Projecting images onto a spherical venue
By segmenting and interpolating color information using a kernel-based sampling technique, the system addresses the processing limitations of traditional systems, enabling effective three-dimensional image projection on sophisticated venue surfaces.
Patent Information
- Application Number
- JP2025536621
- Authority / Receiving Office
- JP · JP
- Patent Type
- Applications
- Current Assignee / Owner
- Priority Date
- 2023-07-10
- Filing Date
- 2023-11-30
- Publication Date
- 2025-12-25
AI Technical Summary
Traditional image projection systems are inadequate for displaying images on large, three-dimensional visual displays due to insufficient processing power, which limits the ability to effectively project images on sophisticated, three-dimensional venue surfaces.
The system converts two-dimensional images into three-dimensional projections by logically segmenting the media surface and image into slices, using a kernel-based sampling technique to project pixels and interpolate color information, enabling real-time or near-real-time image projection on three-dimensional media surfaces.
The system efficiently projects high-quality images on three-dimensional media surfaces by transforming two-dimensional coordinates into three-dimensional coordinates and interpolating color information, providing a seamless and immersive viewing experience.
Smart Images

Figure 2025542339000001_ABST
Abstract
Description
[Background technology]
[0001] (CROSS-REFERENCE TO RELATED APPLICATIONS) This application claims priority to U.S. Patent Application No. 18 / 349,323, filed July 10, 2023, which in turn claims the benefit of U.S. Provisional Patent Application No. 63 / 434,366, filed December 21, 2022, each of which is incorporated by reference in its entirety herein.
[0002] The United States media and entertainment industry is the largest in the world. The U.S. media and entertainment industry accounts for one-third of the global media and entertainment industry, which distributes events, such as music events, theatrical events, sporting events, and / or video events, to audiences for viewing and viewing entertainment. These events often include an image or series of images, often referred to as a video, that can be projected onto a venue's media surface to enhance the audience's immersion in the event. Traditional venues often include large, two-dimensional visual displays, also referred to as jumbotrons, to display these images to the audience. However, as venue media surfaces become more sophisticated, e.g., expanding from large, two-dimensional visual displays to even larger, three-dimensional visual displays that surround the audience, traditional processing power used to display these images on large, two-dimensional visual displays is insufficient to display these images on even larger, three-dimensional visual displays. Summary of the Invention [Means for solving the problem]
[0003] (overview)
[0004] The systems, methods, and devices disclosed herein can retrieve an image or series of images, often referred to as video, that can be projected onto a media surface at a venue. These systems, methods, and devices can convert the image from two dimensions to three dimensions for projection onto the media surface. As part of this conversion, these systems, methods, and devices can logically segment the media surface into multiple slices of the media surface and the image into multiple slices of the image. These systems, methods, and devices can then project one or more pixels of the slice of the media surface onto the image space of the image slice to provide one or more points on the image slice. These systems, methods, and devices then weight and accumulate color information of one or more pixels from the image slices neighboring the one or more points on the image to interpolate the color information of the pixels of the media surface. [Brief explanation of the drawings]
[0005] The present disclosure is described with reference to the accompanying drawings, in which like reference numbers indicate identical or functionally similar elements. Additionally, the left-most digit(s) of a reference number identifies the drawing in which the reference number first appears. In the drawings,
[0006] [Figure 1] FIG. 1 illustrates a simplified block diagram of an exemplary image projection system, according to some exemplary embodiments of the present disclosure.
[0007] [Figure 2A] 2A and 2B illustrate simplified block diagrams of an example venue, according to some example embodiments of the present disclosure. [Figure 2B] 2A and 2B illustrate simplified block diagrams of an example venue, according to some example embodiments of the present disclosure.
[0008] [Figure 3A]3A and 3B illustrate an example kernel-based sampling technique that may be implemented in an example projection system, according to some example embodiments of the present disclosure. [Figure 3B] 3A and 3B illustrate an example kernel-based sampling technique that may be implemented in an example projection system, according to some example embodiments of the present disclosure.
[0009] [Figure 4] FIG. 4 illustrates a flowchart of an example kernel-based sampling technique that may be implemented within an example image projection system, according to some example embodiments of the present disclosure.
[0010] [Figure 5] FIG. 5 schematically illustrates a simplified block diagram of a computer system for executing an electronic design platform, according to some embodiments of the present disclosure.
[0011] The present disclosure will now be described with reference to the accompanying drawings. DETAILED DESCRIPTION OF THE INVENTION
[0012] Detailed Description The following disclosure provides many different embodiments or examples for implementing different features of the provided subject matter. Specific examples of components and arrangements are described below to simplify the disclosure. These, of course, are examples only and are not intended to be limiting. For example, in the following description, the formation of a first feature over a second feature may include embodiments in which the first and second features are formed such that they are in direct contact, and may also include embodiments in which an additional feature may be formed between the first and second features such that the first and second features may not be in direct contact. In addition, the present disclosure may repeat reference numbers and / or letters in various examples. This repetition does not, in itself, dictate a relationship between the various embodiments and / or configurations discussed.
[0013] (Exemplary Image Projection System)
[0014] FIG. 1 illustrates a simplified block diagram of an exemplary image projection system according to some exemplary embodiments of the present disclosure. In the exemplary embodiment illustrated in FIG. 1, the image projection system 100 can retrieve an image or a series of images, often referred to as video, that can be projected onto a media surface of a venue. As described in further detail below, the image projection system 100 can convert the image from two-dimensional to three-dimensional for projection onto the three-dimensional media surface. In some embodiments, the image projection system 100 can logically segment the three-dimensional media surface into multiple slices of the three-dimensional media surface and the two-dimensional image into multiple slices of the two-dimensional image. In these embodiments, the image projection system 100 can utilize a kernel-based sampling technique to project one or more photo elements, also referred to as pixels, of the three-dimensional slice of the three-dimensional media surface onto the two-dimensional image space of the two-dimensional image slice to provide one or more two-dimensional points on the two-dimensional image slice. In these embodiments, the kernel-based sampling technique then weights and accumulates color information of one or more pixels from neighboring images of one or more two-dimensional points on the two-dimensional image slice to interpolate color information of the pixel of the three-dimensional media plane, e.g., the luminance and / or chrominance components of the YUV color model and / or the red, green, and / or blue components of the RGB color model, to name a few. Exemplary embodiments of kernel-based sampling techniques are further described in U.S. Patent Application No. 18 / 332,874, filed June 12, 2023, which is incorporated herein by reference in its entirety. As illustrated in FIG. 1 , image projection system 100 can include an image recording system 102 that can be communicatively coupled to image processing servers 104.1-104.i and venue 106 via a communications network 108. While image projection system 100 is illustrated in FIG. 1 as including multiple discrete devices, those skilled in the art will recognize that one or more of these devices can be combined without departing from the spirit and scope of the present disclosure.For example, the image recording system 102 and one or more of the image processing servers 104.1-104.i can be combined into a single discrete device without the communication network 108, as would be apparent to one skilled in the art without departing from the spirit and scope of the present disclosure.
