human face, a position within a first such captured image  152 - p  and a position within a second such captured image  152 - p  may be said to correspond to each other if they both reside at a same point—or approximately same point—on the face in their respective captured images  152 - p . The embodiments are not limited in this context. 
     In various embodiments, positions identified by a positional correspondence relationship  156 - r  may comprise the locations of pixels and/or groups of pixels within captured images  152 - p . For example, a positional correspondence relationship  156 - r  may identify two positions within two respective captured images  152 - p  that correspond to each other, and each of those two positions may comprise a location of a particular pixel within its respective captured image  152 - p . In such an example, the particular pixels whose locations are identified by the positional correspondence relationship  156 - r  may be said to correspond to each other according to the positional correspondence relationship  156 - r . The embodiments are not limited in this context. 
     An example of a positional correspondence relationship  305  is illustrated in  FIG. 3A . Shown in  FIG. 3A  is a captured image array  300  comprising a set of nine captured images  352 - p , such as may comprise an example of images captured by cameras  202 - n  in the camera array  200  of  FIG. 2A . Each captured image  352 - p  may comprise a respective set of pixels  352 - p - i   p . These captured images  352 - p  are arranged according to the convention, used hereinafter, that in an array of captured images captured by a camera array, the captured images are arranged in rows and columns corresponding to those into which the optical centers of the cameras in the camera array are arranged. Hereinafter, based on this convention, any particular captured image—such as a captured image  352 - p  in  FIG. 3A , for example—shall be said to “reside” in a same row and column of its captured image array—such as captured image array  300  in  FIG. 3A , for example—as the row and column of the camera array in which the optical center of the camera by which it was captured resides. For example, captured image  352 - 6  in  FIG. 3A  resides in row R 2  and column C 3  of captured image array  300 . If captured image array  300  comprises captured images  352 - p  captured by cameras  202 - n  of  FIG. 2A , then according to this convention, captured image  352 - 6  comprises an image captured by camera  202 - 6  of  FIG. 2A , since the optical center  204 - 6  of camera  202 - 6  resides in row R 2  and column C 3  of camera array  200 . It is to be understood that this convention is employed merely for purposes of clarity, and the embodiments are not limited in this context. 
     In the captured image array  300  of  FIG. 3A , each captured image  352 - p  comprises a five-pointed star, the upper most point of which resides at—or approximately at—a respective pixel  352 - p - i   p  within the captured image  352 - p . For example, the upper most point of the five-pointed star in captured image  352 - 1  resides at—or approximately at—a pixel  352 - 1 - 12 . Since each of the pixels  352 - p - i   p  in the various captured images  352 - p  corresponds—or approximately corresponds—to the upper most point of the respective five-pointed star in that captured image  352 - p , each of the pixels  352 - p - i   p  may be said to correspond to each of the other pixels  352 - p - i   p  according to positional correspondence relationship  305 . 
     It is worthy of note that for any particular pixel  352 - p - i   p  in a particular captured image  352 - p , the value of i p  as it is employed herein is meaningful only as an index value for that particular pixel  352 - p - i   p  within the pixels of that particular captured image  352 - p , and is not meaningful when compared to a value of i p  for a pixel  352 - p - i   p  in a different captured image  352 - p . Thus the fact that pixel  352 - 3 - 4  in captured image  352 - 3  has a value of 4 for i 3  and pixel  352 - 7 - 4  in captured image  352 - 7  has that same value of 4 for i 7  does not indicate any meaningful relative relationship, property, or correspondence between pixels  352 - 3 - 4  and  352 - 7 - 4 . Pixels  352 - p - i   p  identified by equal index values i p  within their respective captured images  352 - p  may or may not correspond to each other, and pixels  352 - p - i   p  that correspond to each other may or may not be identified by equal index values i p  within their respective captured images  352 - p . The embodiments are not limited in this context. 
     It is also worthy of note that positional correspondence relationship  305  is only partially illustrated in  FIG. 3A . In  FIG. 3A , corresponding pixels  352 - p - i   p  within captured images  352 - p  residing in common rows of captured image array  300  are connected by dashed lines, and corresponding pixels  352 - p - i   p  within captured images  352 - p  residing in common columns of captured image array  300  are also connected by dashed lines. Thus, for example, pixels  352 - 1 - 12 ,  352 - 4 - 22 , and  352 - 7 - 4  are connected by a dashed line, since they reside in captured images  352 - 1 ,  352 - 4 , and  352 - 7 , respectively, and those three captured images reside in the same column C 1 . However, two particular pixels  352 - p - i   p  need not lie within respective captured images  352 - p  of a common row or column in order to correspond to each other, and dashed lines for such correspondences are omitted from  FIG. 3A  in the interest of clarity. Thus, for example, pixels  352 - 1 - 12  and  352 - 9 - 3  correspond to each other, since they both correspond—or approximately correspond—to the upper most points of the respective five-pointed stars in captured images  352 - 1  and  352 - 9 , despite the fact that captured images  352 - 1  and  352 - 9  do not share a common row or column within captured image array  300 , and thus that pixels  352 - 1 - 12  and  352 - 9 - 3  are not connected by a dashed line. 
     It is further worthy of note that the fact that two particular corresponding pixels  352 - p - i   p  reside in captured images  352 - p  sharing a common row or column within captured image array  300  does not necessarily mean that the two particular corresponding pixels  352 - p - i   p  share a common vertical or horizontal coordinate within their respective captured images  352 - p , a fact that is evidenced by the curvature of the dashed lines partially illustrating positional correspondence relationship  305  in  FIG. 3A . For example, pixel  352 - 1 - 12  in captured image  352 - 1  corresponds to pixel  352 - 4 - 22  in captured image  352 - 4 , and both captured images reside in column C 1 , but pixel  352 - 4 - 22  is found further to the left in captured image  352 - 4  than is pixel  352 - 1 - 12  in captured image  352 - 1 . 
     Determining a particular positional correspondence relationship such as positional correspondence relationship  305  may comprise selecting a point or region of interest in a particular captured image among a set of captured images, identifying characteristics and/or features at that point or region of interest, and searching within other captured images within the set for points or regions comprising those characteristics and/or features. For example, determining positional correspondence relationship  305  may comprise selecting pixel  352 - 3 - 4  in captured image  352 - 3 , determining that pixel  352 - 3 - 4  comprises a feature corresponding to the top of the five-pointed star, and searching within the remaining captured images  352 - p  for pixels that comprise a same or similar feature. Determining whether particular positions and/or pixels comprise the same—or approximately same—characteristics and/or features may comprise the application of one or more matching algorithms. The embodiments are not limited in this context. 
     As noted above, the determination of positional correspondence relationships such as positional correspondence relationship  305  of  FIG. 3A  may be performed in order to facilitate generation of one or more composite images by combining information within the various captured images captured by the cameras of a camera array, such as the generation of a composite image  160 - z  based on the captured images  152 - p  captured by cameras  150 - n  in camera array  150  of  FIG. 1 . However, determining positional correspondence relationships for captured image arrays such as captured image array  300  of  FIG. 3A  may be computationally intensive, because for each position in a particular captured image  352 - p , a search must be conducted over both a horizontal and a vertical range of positions in a second captured image  352 - p  if the correct corresponding position is to be located. For example, in order to locate within captured image  352 - 1  a pixel  352 - 1 - i   1  corresponding to pixel  352 - 4 - 22  of captured image  352 - 4  in  FIG. 3A , a search must be conducted over both a horizontal and a vertical range of pixels  352 - 1 - i   1  in captured image  352 - 1 , since neither the horizontal position or the vertical position of the correct pixel  352 - 1 - i   1  within captured image  352 - 1  (which happens to be pixel  352 - 1 - 12  in the example of  FIG. 3A ) is known in advance. 
     Returning to  FIG. 1 , in order to reduce the scope of such searches for corresponding positions, and thus reduce the computational costs associated with determining positional correspondence relationships  156 - r  and generating composite images  160 - z , in various embodiments, apparatus  100  and/or system  140 , and/or one or more elements external to apparatus  100  and/or system  140 , may be operative to perform image rectification on captured images  152 - p  to obtain a rectified image array  154  comprising rectified images  154 - q , and to determine positional correspondence relationships  156 - r  using the rectified images  154 - q . A rectified image array  154  comprising rectified images  154 - q  derived from captured images  152 - p  in a captured image array  152  may be termed a 2D rectified image array. Performing image rectification on a particular set of captured images  152 - p  may comprise transforming the set of captured images  152 - p  to obtain a set of rectified images  154 - q  in which corresponding positions of rectified images  154 - q  sharing a common row within a rectified image array share a common horizontal coordinate within their respective rectified images  154 - q , and corresponding positions of rectified images  154 - q  sharing a common column within the rectified image array share a common vertical coordinate within their respective rectified images  154 - q . Image rectification may simplify the process of determining inter-image position correspondences, by enabling searches for corresponding positions to be confined within lines defined by a single horizontal coordinate such as a pixel row, and/or a single vertical coordinate such as a pixel column. In some embodiments, performing image rectification on a captured image array such as captured image array  152  to obtain a rectified image array such as rectified image array  154  may comprise identifying a common plane for the underlying camera array  150 , defining a composite orientation for the camera array  150  based on the common plane, and rotationally transforming the captured images  152 - p  in the captured image array  152  based on the deviations of their capturing cameras&#39; orientations from that of the camera array  150 , the locations of their capturing cameras within the common plane, and/or the intrinsic parameters of their capturing cameras. The embodiments are not limited in this context. 