[0015] The image recording system 102 can store one or more digital image signals. In the exemplary embodiment illustrated in FIG. 1 , the image recording system 102 can include or be communicatively coupled to an image capture system. Generally, the image capture system can include a camera lens system and project light captured by the camera lens system onto an image sensor. Exemplary embodiments of image capture systems are further described in U.S. Patent Application No. 18 / 332,855, filed June 12, 2023, which is incorporated herein by reference in its entirety. In some embodiments, the one or more digital image signals can be stored by the image recording system 102 as a raw camera image file having radiometric characteristics of the light captured by the image capture system. These radiometric characteristics can include color information for each pixel of the image sensor, e.g., the luminance and / or chrominance components of the YUV color model and / or the red, green, and / or blue components of the RGB color model, to name a few. Alternatively, or additionally, the images may be stored by image recording system 102 in any suitable well-known image file format, such as the Joint Photographic Experts Group (JPEG) image file format, the Exchangeable Image File Format (EXIF), the Tagged Image File Format (TIFF), the Graphics Interchange Format (GIF), the Bitmap Image File (BMP) format, or the Portable Network Graphics (PNG) image file format, to name a few, as would be apparent to one skilled in the art without departing from the spirit and scope of this disclosure. In some embodiments, image recording system 102 may include a machine-readable medium, which may include any mechanism for storing one or more digital image signals in a form readable by a machine, such as, for example, one or more of image processing servers 104.1-104.i.In these embodiments, the machine-readable medium may include read-only memory (ROM), random-access memory (RAM), magnetic disk storage media, optical storage media, flash memory devices, etc. Alternatively, or in addition, the machine-readable medium may include a hard disk drive, e.g., a solid-state drive, a floppy disk drive and associated removable media, a CD-ROM drive, an optical drive, a flash memory, or a removable media cartridge, capable of persistently storing one or more digital image signals.
[0016] Image Processing Servers 104.1-104.i include one or more computer systems, exemplary embodiments of which are described in further detail below, that retrieve images stored within Image Recording System 102. Alternatively, or additionally, Image Processing Servers 104.1-104.i can reconstruct images from one or more digital image signals stored within Image Recording System 102. In some embodiments, Image Processing Servers 104.1-104.i can implement one or more digital image processing techniques, also referred to as digital photographic processing techniques, to process one or more digital image signals stored within Image Recording System 102 and reconstruct images from the one or more digital image signals. In some embodiments, the one or more digital image processing techniques may include decoding, demosaicing, bad pixel removal, white balance, noise reduction, color conversion, tone reproduction, compression, systematic noise removal, dark frame subtraction, optical correction, contrast manipulation, unsharp masking, and / or any other suitable well-known digital image processing techniques that would be apparent to one skilled in the art without departing from the spirit and scope of the present disclosure.
[0017] In the exemplary embodiment illustrated in FIG. 1 , image processing servers 104.1-104.i can be assigned to different three-dimensional slices of a three-dimensional media plane. Venue 106 is described in further detail below. In some embodiments, different three-dimensional slices of a three-dimensional media plane can be associated with different slices of an image. In these embodiments, one or more of image processing servers 104.1-104.i can assign different three-dimensional slices of a three-dimensional media plane to image processing servers 104.1-104.i and / or associate different three-dimensional slices of a three-dimensional media plane with different slices of an image. After retrieving an image and / or reconstructing an image from one or more digital image signals, image processing servers 104.1-104.i can mathematically transform the two-dimensional coordinates of the slices of the image into three-dimensional coordinates of the three-dimensional slices of the three-dimensional media plane, enabling the image to be projected onto the three-dimensional media plane of venue 106. Image Processing Servers 104.1-104.i operate in a substantially similar manner to one another, and therefore, for convenience, the operation of Image Processing Server 104.1 is described in further detail below.
[0018] 1, the image processing server 104.1 can utilize a kernel-based sampling technique to mathematically transform two-dimensional coordinates of a corresponding slice of an image into three-dimensional coordinates of a corresponding three-dimensional slice of a three-dimensional media plane. In some embodiments, the kernel-based sampling technique projects pixels of the corresponding three-dimensional slice of the three-dimensional media plane onto the two-dimensional image space of the corresponding slice of the image, effectively transforming the pixels of the corresponding three-dimensional slice of the three-dimensional media plane into two-dimensional coordinates of a two-dimensional point that is projected onto the corresponding slice of the image.
[0019] After projecting the three-dimensional coordinates of the corresponding three-dimensional slice of the three-dimensional media plane onto the corresponding slice of the image, the kernel-based sampling technique statistically interpolates color information of the corresponding three-dimensional slice of the three-dimensional media plane from the corresponding slice of the image, e.g., the luminance and / or chrominance components of the YUV color model and / or the red, green, and / or blue components of the RGB color model, to name a few. In some embodiments, the kernel-based sampling technique can statistically interpolate color information of pixels of the corresponding three-dimensional slice of the three-dimensional media plane based on the color information of the corresponding slice of the image. In these embodiments, the kernel-based sampling technique can statistically interpolate color information of pixels of the corresponding three-dimensional slice of the three-dimensional media plane by weighting and accumulating color information of pixels of the corresponding slice of the image in the neighborhood of the two-dimensional point projected onto the corresponding slice of the image.
[0020] After interpolating the color information for the corresponding 3D slice of the three-dimensional media surface, Image Processing Server 104.1 can provide the color information to the venue 106, and the corresponding slice of the image can be projected onto the venue 106. In some embodiments, Image Processing Server 104.1 can generate a quadruple for the color information for the corresponding 3D slice of the three-dimensional media surface, including the three-dimensional coordinates of the corresponding 3D slice of the three-dimensional media surface and the color information for the corresponding 3D slice that has been statistically interpolated from the image.