     An example of a positional correspondence relationship  315  determined using rectified images is illustrated in  FIG. 3B . Shown in  FIG. 3B  is a rectified image array  310 , comprising a set of nine rectified images  354 - q . Each rectified image  354 - q  may comprise a respective set of pixels  354 - q - j   q . The arrangement of these rectified images  354 - q  in rectified image array  310  follows the same convention as that used for captured images  352 - p  in captured image array  300 , such that the rectified images  354 - q  are arranged in rows and columns corresponding to those of captured image array  300  and those into which the optical centers of the cameras in the capturing camera array are arranged. Each rectified image  354 - q  in rectified image array  310  of  FIG. 3B  comprises a rectified version of a corresponding captured image  352 - p  in captured image array  300  of  FIG. 3A . For example, rectified image  354 - 4  of  FIG. 3B  comprises a rectified version of captured image  352 - 4  of  FIG. 3A , and each resides in row R 2  and column C 1  of its corresponding array. The embodiments are not limited to this example. 
     In the rectified image array  310  of  FIG. 3B , each rectified image  354 - q  still comprises a five-pointed star, the upper most point of which resides at—or approximately at—a pixel  354 - q - j   q  within the rectified image  354 - q . Since each of the pixels  354 - q - j   q  in the various rectified images  354 - q  corresponds—or approximately corresponds—to the upper most point of the respective five-pointed star in that rectified image  354 - q , each of the pixels  354 - q - j   q  may be said to correspond to each of the other pixels  354 - q  j q  according to positional correspondence relationship  315 . It is worthy of note that like the value of i p  as employed above, the value of j q  for any particular pixel  354 - q - j   q  as employed herein is meaningful only as an index value for that particular pixel  354 - q  j q  within the pixels of the particular rectified image  354 - q , and is not meaningful when compared to a value of j q  for a pixel  354 - q - j   q  in a different rectified image  354 - q  or when compared to a value of i p  for a pixel  352 - p - i   p  in a captured image  352 - p . It is also worthy of note that like positional correspondence relationship  305  of  FIG. 3A , positional correspondence relationship  315  of  FIG. 3B  is only partially illustrated, as dashed lines are included only for connections between corresponding pixels  354 - q  j q  within rectified images  354 - q  residing in common rows or columns of rectified image array  310 . 
     As shown in  FIG. 3B , in rectified image array  310 , corresponding pixels  354 - q - j   q  residing in rectified images  354 - q  sharing a common row or column will share a common vertical or horizontal coordinate within their respective rectified images  354 - q . This fact is evidenced by the lack of curvature of the dashed lines partially illustrating positional correspondence relationship  315 . For example, rectified images  354 - 4 ,  354 - 5 , and  354 - 6  all reside in row R 2  in rectified image array  310 , and comprise mutually corresponding pixels  354 - 4 - 1 ,  354 - 5 - 10 , and  354 - 6 - 7 , respectively. Since rectified images  354 - 4 ,  354 - 5 , and  354 - 6  all reside in the same row, corresponding pixels of rectified images  354 - 4 ,  354 - 5 , and  354 - 6  will share a common vertical coordinate within their respective rectified images. Thus, although the horizontal positions of pixels  354 - 4 - 1 ,  354 - 5 - 10 , and  354 - 6 - 7  within their respective rectified images  354 - 4 ,  354 - 5 , and  354 - 6  are variable, their vertical positions within their respective rectified images are the same. Similarly, the vertical positions of pixels  354 - 3 - 14 ,  354 - 6 - 7 , and  354 - 9 - 2  within their respective rectified images  354 - 3 ,  354 - 6 , and  354 - 9  are variable, but since rectified images  354 - 3 ,  354 - 6 , and  354 - 9  all reside in column C 3 , the horizontal positions of pixels  354 - 3 - 14 ,  354 - 6 - 7 , and  354 - 9 - 2  within their respective rectified images  354 - 3 ,  354 - 6 , and  354 - 9  are the same. The embodiments are not limited to these examples. 
     Determining a positional correspondence relationship  315  for rectified image array  310  may be less computationally intensive than determining a positional correspondence relationship  305  for captured image array  300  of  FIG. 3A , because some of the searches for positions corresponding to a particular position may be focused based the horizontal and/or vertical coordinates of that position. For example, to locate, within rectified image  354 - 5  of rectified image array  310 , a pixel  354 - 5 - j   5  corresponding to pixel  354 - 8 - 10  in rectified image  354 - 8 , a search may be focused on the pixels within rectified image  354 - 5  that reside at the same horizontal coordinate within rectified image  354 - 5  as does pixel  354 - 8 - 10  in rectified image  354 - 8 . In contrast, a search to locate, within captured image  352 - 5  of captured image array  300  of  FIG. 3A , a pixel  352 - 5 - i   5  corresponding to pixel  352 - 8 - 17  in captured image  352 - 8  cannot be limited to pixels within captured image  352 - 5  that reside at the same horizontal coordinate within captured image  352 - 5  as does pixel  352 - 8 - 17  in captured image  352 - 8 , because it is not known that the two corresponding pixels will share a common horizontal coordinate within their respective captured images. The embodiments are not limited to these examples. 
     Returning to  FIG. 1 , in various embodiments, empirically determining a complete set of positional correspondence relationships  156 - r  for a rectified image array  154  may still be computationally prohibitive, despite the computational load reductions associated with the use of rectified images. Particularly, this may be the case when the number of unique positions and/or pixels within the respective rectified images  154 - q  in the rectified image array  154  is large enough that determining a complete set of positional correspondence relationships  156 - r  would involve the determination of hundreds or thousands of such relationships. In such embodiments, it may be desirable to instead determine one or more generalized parameters that approximately define the complete set of positional correspondence relationships  156 - r  for the rectified image array  154 . To that end, in some embodiments, in order to further facilitate combining information comprised within the various captured images  152 - p , imaging management module  106 , may be operative to determine one or more position determination parameters  157 - s . Position determination parameters  157 - s  may comprise generalized parameters operative to describe the approximate relative locations of corresponding positions within respective rectified images  154 - q  in rectified image array  154 . In various embodiments, given a particular position in a particular rectified image  154 - q , for example, position determination parameters  157 - s  may be operative to identify, within each other rectified image  154 - q  in the rectified image array  154 , a position corresponding to that particular position. As such, position determination parameters  157 - s  may approximately define a complete set of positional correspondence relationships  156 - r  for the rectified image array  154 . The embodiments are not limited to this example. 
     In some embodiments, a particular position determination parameter  157 - s  may comprise a parameter describing a position in a particular rectified image  154 - q  based on a relative location within camera array  150  of a particular camera  150 - n  to which the particular rectified image  154 - q  corresponds. In various such embodiments, the position determination parameter  157 - s  may describe the position in the particular rectified image  154 - q  based on the relative location of the particular camera  150 - n  to which the particular rectified image  154 - q  corresponds with respect to a reference camera within the camera array  150 . The embodiments are not limited in this context. 
     In some embodiments, position determination parameters  157 - s  may comprise a horizontal disparity factor  157 - 1 . Horizontal disparity factor  157 - 1  may comprise a parameter describing the horizontal coordinates—within their respective rectified images  154 - q —of corresponding positions in the various rectified images  154 - q , based on the horizontal locations—within the camera array  150 —of the various cameras  150 - n  to which the various rectified images  154 - q  correspond. In various such embodiments, horizontal disparity factor  157 - 1  may comprise an estimated magnitude by which the horizontal coordinates of a position in a rectified image  154 - q  differ from the horizontal coordinates of a reference position within a reference image as the horizontal distance within the camera array  150  increases between a camera  150 - n  to which the rectified image  154 - q  corresponds and a reference camera to which the reference image corresponds. Based on the above-noted convention employed herein with respect to image arrays, horizontal disparity factor  157 - 1  may also be said to comprise an estimated magnitude by which the horizontal coordinates of the position in the rectified image  154 - q  differ from the horizontal coordinates of the reference position within the reference image as the horizontal distance within a corresponding rectified image array increases between the rectified image  154 - q  and the reference image. The embodiments are not limited in this context. 
     In some embodiments, position determination parameters  157 - s  may comprise a vertical disparity factor  157 - 4 . Vertical disparity factor  157 - 4  may comprise a parameter describing the vertical coordinates—within their respective rectified images  154 - q —of corresponding positions in the various rectified images  154 - q , based on the vertical locations—within the camera array  150 —of the various cameras  150 - n  to which the various rectified images  154 - q  correspond. In various such embodiments, vertical disparity factor  157 - 4  may comprise an estimated magnitude by which the vertical coordinates of a position in a rectified image  154 - q  differ from the vertical coordinates of a reference position within a reference image as the vertical distance within the camera array  150  increases between a camera  150 - n  to which the rectified image  154 - q  corresponds and a reference camera to which the reference image corresponds. Based on the above-noted convention employed herein with respect to image arrays, vertical disparity factor  157 - 4  may also be said to comprise an estimated magnitude by which the vertical coordinates of the position in the rectified image  154 - q  differ from the vertical coordinates of the reference position within the reference image as the vertical distance within a corresponding rectified image array increases between the rectified image  154 - q  and the reference image. The embodiments are not limited in this context. 
       FIG. 4  illustrates an example of a rectified image array  400  in which the positions of corresponding pixels  454 - q - j   g  in the various rectified images  454 - q  are determined using a horizontal disparity factor and a vertical disparity factor. In the interest of clarity, visual features are omitted from the various rectified images  454 - q , dashed positional correspondence lines are also omitted, and a value of j q =1 has been used for each corresponding pixel  454 - q - j   g  among the various rectified images  454 - q . In  FIG. 4 , rectified image  454 - 4  is defined as the reference image  402  upon which the horizontal disparity factor and the vertical disparity factor are based. For each row in rectified image array  400 , a value is specified for Y A , which describes the vertical location of rectified images  454 - q  in that row as a percentage of the difference between the vertical location of the reference image  402  and that of the furthest row from the reference image  402 , which is row R 4 . For example, the value of Y A  for row R 3  is 0.67, indicating that the rectified images  454 - q  in row R 3  are situated 67 percent of the way from the vertical location of reference image  402  to the vertical location of the rectified images  454 - q  in row R 4 . 
     Similarly, for each column in rectified image array  400 , a value is specified for X A , which describes the horizontal location of rectified images  454 - q  in that column as a percentage of the difference between the horizontal location of the reference image  402  and that of the furthest row from the reference image  402 , which is column C 1 . For example, the value of X A  for column C 3  is 0.33, indicating that the rectified images  454 - q  in column C 3  are situated 33 percent of the way from the horizontal location of reference image  402  to the horizontal location of the rectified images  454 - q  in column C 1 . In some embodiments, the difference between the horizontal location of the reference image  402  and that of the furthest row from the reference image  402  may be referred to as the longest horizontal baseline, and the difference between the vertical location of the reference image  402  and that of the furthest row from the reference image  402  may be referred to as the longest vertical baseline. The embodiments are not limited in this context. 
     For each rectified image  454 - q  in rectified image array  400 , the horizontal and vertical coordinates of a pixel  454 - q - j   g  that corresponds to reference pixel  403  in reference image  402  may be determined by multiplying the horizontal disparity factor D H  by X A  and the vertical disparity factor D V  by Y A , and translating the horizontal and vertical coordinates of the reference pixel  403  by the respective results. Thus, for example, the vertical position of the pixel  454 - 12 - 1  is determined by multiplying the vertical disparity factor D V  by 0.67 and translating the vertical coordinate of the reference pixel  403  by the result. Similarly, the horizontal position of the pixel  454 - 2 - 1  is determined by multiplying the horizontal disparity factor D H  by 0.68 and translating the horizontal coordinate of the reference pixel  403  by the result. Likewise, the horizontal position of the pixel  454 - 10 - 1  is determined by multiplying the horizontal disparity factor D H  by 0.68 and translating the horizontal coordinate of the reference pixel  403  by the result, and the vertical position of the pixel  454 - 10 - 1  is determined by multiplying the vertical disparity factor D V  by 0.67 and translating the vertical coordinate of the reference pixel  403  by the result. The embodiments are not limited to these examples. 
     Returning to  FIG. 1 , in general operation, apparatus  100  and/or system  140  may be operative to receive a set of captured images  152 - p  captured by camera array  150 - n , and/or may be operative to generate or to receive a set of rectified images  154 - q  based on such captured images  152 - p . In various embodiments, in order to facilitate the generation of one or more composite images  160 - z  based on the set of captured images  152 - p  and/or the set of rectified images  154 - q , imaging management module  106  may be operative to determine one or more position determination parameters  157 - s  for the set of captured images  152 - p  and/or the set of rectified images  154 - q . In some such embodiments, the position determination parameters  157 - s  may comprise a horizontal disparity factor  157 - 1  and/or a vertical disparity factor  157 - 4  for the set of captured images  152 - p  and/or for the set of rectified images  154 - q . The embodiments are not limited in this context. 
     In various embodiments, in order to determine a horizontal disparity factor  157 - 1  for rectified image array  154 , imaging management module  106  may be operative to first determine a measured horizontal disparity factor  157 - 2  for rectified image array  154 . In some embodiments, the measured horizontal disparity factor  157 - 2  may comprise an estimated number of pixels by which the horizontal coordinates of any particular reference position in a reference image are expected to differ from the horizontal coordinates of corresponding positions in rectified images  154 - q  residing in a furthest column from that of the reference image. 
     In various embodiments, imaging management module  106  may be operative to determine the measured horizontal disparity factor  157 - 2  for the rectified image array  154  by determining a value that minimizes a total pixel matching error over a longest horizontal baseline of the rectified image array  154 . In some embodiments, the rectified image array  154  may comprise a plurality of columns, and the longest horizontal baseline of the rectified image array  154  may comprise a distance between the farthest left column and the farthest right column of the rectified image array  154 . 
     In various embodiments, imaging management module  106  may be operative to determine the measured horizontal disparity factor  157 - 2  for the rectified image array  154  by performing an iterative process. In each iteration, a horizontal candidate value may be selected that comprises a candidate value for a horizontal disparity factor, and a horizontal error associated with that horizontal candidate value may be determined. In some embodiments, each horizontal candidate value may represent a number of pixels. In various embodiments, in each iteration, the horizontal candidate value may be determined by incrementing the horizontal candidate value used in the previous iteration. In some embodiments, the iterative process may conclude when the horizontal candidate value reaches a horizontal disparity value limit. At the conclusion of the iterative process, the horizontal candidate value with which a minimized horizontal error is associated may be determined as the measured horizontal disparity factor  157 - 2  for the rectified image array  154 . In various embodiments, a horizontal pixel matching error value may be computed for each horizontal candidate value according to a horizontal pixel matching error function. In some such embodiments, the horizontal candidate value with which the minimized horizontal error is associated may be determined as a horizontal candidate value among those selected for evaluation for which a smallest horizontal pixel matching error value is computed. The embodiments are not limited in this context. 
       FIG. 5  illustrates an example of a rectified image array based on which a horizontal error may be calculated for a horizontal candidate value. Shown in  FIG. 5  is a rectified image array  500 , which has been truncated to display only a top row R 1 . The rectified image array  500  comprises columns C 1 , C 2 , C 3 , and C 4 , in which rectified images  554 - 1 ,  554 - 2 ,  554 - 3 , and  554 - 4  reside, respectively. Rectified image  554 - 4  is selected as a reference image  502 , and a pixel therein is selected as a reference pixel  503 . Shown within each of rectified images  554 - 1 ,  554 - 2 , and  554 - 3  is the position corresponding to reference pixel  503 , as well as respective pixels  554 - q - a  and  554 - q - e . In each of rectified images  554 - 1 ,  554 - 2 , and  554 - 3 , the respective pixel  554 - q - a  indicates the actual position of the pixel corresponding to the reference pixel  503  in reference image  502 , and the respective pixel  554 - q - e  indicates the expected position of that pixel, based on a horizontal candidate value D H   c . Similarly to  FIG. 4 , the expected positions  554 - q - e  in rectified images  554 - 1 ,  554 - 2 , and  554 - 3  are determined by multiplying the horizontal candidate value D H   c  by X A , where X A  describes the horizontal location of rectified images  554 - q  in a column as a percentage of the difference between the horizontal location of the reference image  502  and that of the furthest column from the reference image  502 , which is column C 1 . 
     In each of rectified images  554 - 1 ,  554 - 2 , and  554 - 3  in  FIG. 5 , the actual location  554 - q - a  of the pixel corresponding to reference pixel  503  differs from the expected location  554 - q - e  of that pixel by a distance  505 - q  in the horizontal direction. For example, the actual location  554 - 2 - a  of the pixel in rectified image  554 - 2  corresponding to reference pixel  503  lies to the right of the expected location  554 - 2 - e  of that pixel by a distance  505 - 2  in the horizontal direction. These distances  505 - q  comprise errors which may weighted and summed to determine a horizontal error associated with the horizontal candidate value D H   c  based upon which the expected locations  554 - q - e  were calculated. The embodiments are not limited in this context. 
     Returning to  FIG. 1 , in some embodiments, imaging management module  106  may be operative, for a particular horizontal candidate value D H   c , to determine an associated horizontal error according to a horizontal pixel matching error function. In various embodiments, imaging management module  106  may be operative to determine the horizontal error according to the horizontal pixel matching error function as a sum of a sum of absolute differences with respect to the inverse distance between multiple camera pairs along the longest horizontal baseline. In some such embodiments, imaging management module  106  may be operative to determine the horizontal error according to the horizontal pixel matching error function described by the equation: 
     