[0021] The venue 106 projects color information of different 3D slices of the 3D media surface provided by the image processing servers 104.1-104.i onto pixels of the different 3D slices of the 3D media surface, projecting different slices of the image onto the 3D media surface. In some embodiments, the image processing servers 104.1-104.i can provide the image projection system 100 with sufficient processing power to project images onto the 3D media surface in real time or near real time. For example, the image processing servers 104.1-104.i can read images at an approximate rate of 24 frames per second. In this example, the image processing servers 104.1-104.i can process images as described above and project images onto the 3D media surface at an approximate rate of 240 frames per second.
[0022] Communications network 108 communicatively couples image recording system 102 and image processing servers 104.1-104.i. Communications network 108 can be implemented as a wireless communications network, a wired communications network, and / or any combination thereof, as would be apparent to one skilled in the art without departing from the spirit and scope of this disclosure. In some embodiments, communications network 108 can include an optical fiber network or a coaxial network that communicatively couples image recording system 102 and image processing servers 104.1-104.i using optical fiber or coaxial cable. In some embodiments, communications network 108 can include a hybrid fiber coaxial (HFC) network that combines optical fiber and coaxial cable and communicatively couples image recording system 102 and image processing servers 104.1-104.i.
[0023] Exemplary Venues That May Be Implemented in Exemplary Image Projection Systems
[0024] 2A and 2B illustrate simplified block diagrams of an exemplary venue according to some exemplary embodiments of the present disclosure. In the exemplary embodiment illustrated in FIGS. 2A and 2B, venue 200 represents a location for hosting an event. For example, venue 200 can represent a music venue, e.g., a music theater, music club, and / or concert hall; a sports venue, e.g., an arena, convention center, and / or stadium; and / or any other suitable venue that would be apparent to one skilled in the art without departing from the spirit and scope of the present disclosure. Events can include music events, theatrical events, sporting events, motion pictures, and / or any other suitable events that would be apparent to one skilled in the art without departing from the spirit and scope of the present disclosure. Venue 200 can represent an exemplary embodiment of venue 106 as described in FIG. 1 above.
[0025] 2A and 2B, venue 200 may represent a three-dimensional structure, e.g., a hemispherical structure, also referred to as a hemispherical dome. In some embodiments, venue 200 may include one or more visual displays, often referred to as three-dimensional media surface 202, that are spread across the interior, i.e., inner surface, of venue 200. In these embodiments, one or more visual displays may include a series of rows and columns of photographic elements, also referred to as pixels, that form three-dimensional media surface 202 in three dimensions. In these embodiments, the pixels may be implemented using one or more light-emitting diode (LED) displays, one or more organic light-emitting diode (OLED) displays, and / or one or more quantum dot (QD) displays, to name a few. For example, three-dimensional media surface 202 may include an approximately 16,000 by 16,000 LED visual display that wraps around the interior of venue 200 and forms an approximately 160,000-square-foot visual display.
[0026] As illustrated in FIG. 2A , the three-dimensional media surface 202 can be logically segmented into three-dimensional slices 204.1-204.i of the three-dimensional media surface 202. In some embodiments, the three-dimensional slices 204.1-204.i can occupy any geometric region of pixels of the three-dimensional media surface 202, e.g., a rectangular shape. In these embodiments, the any geometric region can include a closed geometric region, e.g., a regular curve, e.g., a circle or ellipse, an irregular curve, a regular polygon, e.g., an equilateral triangle or square, and / or an irregular polygon, e.g., a rectangle and / or a parallelogram, to name a few. In these embodiments, one or more of the three-dimensional slices 204.1-204.i can occupy similar geometric regions relative to one another, and / or one or more of the three-dimensional slices 204.1-204.i can occupy different geometric regions relative to one another. For example, one or more of the three-dimensional slices 204.1-204.i can include a similar number of pixels of the three-dimensional media surface 202 relative to one another, and / or one or more of the three-dimensional slices 204.1-204.i can occupy a different number of pixels of the three-dimensional media surface 202 relative to one another. As described above, the three-dimensional media surface 202 can include a series of rows and a series of columns of pixels. In some embodiments, each three-dimensional slice of the three-dimensional slices 204.1-204.i can extend along one or more of the series of rows and / or one or more of the series of columns of pixels of the three-dimensional media surface 202, as illustrated in FIG. 2A . In these embodiments, one or more of the three-dimensional slices of the three-dimensional slices 204.1-204.i can extend along one or more columns along the series of rows of pixels of the three-dimensional media surface 202 from the top, i.e., the apex, of the three-dimensional media surface 202 to the bottom, i.e., the origin, of the three-dimensional media surface 202.In these embodiments, one or more of the three-dimensional slices 204.1-204.i may extend along a series of columns of pixels of the three-dimensional media surface 202, across the interior, i.e., inner surface, of the three-dimensional media surface 202, and along one or more of a series of rows.
[0027] After three-dimensional media surface 202 is logically segmented into three-dimensional slices 204.1-204.i of three-dimensional media surface 202, three-dimensional slices 204.1-204.i can be assigned to image processing servers 206.1-206.i. Image processing servers 206.1-206.i as illustrated in FIG. 2A may represent exemplary embodiments of image processing servers 104.1-104.i as described in FIG. 1 above. As illustrated in FIG. 2A, one or more processing servers of image processing servers 206.1-206.i can be assigned to one or more corresponding three-dimensional slices of three-dimensional slices 204.1-204.i. For example, a processing server of image processing servers 206.1-206.i can be assigned to a single three-dimensional slice of three-dimensional slices 204.1-204.i. As another example, a processing server of image processing servers 206.1-206.i can be assigned to multiple 3D slices of 3D slices 204.1-204.i.
[0028] As illustrated in FIG. 2B , a two-dimensional image 208 to be projected onto a three-dimensional media surface 202 can be logically segmented into two-dimensional slices 210.1-210.i of the two-dimensional image 208. In some embodiments, the two-dimensional slices 210.1-210.i can occupy any geometric region of pixels of the two-dimensional image 208, e.g., a rectangular shape. In these embodiments, the any geometric region can include a closed geometric region, e.g., a regular curve, e.g., a circle or ellipse, an irregular curve, a regular polygon, e.g., an equilateral triangle or square, and / or an irregular polygon, e.g., a rectangle and / or a parallelogram, to name a few. In these embodiments, one or more of the two-dimensional slices 210.1-210.i can occupy similar geometric regions relative to one another, and / or one or more of the two-dimensional slices 210.1-210.i can occupy different geometric regions relative to one another. For example, one or more of the two-dimensional slices 210.1-210.i may include a similar number of pixels of the two-dimensional image 208 relative to one another, and / or one or more of the two-dimensional slices 210.1-210.i may occupy a different number of pixels of the two-dimensional image 208 relative to one another.