       
         
           
             
               Err 
               ⁡ 
               
                 ( 
                 
                   D 
                   H 
                   c 
                 
                 ) 
               
             
             = 
             
               
                 ∑ 
                 
                   n 
                   = 
                   2 
                 
                 N 
               
               ⁢ 
               
                   
               
               ⁢ 
               
                 
                   e 
                   H 
                   n 
                 
                 ⁡ 
                 
                   ( 
                   
                     
                       D 
                       H 
                       c 
                     
                     * 
                     
                       
                         B 
                         
                           ( 
                           
                             1 
                             , 
                             n 
                           
                           ) 
                         
                       
                       
                         B 
                         
                           ( 
                           
                             1 
                             , 
                             N 
                           
                           ) 
                         
                       
                     
                   
                   ) 
                 
               
             
           
         
       
     
     where N represents the number of columns in the rectified image array, B (1,n)  represents the distance between the reference camera and the n th  column, B (1,N)  represents the distance between the reference camera and the farthest column, and e H   n  represents the pairwise block matching error function defined by the equation:
 
 e   H   n ( D   H   c )=Σ i,jεW   |f   (1,1) ( x+j,y+i )− f   (1,n) ( x+j+D   H   c   ,y+i )|
 
     where f represents the intensity function of images and W represents a window size for a sum of absolute differences block matching algorithm. 
     In various embodiments, in order to determine a vertical disparity factor  157 - 4  for rectified image array  154 , imaging management module  106  may be operative to first determine a measured vertical disparity factor  157 - 5  for rectified image array  154 . In some embodiments, the measured vertical disparity factor  157 - 2  may comprise an estimated number of pixels by which the vertical coordinates of any particular reference position in a reference image are expected to differ from the vertical coordinates of corresponding positions in rectified images  154 - q  residing in a furthest row from that of the reference image. 
     In various embodiments, imaging management module  106  may be operative to determine the measured vertical disparity factor  157 - 5  for the rectified image array  154  by determining a value that minimizes a total pixel matching error over a longest vertical baseline of the rectified image array  154 . In some embodiments, the rectified image array  154  may comprise a plurality of rows, and the longest vertical baseline of the rectified image array  154  may comprise a distance between the extreme top row and the extreme bottom row of the rectified image array  154 . 
     In various embodiments, imaging management module  106  may be operative to determine the measured vertical disparity factor  157 - 5  for the rectified image array  154  by performing an iterative process. In each iteration, a vertical candidate value may be selected that comprises a candidate value for a vertical disparity factor, and a vertical error for that vertical candidate value may be determined. In some embodiments, each vertical candidate value may represent a number of pixels. In various embodiments, in each iteration, the vertical candidate value may be determined by incrementing the vertical candidate value used in the previous iteration. In some embodiments, the iterative process may conclude when the vertical candidate value reaches a vertical disparity value limit. At the conclusion of the iterative process, the vertical candidate value with which a minimized vertical error is associated may be determined as the measured vertical disparity factor  157 - 5  for the rectified image array  154 . In various embodiments, a vertical pixel matching error value may be computed for each vertical candidate value according to a vertical pixel matching error function. In some such embodiments, the vertical candidate value with which the minimized vertical error is associated may be determined as a vertical candidate value among those selected for evaluation for which a smallest vertical pixel matching error value is computed. The embodiments are not limited in this context. 
       FIG. 6  illustrates an example of a rectified image array based on which a vertical error may be calculated for a vertical candidate value. Shown in  FIG. 6  is a rectified image array  600 , which has been truncated to display only a far right column C 1 . The rectified image array  600  comprises rows R 1 , R 2 , R 3 , and R 4 , in which rectified images  654 - 4 ,  654 - 8 ,  654 - 12 , and  654 - 16  reside, respectively. Rectified image  654 - 4  is selected as a reference image  602 , and a pixel therein is selected as a reference pixel  603 . Shown within each of rectified images  654 - 8 ,  654 - 12 , and  654 - 16  is the position corresponding to reference pixel  603 , as well as respective pixels  654 - q - a  and  654 - q - e . In each of rectified images  654 - 8 ,  654 - 12 , and  654 - 16 , the respective pixel  654 - q - a  indicates the actual position of the pixel corresponding to the reference pixel  603  in reference image  602 , and the respective pixel  654 - q - e  indicates the expected position of that pixel, based on a vertical candidate value D V   c . Similarly to  FIG. 5 , the expected positions  654 - q - e  in rectified images  654 - 8 ,  654 - 12 , and  654 - 16  are determined by multiplying the vertical candidate value D V   c  by Y A , where Y A  describes the vertical location of rectified images  654 - q  in a row as a percentage of the difference between the vertical location of the reference image  602  and that of the furthest row from the reference image  602 , which is row R 4 . 
     In each of rectified images  654 - 8 ,  654 - 12 , and  654 - 16  in  FIG. 6 , the actual location  654 - q - a  of the pixel corresponding to reference pixel  603  differs from the expected location  654 - q - e  of that pixel by a distance  605 - q  in the vertical direction. For example, the actual location  654 - 12 - a  of the pixel in rectified image  654 - 12  corresponding to reference pixel  603  lies above the expected location  654 - 12 - e  of that pixel by a distance  605 - 12  in the vertical direction. These distances  605 - q  comprise errors which may weighted and summed to determine a vertical error associated with the vertical candidate value D V   c  based upon which the expected locations  654 - q - e  were calculated. The embodiments are not limited in this context. 
     Returning to  FIG. 1 , in various embodiments, imaging management module  106  may be operative, for a particular vertical candidate value D V   c , to determine an associated vertical error according to a vertical pixel matching error function. In some embodiments, imaging management module  106  may be operative to determine the vertical error according to the vertical pixel matching error function as a sum of a sum of absolute differences with respect to the inverse distance between multiple camera pairs along the longest vertical baseline. In various such embodiments, imaging management module  106  may be operative to determine the vertical error according to the vertical pixel matching error function described by the equation: 
     
       
         
           
             
               Err 
               ⁡ 
               
                 ( 
                 
                   D 
                   V 
                   c 
                 
                 ) 
               
             
             = 
             
               
                 ∑ 
                 
                   m 
                   = 
                   2 
                 
                 M 
               
               ⁢ 
               
                   
               
               ⁢ 
               
                 
                   e 
                   V 
                   m 
                 
                 ⁡ 
                 
                   ( 
                   
                     
                       D 
                       V 
                       c 
                     
                     * 
                     
                       
                         B 
                         
                           ( 
                           
                             m 
                             , 
                             1 
                           
                           ) 
                         
                       
                       
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                           ( 
                           
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                   ) 
                 
               
             
           
         
       
     
     where M represents the number of rows in the rectified image array, B (m,1)  represents the distance between the reference camera and the m th  row, B (M,1)  represents the distance between the reference camera and the farthest row, and e V   m  represents the pairwise block matching error function defined by the equation:
 
 e   V   m ( D   V   c )=Σ i,jΣW   |f   (1,1) ( x+j,y+i )− f   (m,1) ( x+j ,( y+i−D   V   c )|
 
     where f represents the intensity function of images and W represents a window size for a sum of absolute differences block matching algorithm. 
     In some embodiments, imaging management module  106  may be operative to cross-check measured horizontal disparity factor  157 - 2  and measured vertical disparity factor  157 - 5  in order to determine horizontal disparity factor  157 - 1  and vertical disparity factor  157 - 4 . As such, horizontal disparity factor  157 - 1  and vertical disparity factor  157 - 4  may comprise adjusted values with respect to measured horizontal disparity factor  157 - 2  and measured vertical disparity factor  157 - 5 , and may comprise more accurate values than measured horizontal disparity factor  157 - 2  and measured vertical disparity factor  157 - 5 . In various embodiments, imaging management module  106  may be operative to cross-check measured horizontal disparity factor  157 - 2  and measured vertical disparity factor  157 - 5  based on an ideal expected relationship between measured horizontal disparity factor  157 - 2  and measured vertical disparity factor  157 - 5 . In some such embodiments, imaging management module  106  may be operative to cross-check measured horizontal disparity factor  157 - 2  and measured vertical disparity factor  157 - 5  based on the ideal expected relationship described by the equation: 
     
       
         
           
             
               
                 
                   B 
                   H 
                 
                 ⁢ 
                 
                   f 
                   x 
                 
               
               
                 D 
                 H 
                 m 
               
             
             = 
             
               
                 
                   B 
                   V 
                 
                 ⁢ 
                 
                   f 
                   y 
                 
               
               
                 D 
                 V 
                 m 
               
             
           
         
       
     
     where D H   m  and D V   m  represent measured horizontal disparity factor  157 - 2  and measured vertical disparity factor  157 - 5 , B H  and B V  represent the lengths of the longest horizontal and vertical baselines of the rectified image array, and f x  and f y  represent the horizontal and vertical focal lengths of the reference camera in its image plane. 
     In various embodiments, imaging management module  106  may be operative to determine an implied horizontal disparity factor  157 - 3  based on measured vertical disparity factor  157 - 5 , and to determine an implied vertical disparity factor  157 - 6  based on measured horizontal disparity factor  157 - 2 . In some embodiments, imaging management module  106  may be operative to determine implied horizontal disparity factor  157 - 3  and implied vertical disparity factor  157 - 6  according to the equations: 
     
       
         
           
             
               D 
               H 
               i 
             
             = 
             
               
                 
                   
                     B 
                     H 
                   
                   ⁢ 
                   
                     f 
                     x 
                   
                 
                 
                   
                     B 
                     V 
                   
                   ⁢ 
                   
                     f 
                     y 
                   
                 
               
               ⁢ 
               
                 D 
                 V 
                 m 
               
             
           
         
       
       
         
           
             
               D 
               V 
               i 
             
             = 
             
               
                 
                   
                     B 
                     V 
                   
                   ⁢ 
                   
                     f 
                     y 
                   
                 
                 
                   
                     B 
                     H 
                   
                   ⁢ 
                   
                     f 
                     x 
                   
                 
               
               ⁢ 
               
                 D 
                 H 
                 m 
               
             
           
         
       
     
     where D H   i  and D V   i  represent implied horizontal disparity factor  157 - 3  and implied vertical disparity factor  157 - 6 , respectively. 
     In various embodiments, imaging management module  106  may be operative to determine horizontal disparity factor  157 - 1  and vertical disparity factor  157 - 4  based on measured horizontal disparity factor  157 - 2 , implied horizontal disparity factor  157 - 3 , measured vertical disparity factor  157 - 5 , and implied vertical disparity factor  157 - 6 . In some embodiments, imaging management module  106  may be operative to determine horizontal disparity factor  157 - 1  by averaging measured horizontal disparity factor  157 - 2  and implied horizontal disparity factor  157 - 3 , and to determine vertical disparity factor  157 - 4  by averaging measured vertical disparity factor  157 - 5  and implied vertical disparity factor  157 - 6 . In various embodiments, imaging management module  106  may be operative to determine horizontal disparity factor  157 - 1  and vertical disparity factor  157 - 4  according to the equations: 
     
       
         
           
             
               D 
               H 
             
             = 
             
               
                 1 
                 2 
               
               ⁢ 
               
                 ( 
                 
                   
                     D 
                     H 
                     m 
                   
                   + 
                   
                     D 
                     H 
                     i 
                   
                 
                 ) 
               
             
           
         
       
       
         
           
             
               D 
               V 
             
             = 
             
               
                 1 
                 2 
               
               ⁢ 
               
                 ( 
                 
                   
                     D 
                     V 
                     m 
                   
                   + 
                   
                     D 
                     V 
                     i 
                   
                 
                 ) 
               
             
           
         
       
     
     where D H  and D V  represent horizontal disparity factor  157 - 1  and vertical disparity factor  157 - 4 , respectively. Since horizontal disparity factor  157 - 1  may be determined as a combined function of measured horizontal disparity factor  157 - 2  and implied horizontal disparity factor  157 - 3 , horizontal disparity factor  157 - 1  may also be termed a composite horizontal disparity factor. Likewise, since vertical disparity factor  157 - 4  may be determined as a combined function of measured vertical disparity factor  157 - 5  and implied vertical disparity factor  157 - 6 , vertical disparity factor  157 - 4  may also be termed a composite vertical disparity factor. The embodiments are not limited in this context. 
     In some embodiments, horizontal disparity factor  157 - 1  may comprise a pixel value by which positions in a rectified image located on the opposite side of the longest horizontal baseline from the reference image may be horizontally translated. For example, in  FIG. 4 , horizontal disparity factor D H  may comprise a pixel value by which positions in rectified image  454 - 1 —which resides at the opposite end of the longest horizontal baseline from reference image  402 —may be horizontally translated. Similarly, vertical disparity factor  157 - 4  may comprise a pixel value by which positions in a rectified image located on the opposite side of the longest vertical baseline from the reference image may be vertically translated. For example, in  FIG. 4 , vertical disparity factor D V  may comprise a pixel value by which positions in rectified image  454 - 16 —which resides at the opposite end of the longest vertical baseline from reference image  402 —may be vertically translated. The embodiments are not limited in this context. 
     The rectified images  154 - q  in a rectified image array  154  that reside at intermediate locations along the longest horizontal and/or vertical baseline may be referred to as the intermediate rectified images  154 - q  in that rectified image array. For example, in rectified image array  400  of  FIG. 4 , rectified image  454 - 10  may comprise an intermediate rectified image, since it resides at an intermediate location along the longest horizontal baseline and an intermediate location along the longest vertical baseline. In various embodiments, once horizontal disparity factor  157 - 1  and vertical disparity factor  157 - 4  have been determined for a rectified image array  154 , integer disparities for each intermediate rectified image  154 - q  in that rectified image array may be estimated based on the determined horizontal disparity factor  157 - 1  and vertical disparity factor  157 - 4  and on horizontal and vertical baseline ratios for that intermediate rectified image  154 - q . Such estimated integer disparities may then be used to estimate the coordinates of positions in the intermediate rectified images  154 - q  of positions corresponding to a reference position in a reference rectified image  154 - q  in the rectified image array  154 . 
     For example, a horizontal disparity factor D H  and a vertical disparity factor D V  may be determined for rectified image array  400  of  FIG. 4 . The position of reference pixel  403  in reference image  402  of  FIG. 4  can be described as P(x,y) where x and y are the horizontal and vertical coordinates of reference pixel  403  within reference image  402 . Positions within intermediate rectified images  454 - q  in rectified image array  400  that correspond to the position of reference pixel  403  in reference image  402  may be estimated based on horizontal disparity factor D H  and vertical disparity factor D V , and on a horizontal baseline ratio X A  and a vertical baseline ratio Y A  for each intermediate rectified image  454 - q . For example, the position  454 - 10 - 1  in intermediate rectified image  454 - 10  that corresponds to the position of reference pixel  403  in reference image  402  may be described as P(x+D H *X A (C 2 ), y+D V *Y A (R 3 )), where X A (C 2 ) represents the horizontal baseline ratio X A  for column C 2 , and Y A (R 3 ) represents the vertical baseline ratio Y A  for row R 3 . In the example of  FIG. 4 , the horizontal baseline ratio X A (C 2 ) has a value of 0.68, and the vertical baseline ratio Y A (R 3 ) has a value of 0.67. As such, the position  454 - 10 - 1  in intermediate rectified image  454 - 10  that corresponds to the position of reference pixel  403  in reference image  402  may be described as P(x+0.068*D H , y+0.067*D V ). The coordinates of corresponding positions in other intermediate rectified images  454 - q  may be computed in the same fashion. As such, integer disparities for the intermediate rectified images  454 - q  may be estimated without it being necessary to perform additional iterative candidate evaluation processes such as that performed in the course of determining the horizontal disparity factor D H  and the vertical disparity factor D V  for the longest horizontal and vertical baselines. The embodiments are not limited in this context. 
     Returning to  FIG. 1 , in some embodiments, horizontal disparity factor  157 - 1  and vertical disparity factor  157 - 4  may be initially determined to a unit pixel level of accuracy. In various such embodiments, imaging management module  106  may be operative to refine horizontal disparity factor  157 - 1  and vertical disparity factor  157 - 4  to a sub-pixel level of accuracy by up-scaling regions of rectified images  154 - q  and determining an optimal sub-pixel disparity factor pair comprising a horizontal sub-pixel disparity factor and a vertical sub-pixel disparity factor for the up-scaled regions. In some embodiments, the optimal sub-pixel disparity factor pair may comprise a sub-pixel disparity factor pair with which a minimized joint error for the up-scaled regions is associated. In various embodiments, a joint pixel matching error value may be computed for the up-scaled regions for each sub-pixel candidate value pair according to a joint pixel matching error function. In some such embodiments, the sub-pixel candidate value pair with which the minimized joint error is associated may be determined as a sub-pixel candidate value pair among those selected for evaluation for which a smallest joint pixel matching error is computed. In various embodiments, the joint pixel matching error function may comprise a sum of a joint pairwise block matching error function over the up-scaled regions. In some embodiments, the joint pairwise block matching error function may be described by the equation:
 
 e   (m,n) ( s,t )=Σ i,jεW   |f   (1,1) ( x+j,y+i )− f   (m,n) ( x+j+s,y+i+t )|
 
     where W represents a difference between the size of the up-scaled region in the reference image and the size of the up-scaled region in the image residing at row m and column n of the rectified image array  154 . In various embodiments, the values of the horizontal and vertical sub-pixel disparity factors may be described by the equations: 
     
       
         
           
             