[0029] After the two-dimensional image 208 is logically segmented into two-dimensional slices 210.1-210.i, the three-dimensional slices 204.1-204.i can be associated with the two-dimensional slices 210.1-210.i. As shown in FIG. 2B , one or more of the three-dimensional slices 204.1-204.i can be associated with one or more corresponding two-dimensional slices of the two-dimensional slices 210.1-210.i. For example, a three-dimensional slice of the three-dimensional slices 204.1-204.i can be associated with a single two-dimensional slice of the two-dimensional slices 210.1-210.i. As another example, a three-dimensional slice of the three-dimensional slices 204.1-204.i can be associated with multiple two-dimensional slices of the two-dimensional slices 210.1-210.i.
[0030] After the three-dimensional slices 204.1-204.i are assigned to the image processing servers 206.1-206.i and the three-dimensional slices 204.1-204.i are associated with the two-dimensional slices 210.1-210.i of the image 208, the image processing servers 206.1-206.i can mathematically transform the two-dimensional slices 210.1-210.i into three-dimensional slices 204.1-204.i of the three-dimensional media surface 202, as described in further detail below, to enable the image 202 to be projected onto the three-dimensional media surface 202 of the venue 200. As described in further detail below, image processing servers 206.1-206.i may implement a kernel-based sampling technique, as described above in FIG. 1, to project pixels of three-dimensional slices 204.1-204.i of three-dimensional media plane 202 onto the two-dimensional image space of two-dimensional slices 210.1-210.i of image 208, effectively converting pixels of three-dimensional slices 204.1-204.i of three-dimensional media plane 202 into two-dimensional coordinates of two-dimensional points projected onto two-dimensional slices 210.1-210.i of image 208. In some embodiments, the kernel-based sampling technique may statistically interpolate color information of pixels of three-dimensional slices 204.1-204.i of three-dimensional media plane 202 based on color information of two-dimensional slices 210.1-210.i of image 208. In these embodiments, the kernel-based sampling technique can statistically interpolate color information of pixels in three-dimensional slices 204.1-204.i of the three-dimensional media surface 202 by weighting and accumulating color information of pixels in two-dimensional slices 210.1-210.i of image 208 that are in the neighborhood of two-dimensional points projected onto the two-dimensional slices 210.1-210.i of image 208.
[0031] Exemplary Kernel-Based Sampling Techniques That May Be Implemented in Exemplary Image Projection Systems
[0032] 3A and 3B illustrate an exemplary kernel-based sampling technique that may be implemented within an exemplary image projection system according to some exemplary embodiments of the present disclosure. The following discussion of FIGS. 3A and 3B further describes kernel-based sampling techniques such as those described in FIGS. 1, 2A, and / or 2B above. In the exemplary embodiment illustrated in FIGS. 3A and 3B, the kernel-based sampling technique 300 mathematically transforms two-dimensional coordinates of an image 302 onto three-dimensional coordinates of a three-dimensional media plane 304 of a venue 306. When executed by an image processing server 308, the kernel-based sampling technique 300 can mathematically transform two-dimensional coordinates of pixels of a two-dimensional slice 310 of the image 302 onto pixels of a three-dimensional slice 312 of the three-dimensional media plane 304, as described in further detail below. In some embodiments, image processing server 308 may represent an example embodiment of one or more of image processing servers 104.1-104.i as described above in Figure 1 and / or one or more of image processing servers 206.1-206.i as described above in Figures 2A and 2B. Also, venue 306 may represent an example embodiment of venue 106 as described above in Figure 1 and / or venue 200 as described above in Figures 2A and 2B.
[0033] 3A and 3B, image processing server 308 can be assigned to one or more three-dimensional slices, such as three-dimensional slice 312, of three-dimensional media plane 304, in a manner substantially similar to that described in, for example, FIG. 1 and / or 2A above. Three-dimensional slice 312 can also be associated with one or more two-dimensional slices, such as two-dimensional slice 310, of image 302, in a manner substantially similar to that described in, for example, FIG. 1 and / or 2B above. After image processing server 308 is assigned to three-dimensional slice 312, which is associated with two-dimensional slice 310, kernel-based sampling technique 300 can mathematically transform two-dimensional coordinates of two-dimensional slice 310 into three-dimensional coordinates of three-dimensional slice 312, enabling image 302 to be projected onto three-dimensional media plane 304. As illustrated in Figures 3A and 3B, the kernel-based sampling technique 300 can project pixels of a three-dimensional slice 312 onto the two-dimensional space of a two-dimensional slice 310, effectively converting the pixels into two-dimensional points projected onto the two-dimensional space of the two-dimensional slice 310.
[0034] After projecting the pixels of the three-dimensional slice 312, the kernel-based sampling technique 300 statistically interpolates color information of the pixels of the three-dimensional slice 312, e.g., the luminance and / or chrominance components of the YUV color model and / or the red, green, and / or blue color components of the RGB color model, from the pixels of the two-dimensional slice 310, to name a few examples. In some embodiments, the kernel-based sampling technique 300 can statistically interpolate color information of the pixels of the three-dimensional slice 312 based on the color information of the pixels of the two-dimensional slice 310. In these embodiments, the kernel-based sampling technique 300 can statistically interpolate color information of the pixels of the three-dimensional slice 312 by weighting and accumulating color information of pixels of the two-dimensional slice 310 that are neighboring two-dimensional points of the two-dimensional slice 310 that are projected onto the two-dimensional space of the two-dimensional slice 310.