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     where d′ H  and d′ V  represent the horizontal and vertical sub-pixel disparity factors, d H  and d V  represent the integer horizontal and vertical disparity factors, and e (m,n) (s,t) represents the joint pairwise block matching error function. The embodiments are not limited in this context. 
     Operations for the above embodiments may be further described with reference to the following figures and accompanying examples. Some of the figures may include a logic flow. Although such figures presented herein may include a particular logic flow, it can be appreciated that the logic flow merely provides an example of how the general functionality as described herein can be implemented. Further, the given logic flow does not necessarily have to be executed in the order presented unless otherwise indicated. In addition, the given logic flow may be implemented by a hardware element, a software element executed by a processor, or any combination thereof. The embodiments are not limited in this context. 
       FIG. 7  illustrates one embodiment of a logic flow  700 , which may be representative of the operations executed by one or more embodiments described herein. More particularly, logic flow  700  may illustrate an example of a process for determining a measured horizontal disparity factor for a rectified image array according to various embodiments. As shown in logic flow  700 , a horizontal candidate value may be selected at  702 . For example, imaging management module  106  of  FIG. 1  may select a horizontal candidate value. At  704 , a horizontal error may be measured for the horizontal candidate value. For example, imaging management module  106  of  FIG. 1  may measure a horizontal error for the horizontal candidate value. At  706 , the horizontal error may be compared to a cumulative minimum horizontal error. For example, imaging management module  106  of  FIG. 1  may compare the horizontal error to a cumulative minimum horizontal error. At  708 , it may be determined whether the horizontal error is less than the cumulative minimum horizontal error. For example, imaging management module  106  of  FIG. 1  may determine whether the horizontal error is less than the cumulative minimum horizontal error. 
     If it is determined at  708  that the horizontal error is less than the cumulative minimum horizontal error, flow may pass to  710 . At  710 , the cumulative minimum horizontal error may be set equal to the horizontal error. For example, imaging management module  106  of  FIG. 1  may set the cumulative minimum horizontal error equal to the horizontal error. Flow may then pass to  712 . If, at  708 , it is determined that the horizontal error is not less than the cumulative minimum horizontal error, flow may pass directly to  712 . At  712 , it may be determined whether all horizontal candidate values have been processed. For example, imaging management module  106  of  FIG. 1  may determine whether all horizontal candidate values have been processed. If it is determined that all horizontal candidate values have not been processed, flow may return to  702 , where a new horizontal candidate value may be selected. If it is determined that all horizontal candidate values have been processed, flow may pass to  714 . At  714 , the measured horizontal disparity factor may be set equal to the horizontal candidate value corresponding to the cumulative minimum horizontal error. For example, imaging management module  106  of  FIG. 1  may set the measured horizontal disparity factor  157 - 2  equal to the horizontal candidate value corresponding to the cumulative minimum horizontal error. The embodiments are not limited to these examples. 
       FIG. 8  illustrates one embodiment of a logic flow  800 , which may be representative of the operations executed by one or more embodiments described herein. More particularly, logic flow  800  may illustrate an example of a process for determining a measured vertical disparity factor for a rectified image array according to some embodiments. As shown in logic flow  800 , a vertical candidate value may be selected at  802 . For example, imaging management module  106  of  FIG. 1  may select a vertical candidate value. At  804 , a vertical error may be measured for the vertical candidate value. For example, imaging management module  106  of  FIG. 1  may measure a vertical error for the vertical candidate value. At  806 , the vertical error may be compared to a cumulative minimum vertical error. For example, imaging management module  106  of  FIG. 1  may compare the vertical error to a cumulative minimum vertical error. At  808 , it may be determined whether the vertical error is less than the cumulative minimum vertical error. For example, imaging management module  106  of  FIG. 1  may determine whether the vertical error is less than the cumulative minimum vertical error. 
     If it is determined at  808  that the vertical error is less than the cumulative minimum vertical error, flow may pass to  810 . At  810 , the cumulative minimum vertical error may be set equal to the vertical error. For example, imaging management module  106  of  FIG. 1  may set the cumulative minimum vertical error equal to the vertical error. Flow may then pass to  812 . If, at  808 , it is determined that the vertical error is not less than the cumulative minimum vertical error, flow may pass directly to  812 . At  812 , it may be determined whether all vertical candidate values have been processed. For example, imaging management module  106  of  FIG. 1  may determine whether all vertical candidate values have been processed. If it is determined that all vertical candidate values have not been processed, flow may return to  802 , where a new vertical candidate value may be selected. If it is determined that all vertical candidate values have been processed, flow may pass to  814 . At  814 , the measured vertical disparity factor may be set equal to the vertical candidate value corresponding to the cumulative minimum vertical error. For example, imaging management module  106  of  FIG. 1  may set the measured vertical disparity factor  157 - 5  equal to the vertical candidate value corresponding to the cumulative minimum vertical error. The embodiments are not limited to these examples. 
       FIG. 9  illustrates one embodiment of a logic flow  900 , which may be representative of the operations executed by one or more embodiments described herein. More particularly, logic flow  900  may illustrate an example of a process for determining a horizontal sub-pixel disparity factor and a vertical sub-pixel disparity factor for a rectified image array according to various embodiments. As shown in logic flow  900 , a sub-pixel candidate value pair may be selected at  902 . For example, imaging management module  106  of  FIG. 1  may select a sub-pixel candidate value pair. At  904 , a joint error may be measured for the sub-pixel candidate value pair. For example, imaging management module  106  of  FIG. 1  may measure a joint error for the sub-pixel candidate value pair. At  906 , the joint error may be compared to a cumulative minimum joint error. For example, imaging management module  106  of  FIG. 1  may compare the joint error to a cumulative minimum joint error. At  908 , it may be determined whether the joint error is less than the cumulative minimum joint error. For example, imaging management module  106  of  FIG. 1  may determine whether the joint error is less than the cumulative minimum joint error. 
     If it is determined at  908  that the joint error is less than the cumulative minimum joint error, flow may pass to  910 . At  910 , the cumulative minimum joint error may be set equal to the joint error. For example, imaging management module  106  of  FIG. 1  may set the cumulative minimum joint error equal to the joint error. Flow may then pass to  912 . If, at  908 , it is determined that the joint error is not less than the cumulative minimum joint error, flow may pass directly to  912 . At  912 , it may be determined whether all sub-pixel candidate value pairs have been processed. For example, imaging management module  106  of  FIG. 1  may determine whether all sub-pixel candidate value pairs have been processed. If it is determined that all sub-pixel candidate value pairs have not been processed, flow may return to  902 , where a new sub-pixel candidate value pair may be selected. If it is determined that all sub-pixel candidate value pairs have been processed, flow may pass to  914 . At  914 , the horizontal sub-pixel disparity factor may be set equal to the horizontal sub-pixel candidate value comprised within the sub-pixel candidate value pair corresponding to the cumulative minimum joint error, and the vertical sub-pixel disparity factor may be set equal to the vertical sub-pixel candidate value comprised within the sub-pixel candidate value pair corresponding to the cumulative minimum joint error. For example, imaging management module  106  of  FIG. 1  may set the horizontal sub-pixel disparity factor equal to the horizontal sub-pixel candidate value comprised within the sub-pixel candidate value pair corresponding to the cumulative minimum joint error, and may set the vertical sub-pixel disparity factor equal to the vertical sub-pixel candidate value comprised within the sub-pixel candidate value pair corresponding to the cumulative minimum joint error. The embodiments are not limited to these examples. 
       FIG. 10  illustrates one embodiment of a system  1000 . In various embodiments, system  1000  may be representative of a system or architecture suitable for use with one or more embodiments described herein, such as apparatus  100  and/or system  140  of  FIG. 1 , logic flow  700  of  FIG. 7 , logic flow  800  of  FIG. 8 , and/or logic flow  900  of  FIG. 9 . The embodiments are not limited in this respect. 
     As shown in  FIG. 10 , system  1000  may include multiple elements. One or more elements may be implemented using one or more circuits, components, registers, processors, software subroutines, modules, or any combination thereof, as desired for a given set of design or performance constraints. Although  FIG. 10  shows a limited number of elements in a certain topology by way of example, it can be appreciated that more or less elements in any suitable topology may be used in system  1000  as desired for a given implementation. The embodiments are not limited in this context. 
     In various embodiments, system  1000  may include a processor circuit  1002 . Processor circuit  1002  may be implemented using any processor or logic device, and may be the same as or similar to processor circuit  102  of  FIG. 1 . 
     In one embodiment, system  1000  may include a memory unit  1004  to couple to processor circuit  1002 . Memory unit  1004  may be coupled to processor circuit  1002  via communications bus  1043 , or by a dedicated communications bus between processor circuit  1002  and memory unit  1004 , as desired for a given implementation. Memory unit  1004  may be implemented using any machine-readable or computer-readable media capable of storing data, including both volatile and non-volatile memory, and may be the same as or similar to memory unit  104  of  FIG. 1 . In some embodiments, the machine-readable or computer-readable medium may include a non-transitory medium. The embodiments are not limited in this context. 
     In various embodiments, system  1000  may include a transceiver  1044 . Transceiver  1044  may include one or more radios capable of transmitting and receiving signals using various suitable wireless communications techniques. Such techniques may involve communications across one or more wireless networks. Exemplary wireless networks include (but are not limited to) wireless local area networks (WLANs), wireless personal area networks (WPANs), wireless metropolitan area network (WMANs), cellular networks, and satellite networks. In communicating across such networks, transceiver  1044  may operate in accordance with one or more applicable standards in any version. The embodiments are not limited in this context. 
     In various embodiments, system  1000  may include a display  1045 . Display  1045  may constitute any display device capable of displaying information received from processor circuit  1002 , and may be the same as or similar to display  142  of  FIG. 1 . 
     In various embodiments, system  1000  may include storage  1046 . Storage  1046  may be implemented as a non-volatile storage device such as, but not limited to, a magnetic disk drive, optical disk drive, tape drive, an internal storage device, an attached storage device, flash memory, battery backed-up SDRAM (synchronous DRAM), and/or a network accessible storage device. In embodiments, storage  1046  may include technology to increase the storage performance enhanced protection for valuable digital media when multiple hard drives are included, for example. Further examples of storage  1046  may include a hard disk, floppy disk, Compact Disk Read Only Memory (CD-ROM), Compact Disk Recordable (CD-R), Compact Disk Rewriteable (CD-RW), optical disk, magnetic media, magneto-optical media, removable memory cards or disks, various types of DVD devices, a tape device, a cassette device, or the like. The embodiments are not limited in this context. 
     In various embodiments, system  1000  may include one or more I/O adapters  1047 . Examples of I/O adapters  1047  may include Universal Serial Bus (USB) ports/adapters, IEEE 1394 Firewire ports/adapters, and so forth. The embodiments are not limited in this context. 
       FIG. 11  illustrates an embodiment of a system  1100 . In various embodiments, system  1100  may be representative of a system or architecture suitable for use with one or more embodiments described herein, such as apparatus  100  and/or system  140  of  FIG. 1 , logic flow  700  of  FIG. 7 , logic flow  800  of  FIG. 8 , logic flow  900  of  FIG. 9 , and/or system  1000  of  FIG. 10 . The embodiments are not limited in this respect. 
     As shown in  FIG. 11 , system  1100  may include multiple elements. One or more elements may be implemented using one or more circuits, components, registers, processors, software subroutines, modules, or any combination thereof, as desired for a given set of design or performance constraints. Although  FIG. 11  shows a limited number of elements in a certain topology by way of example, it can be appreciated that more or less elements in any suitable topology may be used in system  1100  as desired for a given implementation. The embodiments are not limited in this context. 
     In embodiments, system  1100  may be a media system although system  1100  is not limited to this context. For example, system  1100  may be incorporated into a personal computer (PC), laptop computer, ultra-laptop computer, tablet, touch pad, portable computer, handheld computer, palmtop computer, personal digital assistant (PDA), cellular telephone, combination cellular telephone/PDA, television, smart device (e.g., smart phone, smart tablet or smart television), mobile internet device (MID), messaging device, data communication device, and so forth. 
     In embodiments, system  1100  includes a platform  1101  coupled to a display  1145 . Platform  1101  may receive content from a content device such as content services device(s)  1148  or content delivery device(s)  1149  or other similar content sources. A navigation controller  1150  including one or more navigation features may be used to interact with, for example, platform  1101  and/or display  1145 . Each of these components is described in more detail below. 
     In embodiments, platform  1101  may include any combination of a processor circuit  1102 , chipset  1103 , memory unit  1104 , transceiver  1144 , storage  1146 , applications  1151 , and/or graphics subsystem  1152 . Chipset  1103  may provide intercommunication among processor circuit  1102 , memory unit  1104 , transceiver  1144 , storage  1146 , applications  1151 , and/or graphics subsystem  1152 . For example, chipset  1103  may include a storage adapter (not depicted) capable of providing intercommunication with storage  1146 . 
     Processor circuit  1102  may be implemented using any processor or logic device, and may be the same as or similar to processor circuit  1002  in  FIG. 10 . 
     Memory unit  1104  may be implemented using any machine-readable or computer-readable media capable of storing data, and may be the same as or similar to memory unit  1004  in  FIG. 10 . 
     Transceiver  1144  may include one or more radios capable of transmitting and receiving signals using various suitable wireless communications techniques, and may be the same as or similar to transceiver  1044  in  FIG. 10 . 
     Display  1145  may include any television type monitor or display, and may be the same as or similar to display  1045  in  FIG. 10 . 
     Storage  1146  may be implemented as a non-volatile storage device, and may be the same as or similar to storage  1046  in  FIG. 10 . 
     Graphics subsystem  1152  may perform processing of images such as still or video for display. Graphics subsystem  1152  may be a graphics processing unit (GPU) or a visual processing unit (VPU), for example. An analog or digital interface may be used to communicatively couple graphics subsystem  1152  and display  1145 . For example, the interface may be any of a High-Definition Multimedia Interface, DisplayPort, wireless HDMI, and/or wireless HD compliant techniques. Graphics subsystem  1152  could be integrated into processor circuit  1102  or chipset  1103 . Graphics subsystem  1152  could be a stand-alone card communicatively coupled to chipset  1103 . 
     The graphics and/or video processing techniques described herein may be implemented in various hardware architectures. For example, graphics and/or video functionality may be integrated within a chipset. Alternatively, a discrete graphics and/or video processor may be used. As still another embodiment, the graphics and/or video functions may be implemented by a general purpose processor, including a multi-core processor. In a further embodiment, the functions may be implemented in a consumer electronics device. 
     In embodiments, content services device(s)  1148  may be hosted by any national, international and/or independent service and thus accessible to platform  1101  via the Internet, for example. Content services device(s)  1148  may be coupled to platform  1101  and/or to display  1145 . Platform  1101  and/or content services device(s)  1148  may be coupled to a network  1153  to communicate (e.g., send and/or receive) media information to and from network  1153 . Content delivery device(s)  1149  also may be coupled to platform  1101  and/or to display  1145 . 
     In embodiments, content services device(s)  1148  may include a cable television box, personal computer, network, telephone, Internet enabled devices or appliance capable of delivering digital information and/or content, and any other similar device capable of unidirectionally or bidirectionally communicating content between content providers and platform  1101  and/display  1145 , via network  1153  or directly. It will be appreciated that the content may be communicated unidirectionally and/or bidirectionally to and from any one of the components in system  1100  and a content provider via network  1153 . Examples of content may include any media information including, for example, video, music, medical and gaming information, and so forth. 
     Content services device(s)  1148  receives content such as cable television programming including media information, digital information, and/or other content. Examples of content providers may include any cable or satellite television or radio or Internet content providers. The provided examples are not meant to limit embodiments of the invention. 
     In embodiments, platform  1101  may receive control signals from navigation controller  1150  having one or more navigation features. The navigation features of navigation controller  1150  may be used to interact with a user interface  1154 , for example. In embodiments, navigation controller  1150  may be a pointing device that may be a computer hardware component (specifically human interface device) that allows a user to input spatial (e.g., continuous and multi-dimensional) data into a computer. Many systems such as graphical user interfaces (GUI), and televisions and monitors allow the user to control and provide data to the computer or television using physical gestures. 
     Movements of the navigation features of navigation controller  1150  may be echoed on a display (e.g., display  1145 ) by movements of a pointer, cursor, focus ring, or other visual indicators displayed on the display. For example, under the control of software applications  1151 , the navigation features located on navigation controller  1150  may be mapped to virtual navigation features displayed on user interface  1154 . In embodiments, navigation controller  1150  may not be a separate component but integrated into platform  1101  and/or display  1145 . Embodiments, however, are not limited to the elements or in the context shown or described herein. 
     In embodiments, drivers (not shown) may include technology to enable users to instantly turn on and off platform  1101  like a television with the touch of a button after initial boot-up, when enabled, for example. Program logic may allow platform  1101  to stream content to media adaptors or other content services device(s)  1148  or content delivery device(s)  1149  when the platform is turned “off.” In addition, chip set  1103  may include hardware and/or software support for 5.1 surround sound audio and/or high definition 7.1 surround sound audio, for example. Drivers may include a graphics driver for integrated graphics platforms. In embodiments, the graphics driver may include a peripheral component interconnect (PCI) Express graphics card. 
     In various embodiments, any one or more of the components shown in system  1100  may be integrated. For example, platform  1101  and content services device(s)  1148  may be integrated, or platform  1101  and content delivery device(s)  1149  may be integrated, or platform  1101 , content services device(s)  1148 , and content delivery device(s)  1149  may be integrated, for example. In various embodiments, platform  1101  and display  1145  may be an integrated unit. Display  1145  and content service device(s)  1148  may be integrated, or display  1145  and content delivery device(s)  1149  may be integrated, for example. These examples are not meant to limit the invention. 
     In various embodiments, system  1100  may be implemented as a wireless system, a wired system, or a combination of both. When implemented as a wireless system, system  1100  may include components and interfaces suitable for communicating over a wireless shared media, such as one or more antennas, transmitters, receivers, transceivers, amplifiers, filters, control logic, and so forth. An example of wireless shared media may include portions of a wireless spectrum, such as the RF spectrum and so forth. When implemented as a wired system, system  1100  may include components and interfaces suitable for communicating over wired communications media, such as I/O adapters, physical connectors to connect the I/O adapter with a corresponding wired communications medium, a network interface card (NIC), disc controller, video controller, audio controller, and so forth. Examples of wired communications media may include a wire, cable, metal leads, printed circuit board (PCB), backplane, switch fabric, semiconductor material, twisted-pair wire, co-axial cable, fiber optics, and so forth. 
     Platform  1101  may establish one or more logical or physical channels to communicate information. The information may include media information and control information. Media information may refer to any data representing content meant for a user. Examples of content may include, for example, data from a voice conversation, videoconference, streaming video, electronic mail (“email”) message, voice mail message, alphanumeric symbols, graphics, image, video, text and so forth. Data from a voice conversation may be, for example, speech information, silence periods, background noise, comfort noise, tones and so forth. Control information may refer to any data representing commands, instructions or control words meant for an automated system. For example, control information may be used to route media information through a system, or instruct a node to process the media information in a predetermined manner. The embodiments, however, are not limited to the elements or in the context shown or described in  FIG. 11 . 
     As described above, system  1100  may be embodied in varying physical styles or form factors.  FIG. 12  illustrates embodiments of a small form factor device  1200  in which system  1100  may be embodied. In embodiments, for example, device  1200  may be implemented as a mobile computing device having wireless capabilities. A mobile computing device may refer to any device having a processing system and a mobile power source or supply, such as one or more batteries, for example. 
     As described above, examples of a mobile computing device may include a personal computer (PC), laptop computer, ultra-laptop computer, tablet, touch pad, portable computer, handheld computer, palmtop computer, personal digital assistant (PDA), cellular telephone, combination cellular telephone/PDA, television, smart device (e.g., smart phone, smart tablet or smart television), mobile internet device (MID), messaging device, data communication device, and so forth. 
     Examples of a mobile computing device also may include computers that are arranged to be worn by a person, such as a wrist computer, finger computer, ring computer, eyeglass computer, belt-clip computer, arm-band computer, shoe computers, clothing computers, and other wearable computers. In embodiments, for example, a mobile computing device may be implemented as a smart phone capable of executing computer applications, as well as voice communications and/or data communications. Although some embodiments may be described with a mobile computing device implemented as a smart phone by way of example, it may be appreciated that other embodiments may be implemented using other wireless mobile computing devices as well. The embodiments are not limited in this context. 
     As shown in  FIG. 12 , device  1200  may include a display  1245 , a navigation controller  1250 , a user interface  1254 , a housing  1255 , an I/O device  1256 , and an antenna  1257 . Display  1245  may include any suitable display unit for displaying information appropriate for a mobile computing device, and may be the same as or similar to display  1145  in  FIG. 11 . Navigation controller  1250  may include one or more navigation features which may be used to interact with user interface  1254 , and may be the same as or similar to navigation controller  1150  in  FIG. 11 . I/O device  1256  may include any suitable I/O device for entering information into a mobile computing device. Examples for I/O device  1256  may include an alphanumeric keyboard, a numeric keypad, a touch pad, input keys, buttons, switches, rocker switches, microphones, speakers, voice recognition device and software, and so forth. Information also may be entered into device  1200  by way of microphone. Such information may be digitized by a voice recognition device. The embodiments are not limited in this context. 
     Various embodiments may be implemented using hardware elements, software elements, or a combination of both. Examples of hardware elements may include processors, microprocessors, circuits, circuit elements (e.g., transistors, resistors, capacitors, inductors, and so forth), integrated circuits, application specific integrated circuits (ASIC), programmable logic devices (PLD), digital signal processors (DSP), field programmable gate array (FPGA), logic gates, registers, semiconductor device, chips, microchips, chip sets, and so forth. Examples of software may include software components, programs, applications, computer programs, application programs, system programs, machine programs, operating system software, middleware, firmware, software modules, routines, subroutines, functions, methods, procedures, software interfaces, application program interfaces (API), instruction sets, computing code, computer code, code segments, computer code segments, words, values, symbols, or any combination thereof. Determining whether an embodiment is implemented using hardware elements and/or software elements may vary in accordance with any number of factors, such as desired computational rate, power levels, heat tolerances, processing cycle budget, input data rates, output data rates, memory resources, data bus speeds and other design or performance constraints. 
     One or more aspects of at least one embodiment may be implemented by representative instructions stored on a machine-readable medium which represents various logic within the processor, which when read by a machine causes the machine to fabricate logic to perform the techniques described herein. Such representations, known as “IP cores” may be stored on a tangible, machine readable medium and supplied to various customers or manufacturing facilities to load into the fabrication machines that actually make the logic or processor. Some embodiments may be implemented, for example, using a machine-readable medium or article which may store an instruction or a set of instructions that, if executed by a machine, may cause the machine to perform a method and/or operations in accordance with the embodiments. Such a machine may include, for example, any suitable processing platform, computing platform, computing device, processing device, computing system, processing system, computer, processor, or the like, and may be implemented using any suitable combination of hardware and/or software. The machine-readable medium or article may include, for example, any suitable type of memory unit, memory device, memory article, memory medium, storage device, storage article, storage medium and/or storage unit, for example, memory, removable or non-removable media, erasable or non-erasable media, writeable or rewriteable media, digital or analog media, hard disk, floppy disk, Compact Disk Read Only Memory (CD-ROM), Compact Disk Recordable (CD-R), Compact Disk Rewriteable (CD-RW), optical disk, magnetic media, magneto-optical media, removable memory cards or disks, various types of Digital Versatile Disk (DVD), a tape, a cassette, or the like. The instructions may include any suitable type of code, such as source code, compiled code, interpreted code, executable code, static code, dynamic code, encrypted code, and the like, implemented using any suitable high-level, low-level, object-oriented, visual, compiled and/or interpreted programming language. 
     The following examples pertain to further embodiments: 
     At least one machine-readable medium may comprise a plurality of instructions that, in response to being executed on a computing device, cause the computing device to determine a measured horizontal disparity factor for a rectified image array comprising a plurality of rectified images by a first process arranged to iteratively select a horizontal candidate value, measure a horizontal error associated with the selected horizontal candidate value, and determine as the measured horizontal disparity factor a horizontal candidate value with which a minimized horizontal error is associated, and determine a measured vertical disparity factor for the rectified image array by a second process arranged to iteratively select a vertical candidate value, measure a vertical error associated with the selected vertical candidate value, and determine as the measured vertical disparity factor a vertical candidate value with which a minimized vertical error is associated. 
     Such at least one machine-readable medium may comprise instructions that, in response to being executed on the computing device, cause the computing device to determine an implied horizontal disparity factor for the rectified image array based on the measured vertical disparity factor and determine an implied vertical disparity factor for the rectified image array based on the measured horizontal disparity factor. 