[0035] 3A and 3B , the kernel-based sampling technique 300 can weight color information of pixels of the two-dimensional slice 310 that are neighbors of two-dimensional points projected onto the two-dimensional space of the two-dimensional slice 310. In some embodiments, the kernel-based sampling technique 300 can identify pixels of the two-dimensional slice 310 that are neighbors of two-dimensional points projected onto the two-dimensional space of the two-dimensional slice 310. In these embodiments, the pixels of the two-dimensional slice 310 that are neighbors of these two-dimensional points can be placed within a region of interest (ROI), also referred to as a sampling kernel space 314 as illustrated in FIG. 3A and / or a sampling kernel space 316 as illustrated in FIG. 3B , within the two-dimensional slice 310. In general, the sampling kernel space 314 and / or the sampling kernel space 316 can be any geometric region within the two-dimensional slice 310 that includes one or more of the pixels of the two-dimensional slice 310, as would be apparent to one skilled in the art without departing from the spirit and scope of the present disclosure. In some embodiments, any geometric region can include a closed geometric region, such as a regular curve, e.g., a circle or an ellipse, an irregular curve, a regular polygon, e.g., an equilateral triangle or a square, and / or an irregular polygon, e.g., a rectangle and / or a parallelogram, to name a few. Alternatively, or additionally, any geometric region can be associated with one or more mathematical functions, such as an A.C. Kley function, a Himmelblau function, a Rastrigin function, a Rosenbrock function, also known as Rosenbrock's banana function, and / or a Shekel function, to name a few.
[0036] 3A and 3B , the kernel-based sampling technique 300 can weight pixels of a statistical interpolation region 318 within the sampling kernel space 314 and / or sampling kernel space 316 that are neighbors of a two-dimensional point projected onto the two-dimensional space of the two-dimensional slice 310. In some embodiments, the kernel-based sampling technique 300 can implement one or more digital image processing techniques, such as, for example, digital image cropping techniques, to statistically interpolate color information of pixels of the three-dimensional slice 312 to generate the statistical interpolation region 318. In these embodiments, the statistical interpolation region 318 includes pixels of a first region of the two-dimensional slice 310 and pixels of a second region of another two-dimensional slice 320 associated with another three-dimensional slice of the three-dimensional media plane that is assigned to another image processing server. In some embodiments, the pixels of the other two-dimensional slices 320 may include one or more rows and / or one or more columns of pixels associated with other three-dimensional slices of the three-dimensional media plane that surround, i.e., are adjacent to, the periphery of the two-dimensional slice 310 and / or are assigned to other image processing servers. In these embodiments, the pixels of the other two-dimensional slices 320 may include between 5 and 200 rows and / or columns of pixels, depending on the shape of the sampling kernel space 314 and / or the sampling kernel space 316. As illustrated in FIG. 3A , digital image cropping techniques can isolate the pixels of the two-dimensional slice 310 and the other two-dimensional slices 320 from the image 302 to generate a statistically interpolated region 318. In the exemplary embodiment illustrated in FIG. 3A , pixels in the sampling kernel space 314 that are neighbors of the two-dimensional point projected onto the two-dimensional space of the two-dimensional slice 310 are within the two-dimensional slice 310. Thus, the kernel-based sampling technique 300 can statistically interpolate color information for pixels in the 3D slice 312 from pixels in the 2D slice 310 .3B , however, pixels in the sampling kernel space 316 that are neighbors of a two-dimensional point projected onto the two-dimensional space of the two-dimensional slice 310 are within the pixels of the two-dimensional slice 310 and other two-dimensional slices 320. Therefore, the kernel-based sampling technique 300 can statistically interpolate color information of pixels in the three-dimensional slice 312 from the pixels of the two-dimensional slice 310 and other two-dimensional slices 320.
[0037] After identifying the pixels of the statistical interpolation region 318 in the sampling kernel space 314 and / or the sampling kernel space 316, the kernel-based sampling technique 300 may weight the color information of these pixels, e.g., the luminance and / or chrominance components of the YUV color model and / or the red, green, and / or blue components of the RGB color model, to name a few. In some embodiments, the weighting may be a distance-based weighting of the color information of the pixels of the statistical interpolation region 318 in the sampling kernel space 314 and / or the sampling kernel space 316. For example, pixels of the statistical interpolation region 318 in the sampling kernel space 314 and / or the sampling kernel space 316 that are closer to a two-dimensional point projected onto the two-dimensional space of the two-dimensional slice 310 are weighted more heavily than pixels of the statistical interpolation region 318 in the sampling kernel space 314 and / or the sampling kernel space 316 that are farther from the two-dimensional point projected onto the two-dimensional space of the two-dimensional slice 310. In some embodiments, if the distance between the pixels of the statistical interpolation region 318 in the sampling kernel space 314 and / or the sampling kernel space 316 and the two-dimensional point projected onto the two-dimensional space of the two-dimensional slice 310 can be considered a random variable, the kernel-based sampling technique 300 can weight the pixels of the statistical interpolation region 318 in the sampling kernel space 314 and / or the sampling kernel space 316 according to a probability density function, such as a Gaussian distribution, a normal distribution, a standard normal distribution, a Student's t distribution, a chi-squared distribution, a continuous uniform distribution, and / or any other well-known probability density function that would be apparent to one skilled in the art without departing from the spirit and scope of the present disclosure.
[0038] Once the color information of the pixels of the statistical interpolation region 318 in the sampling kernel space 314 and / or the sampling kernel space 316 has been weighted, the kernel-based sampling technique 300 can accumulate the weighted color information of these pixels and statistically interpolate the color information of the pixels of the three-dimensional slice 312. In the exemplary embodiments illustrated in FIGS. 3A and 3B , the kernel-based sampling technique 300 can accumulate the color information of the pixels of the statistical interpolation region 318 in the sampling kernel space 314 and / or the sampling kernel space 316 weighted as described above and statistically interpolate the color information of the pixels of the three-dimensional slice 312. In these embodiments, the kernel-based sampling technique 300 can associate two-dimensional points projected onto the two-dimensional space of the two-dimensional slice 310 with their corresponding ones of the pixels of the three-dimensional slice 312. The kernel-based sampling technique 300 can then associate color information of the two-dimensional points projected onto the two-dimensional space of the two-dimensional slice 310 with their corresponding pixels of the three-dimensional slice 312 and statistically interpolate the color information of the pixels of the three-dimensional slice 312. In some embodiments, the kernel-based sampling technique 300 can generate quadruples for the three-dimensional slice 312 that include the pixels of the three-dimensional slice 312n and color information for the pixels of the three-dimensional slice 312 that has been statistically interpolated from the statistical interpolation region 318.