     Such at least one machine-readable medium may comprise instructions that, in response to being executed on the computing device, cause the computing device to determine a composite horizontal disparity factor for the rectified image array based on the measured horizontal disparity factor and the implied horizontal disparity factor, and determine a composite vertical disparity factor for the rectified image array based on the measured vertical disparity factor and the implied vertical disparity factor. 
     With respect to such at least one machine-readable medium, the minimized horizontal error may comprise a minimum value of a horizontal pixel matching error function, and the minimized vertical error may comprise a minimum value of a vertical pixel matching error function. 
     With respect to such at least one machine-readable medium, the horizontal pixel matching error function and the vertical pixel matching error function may comprise sums of pairwise block matching error functions. 
     Such at least one machine-readable medium may comprise instructions that, in response to being executed on the computing device, cause the computing device to determine the measured horizontal disparity factor for a longest horizontal baseline of the rectified image array and determine the measured vertical disparity factor for a longest vertical baseline of the rectified image array. 
     With respect to such at least one machine-readable medium, one or both of the measured horizontal disparity factor or the measured vertical disparity factor may comprise a number of pixels. 
     With respect to such at least one machine-readable medium, the composite horizontal disparity factor and the composite vertical disparity factor may comprise integer pixel disparities. 
     Such at least one machine-readable medium may comprise instructions that, in response to being executed on the computing device, cause the computing device to determine a horizontal sub-pixel disparity factor and a vertical sub-pixel disparity factor for the rectified image array by a third process arranged to iteratively select a sub-pixel candidate value pair comprising a horizontal sub-pixel candidate value and a vertical sub-pixel candidate value, measure a joint error associated with the selected sub-pixel candidate value pair, determine as the horizontal sub-pixel disparity factor a horizontal sub-pixel candidate value comprised within a sub-pixel candidate value pair with which a minimized joint error is associated, and determine as the vertical sub-pixel disparity factor a vertical sub-pixel candidate value comprised within the sub-pixel candidate value pair with which the minimized joint error is associated. 
     An apparatus may comprise a processor circuit and an imaging management module to determine a measured horizontal disparity factor for a rectified image array comprising a plurality of rectified images by a first process arranged to iteratively select a horizontal candidate value, measure a horizontal error associated with the selected horizontal candidate value, and determine as the measured horizontal disparity factor a horizontal candidate value with which a minimized horizontal error is associated, and determine a measured vertical disparity factor for the rectified image array by a second process arranged to iteratively select a vertical candidate value, measure a vertical error associated with the selected vertical candidate value, and determine as the measured vertical disparity factor a vertical candidate value with which a minimized vertical error is associated. 
     With respect to such an apparatus, the imaging management module may determine an implied horizontal disparity factor for the rectified image array based on the measured vertical disparity factor and determine an implied vertical disparity factor for the rectified image array based on the measured horizontal disparity factor. 
     With respect to such an apparatus, the imaging management module may determine a composite horizontal disparity factor for the rectified image array based on the measured horizontal disparity factor and the implied horizontal disparity factor, and determine a composite vertical disparity factor for the rectified image array based on the measured vertical disparity factor and the implied vertical disparity factor. 
     With respect to such an apparatus, the minimized horizontal error may comprise a minimum value of a horizontal pixel matching error function, and the minimized vertical error may comprise a minimum value of a vertical pixel matching error function. 
     With respect to such an apparatus, the horizontal pixel matching error function and the vertical pixel matching error function may comprise sums of pairwise block matching error functions. 
     With respect to such an apparatus, the imaging management module may determine the measured horizontal disparity factor for a longest horizontal baseline of the rectified image array and determine the measured vertical disparity factor for a longest vertical baseline of the rectified image array. 
     With respect to such an apparatus, one or both of the measured horizontal disparity factor or the measured vertical disparity factor may comprise a number of pixels. 
     With respect to such an apparatus, the composite horizontal disparity factor and the composite vertical disparity factor may comprise integer pixel disparities. 
     With respect to such an apparatus, the imaging management module may determine a horizontal sub-pixel disparity factor and a vertical sub-pixel disparity factor for the rectified image array by a third process arranged to iteratively select a sub-pixel candidate value pair comprising a horizontal sub-pixel candidate value and a vertical sub-pixel candidate value, measure a joint error associated with the selected sub-pixel candidate value pair, determine as the horizontal sub-pixel disparity factor a horizontal sub-pixel candidate value comprised within a sub-pixel candidate value pair with which a minimized joint error is associated, and determine as the vertical sub-pixel disparity factor a vertical sub-pixel candidate value comprised within the sub-pixel candidate value pair with which the minimized joint error is associated. 
     A method may comprise determining a measured horizontal disparity factor for a rectified image array comprising a plurality of rectified images by performing a first process comprising iteratively selecting a horizontal candidate value measuring a horizontal error associated with the selected horizontal candidate value, and determining as the measured horizontal disparity factor a horizontal candidate value with which a minimized horizontal error is associated and determining a measured vertical disparity factor for the rectified image array by performing a second process comprising iteratively selecting a vertical candidate value, measuring a vertical error associated with the selected vertical candidate value, and determining as the measured vertical disparity factor a vertical candidate value with which a minimized vertical error is associated. 
     Such a method may comprise determining an implied horizontal disparity factor for the rectified image array based on the measured vertical disparity factor and determining an implied vertical disparity factor for the rectified image array based on the measured horizontal disparity factor. 
     Such a method may comprise determining a composite horizontal disparity factor for the rectified image array based on the measured horizontal disparity factor and the implied horizontal disparity factor, and determining a composite vertical disparity factor for the rectified image array based on the measured vertical disparity factor and the implied vertical disparity factor. 
     With respect to such a method, the minimized horizontal error may comprise a minimum value of a horizontal pixel matching error function, the minimized vertical error comprising a minimum value of a vertical pixel matching error function. 
     With respect to such a method, the horizontal pixel matching error function and the vertical pixel matching error function may comprise sums of pairwise block matching error functions. 
     Such a method may comprise determining the measured horizontal disparity factor for a longest horizontal baseline of the rectified image array and determining the measured vertical disparity factor for a longest vertical baseline of the rectified image array. 
     Such a method may comprise determining a horizontal sub-pixel disparity factor and a vertical sub-pixel disparity factor for the rectified image array by performing a third process comprising iteratively selecting a sub-pixel candidate value pair comprising a horizontal sub-pixel candidate value and a vertical sub-pixel candidate value, measuring a joint error associated with the selected sub-pixel candidate value pair, determining as the horizontal sub-pixel disparity factor a horizontal sub-pixel candidate value comprised within a sub-pixel candidate value pair with which a minimized joint error is associated, and determining as the vertical sub-pixel disparity factor a vertical sub-pixel candidate value comprised within the sub-pixel candidate value pair with which the minimized joint error is associated. 
     A system may comprise a processor circuit, a camera array comprising a plurality of cameras, and an imaging management module to determine a measured horizontal disparity factor for a rectified image array comprising a plurality of rectified images of the plurality of cameras by a first process arranged to iteratively select a horizontal candidate value, measure a horizontal error associated with the selected horizontal candidate value, and determine as the measured horizontal disparity factor a horizontal candidate value with which a minimized horizontal error is associated, and determine a measured vertical disparity factor for the rectified image array by a second process arranged to iteratively select a vertical candidate value, measure a vertical error associated with the selected vertical candidate value, and determine as the measured vertical disparity factor a vertical candidate value with which a minimized vertical error is associated. 
     With respect to such a system, the imaging management module may determine an implied horizontal disparity factor for the rectified image array based on the measured vertical disparity factor and determine an implied vertical disparity factor for the rectified image array based on the measured horizontal disparity factor. 
     With respect to such a system, the imaging management module may determine a composite horizontal disparity factor for the rectified image array based on the measured horizontal disparity factor and the implied horizontal disparity factor, and determine a composite vertical disparity factor for the rectified image array based on the measured vertical disparity factor and the implied vertical disparity factor. 
     With respect to such a system, the minimized horizontal error may comprise a minimum value of a horizontal pixel matching error function, the minimized vertical error may comprise a minimum value of a vertical pixel matching error function, and the horizontal pixel matching error function and the vertical pixel matching error function may comprise sums of pairwise block matching error functions. 
     With respect to such a system, the imaging management module may determine a horizontal sub-pixel disparity factor and a vertical sub-pixel disparity factor for the rectified image array by a third process arranged to iteratively select a sub-pixel candidate value pair comprising a horizontal sub-pixel candidate value and a vertical sub-pixel candidate value, measure a joint error associated with the selected sub-pixel candidate value pair, determine as the horizontal sub-pixel disparity factor a horizontal sub-pixel candidate value comprised within a sub-pixel candidate value pair with which a minimized joint error is associated, and determine as the vertical sub-pixel disparity factor a vertical sub-pixel candidate value comprised within the sub-pixel candidate value pair with which the minimized joint error is associated. 
     Numerous specific details have been set forth herein to provide a thorough understanding of the embodiments. It will be understood by those skilled in the art, however, that the embodiments may be practiced without these specific details. In other instances, well-known operations, components, and circuits have not been described in detail so as not to obscure the embodiments. It can be appreciated that the specific structural and functional details disclosed herein may be representative and do not necessarily limit the scope of the embodiments. 
     Some embodiments may be described using the expression “coupled” and “connected” along with their derivatives. These terms are not intended as synonyms for each other. For example, some embodiments may be described using the terms “connected” and/or “coupled” to indicate that two or more elements are in direct physical or electrical contact with each other. The term “coupled,” however, may also mean that two or more elements are not in direct contact with each other, but yet still co-operate or interact with each other. 
     Unless specifically stated otherwise, it may be appreciated that terms such as “processing,” “computing,” “calculating,” “determining,” or the like, refer to the action and/or processes of a computer or computing system, or similar electronic computing device, that manipulates and/or transforms data represented as physical quantities (e.g., electronic) within the computing system&#39;s registers and/or memories into other data similarly represented as physical quantities within the computing system&#39;s memories, registers or other such information storage, transmission or display devices. The embodiments are not limited in this context. 
     It should be noted that the methods described herein do not have to be executed in the order described, or in any particular order. Moreover, various activities described with respect to the methods identified herein can be executed in serial or parallel fashion. 
     Although specific embodiments have been illustrated and described herein, it should be appreciated that any arrangement calculated to achieve the same purpose may be substituted for the specific embodiments shown. This disclosure is intended to cover any and all adaptations or variations of various embodiments. It is to be understood that the above description has been made in an illustrative fashion, and not a restrictive one. Combinations of the above embodiments, and other embodiments not specifically described herein will be apparent to those of skill in the art upon reviewing the above description. Thus, the scope of various embodiments includes any other applications in which the above compositions, structures, and methods are used. 
     It is emphasized that the Abstract of the Disclosure is provided to comply with 37 C.F.R. §1.72(b), requiring an abstract that will allow the reader to quickly ascertain the nature of the technical disclosure. It is submitted with the understanding that it will not be used to interpret or limit the scope or meaning of the claims. In addition, in the foregoing Detailed Description, it can be seen that various features are grouped together in a single embodiment for the purpose of streamlining the disclosure. This method of disclosure is not to be interpreted as reflecting an intention that the claimed embodiments require more features than are expressly recited in each claim. Rather, as the following claims reflect, inventive subject matter lies in less than all features of a single disclosed embodiment. Thus the following claims are hereby incorporated into the Detailed Description, with each claim standing on its own as a separate preferred embodiment. In the appended claims, the terms “including” and “in which” are used as the plain-English equivalents of the respective terms “comprising” and “wherein,” respectively. Moreover, the terms “first,” “second,” and “third,” etc. are used merely as labels, and are not intended to impose numerical requirements on their objects. 
     Although the subject matter has been described in language specific to structural features and/or methodological acts, it is to be understood that the subject matter defined in the appended claims is not necessarily limited to the specific features or acts described above. Rather, the specific features and acts described above are disclosed as example forms of implementing the claims.