[0039] FIG. 4 illustrates a flowchart of an exemplary kernel-based sampling technique that may be implemented in an exemplary image projection system according to some exemplary embodiments of the present disclosure. The present disclosure is not limited to this operational description. Rather, other operational control flows will be apparent to those of ordinary skill in the art and are within the scope and spirit of the present disclosure. The following discussion describes an exemplary operational control flow 400 for mathematically transforming two-dimensional coordinates of pixels of a slice of an image onto three-dimensional coordinates of a slice of a three-dimensional media plane of a venue, such as venue 106 as described in FIG. 1 above, venue 200 as described in FIGS. 2A and 2B above, and / or venue 306 as described in FIGS. 3A and 3B above. Operational control flow 400 can be executed by one or more computer systems, such as one or more of image processing servers 104.1-104.i as described above in FIG. 1, image processing servers 206.1-206.i as described above in FIGS. 2A and 2B, and / or image processing servers 308 as described above in FIGS. 3A and 3B.
[0040] In operation 402, operation control flow 400 projects pixels of a three-dimensional slice of a three-dimensional media surface onto a two-dimensional slice of a two-dimensional image, effectively converting the pixels of the three-dimensional slice of the three-dimensional media surface into two-dimensional coordinates of two-dimensional points projected onto the two-dimensional image. In some embodiments, operation control flow 400 can logically segment the three-dimensional media surface into multiple three-dimensional slices of the three-dimensional media surface. In these embodiments, a three-dimensional slice of the three-dimensional media surface can represent one or more three-dimensional slices of the three-dimensional media surface of the multiple three-dimensional slices of the three-dimensional media surface in a manner substantially similar to that described in FIG. 2A above. In some embodiments, operation control flow 400 can logically segment the two-dimensional image into multiple two-dimensional slices of the two-dimensional image. In these embodiments, a two-dimensional slice of the two-dimensional image can represent one or more two-dimensional slices of the two-dimensional image of the multiple two-dimensional images in a manner substantially similar to that described in FIG. 2B above.
[0041] In operation 404, operational control flow 400 statistically interpolates color information of pixels of a three-dimensional slice of a three-dimensional media plane, e.g., luminance and / or chrominance components of a YUV color model and / or red, green, and / or blue components of an RGB color model, to name a few, from pixels of the statistical interpolation region of the two-dimensional image from operation 402. In some embodiments, the statistical interpolation region can include pixels of the two-dimensional slice of the two-dimensional image from operation 402 and pixels from other two-dimensional slices of the two-dimensional image from operation 402, as described above in FIGS. 3A and 3B. In some embodiments, operational control flow 400 can statistically interpolate color information of pixels of the three-dimensional slice of the three-dimensional media plane from operation 402 based on color information of pixels of the statistical interpolation region. In these embodiments, operation control flow 400 can statistically interpolate color information for pixels of a three-dimensional slice of a three-dimensional media surface from operation 402 by weighting and accumulating color information for pixels in statistically interpolated regions neighboring two-dimensional points projected onto the image from operation 402 in a manner substantially similar to that described in Figures 3A and 3B above.
[0042] In operation 406, the operation control flow 400 provides pixel color information to the venue for projection onto the venue in a manner substantially similar to that described in Figures 1, 2A, 2B, 3A, and / or 3B above.
[0043] Example Computer Systems That May Be Implemented in Example Image Projection Systems
[0044] 5 schematically illustrates a simplified block diagram of a computer system for executing an electronic design platform according to some embodiments of the present disclosure. As described above, one or more electronic design software tools may be executed by one or more computing devices, processors, controllers, or other electrical, mechanical, and / or electromechanical devices, as will be apparent to those skilled in the art, to design, simulate, analyze, and / or verify architectural design layouts of electronic circuitry for electronic devices without departing from the spirit and scope of the present disclosure. The following discussion of FIG. 5 describes a computer system 500 that may be implemented within image projection system 100 as described in FIG. 1 above.
[0045] In the embodiment illustrated in FIG. 5, computer system 500 includes one or more processors 502 and executes one or more electronic design software tools such as those described in FIG. 1 above. In some embodiments, one or more processors 502 can include or be any of a microprocessor, a graphics processing unit, or a digital signal processor, and their electronic processing equivalents (e.g., an application-specific integrated circuit ("ASIC") or a field-programmable gate array ("FPGA"), etc.). As used herein, the term "processor" refers to a tangible data and information processing device that physically transforms data and information using sequence transformations (also referred to as "operations"). Data and information can be physically represented by electrical, magnetic, optical, or acoustic signals that can be stored, accessed, transferred, combined, compared, or otherwise manipulated by the processor. The term "processor" can refer to a single processor as well as a multi-core system or multi-processor array that includes a graphics processing unit, a digital signal processor, a digital processor, or a combination of these elements. The processor can be, for example, an electronic device comprising digital logic circuitry (e.g., binary logic) or analog (e.g., operational amplifiers). The processor may also operate to support the performance of related operations within a "cloud computing" environment or as "software as a service" (SaaS). For example, at least some of the operations may be performed by a group of processors available in a distributed or remote system, which are accessible via a communications network (e.g., the Internet) and via one or more software interfaces (e.g., application program interfaces (APIs)).In some embodiments, computer system 500 may include an operating system such as Microsoft Windows, Sun Microsystems' Solaris, Apple Computer's Mac OS, Linux, or UNIX. In some embodiments, computer system 500 may also include a basic input / output system (BIOS) and processor firmware. The operating system, BIOS, and firmware are used by one or more processors 502 to control subsystems and interfaces coupled to one or more processors 502. In some embodiments, one or more processors 502 may include Pentium and Itanium processors manufactured by Intel, Opteron and Athlon processors manufactured by Advanced Micro Devices, and ARM processors manufactured by ARM Holdings.
[0046] 5, computer system 500 can include machine-readable media 504. In some embodiments, machine-readable media 504 can further include main random access memory (“RAM”) 506, read-only memory (“ROM”) 508, and / or file storage subsystem 510. RAM 530 can store instructions and data during program execution, and ROM 532 can store fixed instructions. File storage subsystem 510 provides persistent storage for program and data files and may include hard disk drives, floppy disk drives and associated removable media, CD-ROM drives, optical drives, flash memory, or removable media cartridges.
[0047] The computer system 500 may further include a user interface input device 512 and a user interface output device 514. The user interface input device 512 may include a pointing device such as an alphanumeric keyboard, keypad, mouse, trackball, touchpad, stylus, or graphics tablet, a scanner, a touchscreen integrated into a display, an audio input device such as a voice recognition system or microphone, eye gaze recognition, electroencephalogram pattern recognition, and other types of input devices, to name a few. The user interface input device 512 may be connected to the computer system 500 by wire or wirelessly. Generally, the user interface input device 512 is intended to include all possible types of devices and methods for inputting information into the computer system 500. The user interface input device 512 typically allows a user to identify objects, icons, text, and the like that appear on some type of user interface output device, e.g., a display subsystem. The user interface output device 520 may include a non-visual display such as a display subsystem, a printer, a fax machine, or an audio output device. The display subsystem may include a flat panel device such as a cathode ray tube (CRT), a liquid crystal display (LCD), a projection device, or some other device for producing a visible image, such as a virtual reality system. The display subsystem may also provide a non-visual display, such as via audio output or tactile output (e.g., vibration) devices. Generally, user interface output devices 520 are intended to include all possible types of devices and methods for outputting information from computer system 500.
[0048] The computer system 500 may further include a network interface 516 for providing an interface to outside networks, including an interface to a communications network 518, via which the computer system 500 is coupled to corresponding interface devices in other computer systems or machines. The communications network 518 may comprise many interconnected computer systems, machines, and communications links. These communications links may be wired, optical, wireless, or any other device for communicating information. The communications network 518 may be any suitable computer network, for example, a wide area network such as the Internet and / or a local area network such as Ethernet. The communications network 518 may be wired and / or wireless, and the communications network may use encryption and decryption methods such as those available with virtual private networks. The communications network uses one or more communications interfaces that may receive data from other systems and transmit data to other systems. Embodiments of the communication interface typically include an Ethernet card, a modem (e.g., telephone, satellite, cable, or ISDN), an (asynchronous) Digital Subscriber Line (DSL) unit, a Firewire interface, a USB interface, and the like. One or more communication protocols, such as HTTP, TCP / IP, RTP / RTSP, IPX, and / or UDP, can be used.
[0049] 5, one or more processors 502, machine-readable media 504, user interface input devices 512, user interface output devices 514, and / or network interface 516 can be communicatively coupled to each other using a bus subsystem 520. Although the bus subsystem 520 is shown diagrammatically as a single bus, alternative embodiments of the bus subsystem may use multiple buses. For example, a RAM-based main memory can communicate directly with a file storage system using a direct memory access (“DMA”) system. conclusion
[0050] The detailed description has referred to the accompanying figures to illustrate exemplary embodiments consistent with this disclosure. References in this disclosure to "an exemplary embodiment" indicate that the described exemplary embodiment may include a particular feature, structure, or characteristic, but that not all exemplary embodiments necessarily include the particular feature, structure, or characteristic. Also, such phrases do not necessarily refer to the same exemplary embodiment. Furthermore, any feature, structure, or characteristic described in connection with an exemplary embodiment may be included independently or in any combination with features, structures, or characteristics of other exemplary embodiments, whether or not explicitly described.
[0051] The Detailed Description is not intended to be limiting. Rather, the scope of the present disclosure is defined solely by the following claims and their equivalents. It is understood that the Detailed Description section, and not the Abstract section, is intended to be used to interpret the claims. The Abstract section may describe one or more example embodiments of the present disclosure, but is not exhaustive, and thus is not intended to limit the present disclosure and the following claims and their equivalents in any way.
[0052] The exemplary embodiments described within this disclosure are provided for illustrative purposes and are not intended to be limiting. Other exemplary embodiments are possible, and modifications may be made to the exemplary embodiments while remaining within the spirit and scope of this disclosure. This disclosure is described with the help of functional components that illustrate implementations of defined functions and their relationships. The boundaries of these functional building blocks are arbitrarily defined herein for convenience of description. Alternative boundaries may be defined so long as the defined functions and relationships are appropriately performed.
[0053] Embodiments of the present disclosure may be implemented in hardware, firmware, a software application, or any combination thereof. Embodiments of the present disclosure may also be implemented as instructions stored on a machine-readable medium, which may be read and executed by one or more processors. A machine-readable medium may include any mechanism for storing or transmitting information in a form readable by a machine (e.g., a computing network). For example, a machine-readable medium may include non-transitory machine-readable media, such as read-only memory (ROM), random-access memory (RAM), magnetic disk storage media, optical storage media, flash memory devices, and others. As another example, a machine-readable medium may include a transitory machine-readable medium, such as an electrical, optical, acoustic, or other form of propagated signal (e.g., carrier wave, infrared signal, digital signal, etc.). Furthermore, firmware, software applications, routines, and instructions may be described herein as performing certain actions. However, it should be understood that such description is for convenience only and that such actions actually result from a computing device, processor, controller, or other device executing firmware, software applications, routines, instructions, etc.
[0054] The detailed description of the exemplary embodiments has fully revealed the general nature of the present disclosure, such that others, by applying the knowledge of those skilled in the art, may readily modify and / or adapt such exemplary embodiments for various applications without departing from the spirit and scope of the present disclosure and without undue experimentation. Moreover, such adaptations and modifications are intended to be within the meaning and equivalents of the exemplary embodiments, based on the teaching and guidance presented herein. It is to be understood that the phraseology or terminology used herein is for purposes of description and not of limitation, as the terminology or terminology used herein would be interpreted by one of ordinary skill in the art in light of the teachings herein.
Claims
1. 1. An image processing server for converting images for projection onto a media surface at a venue, said image processor comprising: a memory configured to store instructions; a processor configured to execute the instructions, the instructions, when executed by the processor, projecting three-dimensional coordinates of a plurality of pixels of a three-dimensional slice of the media surface assigned to the image processing server from among a plurality of three-dimensional slices of the media surface onto two-dimensional coordinates of a two-dimensional slice of the image associated with the three-dimensional slice from among a plurality of two-dimensional slices of the image to provide a plurality of two-dimensional points; interpolating color information for the plurality of pixels of the three-dimensional slice of the media plane based on color information for a first plurality of pixels in the two-dimensional slice of the image associated with the three-dimensional slice of the media plane and color information for a second plurality of pixels of the image surrounding the two-dimensional slice; providing the color information of the plurality of pixels of the three-dimensional slice of the media plane to the venue and projecting the two-dimensional slice of the image onto the three-dimensional media plane; a processor, the processor configured to: An image processing server comprising:
2. The instructions, when executed by the processor, logically segmenting the media surface into the plurality of three-dimensional slices of the media surface; assigning the plurality of three-dimensional slices of the media plane to a plurality of image processing servers; The image processing server of claim 1 , further configured to:
3. The instructions, when executed by the processor, logically segmenting the image into the plurality of two-dimensional slices of the image; correlating the plurality of two-dimensional slices of the image with the plurality of three-dimensional slices of the media plane; The image processing server of claim 2 , further configured to:
4. 2. The image processing server of claim 1, wherein the instructions, when executed by the processor, further configure the processor to crop the image and generate a statistically interpolated region of the image, the statistically interpolated region including the first plurality of pixels and the second plurality of pixels.
5. 2. The image processing server of claim 1, wherein the second plurality of pixels are within a second two-dimensional slice of the image among the plurality of two-dimensional slices of the image, the second two-dimensional slice of the image is associated with a second three-dimensional slice of the media plane among the plurality of three-dimensional slices of the media plane, and the second three-dimensional slice of the media plane is assigned to a second image processing server among a plurality of image processing servers.
6. 2. The image processing server of claim 1, wherein the instructions, when executed by the processor, configure the processor to interpolate the color information of the plurality of pixels of the three-dimensional slice of the media plane by weighting and accumulating the color information of the first plurality of pixels and the color information of the second plurality of pixels located within a sample kernel space.
7. 7. The image processing server of claim 6, wherein the instructions, when executed by the processor, configure the processor to weight the color information of the first plurality of pixels and the color information of the second plurality of pixels located within the sample kernel space according to a probability density function.
8. 1. A method for operating an image processing server to transform an image for projection onto a media surface at a venue, the method comprising: projecting, by the image processing server, three-dimensional coordinates of a plurality of pixels of a three-dimensional slice of the media surface assigned to the image processing server from among a plurality of three-dimensional slices of the media surface onto two-dimensional coordinates of a two-dimensional slice of the image associated with the three-dimensional slice from among a plurality of two-dimensional slices of the image to provide a plurality of two-dimensional points; interpolating, by the image processing server, color information for the plurality of pixels of the three-dimensional slice of the media plane based on color information for a first plurality of pixels in the two-dimensional slice of the image associated with the three-dimensional slice of the media plane and color information for a second plurality of pixels of the image surrounding the two-dimensional slice; providing, by the image processing server, the color information for the plurality of pixels of the three-dimensional slice of the media surface to the venue, and projecting the two-dimensional slice of the image onto the three-dimensional media surface; A method comprising:
9. logically segmenting the media surface into the plurality of three-dimensional slices of the media surface; assigning the plurality of three-dimensional slices of the media plane to a plurality of image processing servers; The method of claim 8 further comprising:
10. logically segmenting the image into the plurality of two-dimensional slices of the image; correlating the plurality of two-dimensional slices of the image with the plurality of three-dimensional slices of the media plane; 10. The method of claim 9, further comprising:
11. 9. The method of claim 8, wherein the instructions, when executed by the processor, further configure the processor to crop the image and generate a statistically interpolated region of the image, the statistically interpolated region including the first plurality of pixels and the second plurality of pixels.
12. 9. The method of claim 8, wherein the second plurality of pixels is within a second two-dimensional slice of the image among the plurality of two-dimensional slices of the image, the second two-dimensional slice of the image is associated with a second three-dimensional slice of the media plane among the plurality of three-dimensional slices of the media plane, and the second three-dimensional slice of the media plane is assigned to a second image processing server among a plurality of image processing servers.
13. 9. The method of claim 8, wherein the interpolating comprises interpolating the color information of the plurality of pixels of the three-dimensional slice of the media plane by weighting and accumulating the color information of the first plurality of pixels and the color information of the second plurality of pixels located in a sample kernel space.
14. 14. The method of claim 13, wherein the interpolating further comprises weighting the color information of the first plurality of pixels and the color information of the second plurality of pixels located within the sample kernel space according to a probability density function.
15. 1. A system for converting an image for projection onto a media surface at a venue, the system comprising: a first image processing server among a plurality of image processing servers, the first image processing server comprising: projecting three-dimensional coordinates of a plurality of pixels of a first three-dimensional slice of the media surface assigned to the first image processing server from among the plurality of three-dimensional slices of the media surface onto two-dimensional coordinates of a first two-dimensional slice of the image associated with the first three-dimensional slice from among the plurality of two-dimensional slices of the image to provide a plurality of two-dimensional points; interpolating color information for a first plurality of pixels in the first three-dimensional slice of the media plane based on color information for the first plurality of pixels in the first two-dimensional slice of the image associated with the first three-dimensional slice of the media plane and color information for a second plurality of pixels of the image surrounding the first two-dimensional slice; providing the color information of the plurality of pixels of the first three-dimensional slice of the media plane to the venue and projecting the first two-dimensional slice of the image onto the three-dimensional media plane; a first image processing server configured to: a second image processing server among the plurality of image processing servers, the first image processing server comprising: projecting three-dimensional coordinates of a plurality of pixels of a second three-dimensional slice of the media plane assigned to the second image processing server onto two-dimensional coordinates of a second two-dimensional slice of the image associated with the second three-dimensional slice of the plurality of two-dimensional slices of the image to provide a plurality of two-dimensional points; interpolating color information for the pixels of the second three-dimensional slice of the media plane based on color information for a third plurality of pixels in the second two-dimensional slice of the image associated with the second three-dimensional slice of the media plane and color information for a fourth plurality of pixels of the image surrounding the second two-dimensional slice; providing the color information of the plurality of pixels of the second three-dimensional slice of the media plane to the venue and projecting the second two-dimensional slice of the image onto the three-dimensional media plane; a second image processing server configured to perform A system comprising:
16. The first image processing server logically segmenting the media surface into the plurality of three-dimensional slices of the media surface; assigning the second three-dimensional slice of the media plane to the second image processing server; The system of claim 15 , further configured to:
17. The first image processing server logically segmenting the image into the plurality of two-dimensional slices of the image; correlating the second two-dimensional slice of the image with the second three-dimensional slice of the media plane; The system of claim 16 , further configured to:
18. 16. The system of claim 15, wherein the first image processing server is further configured to crop the image and generate a statistically interpolated region of the image, the statistically interpolated region including the first plurality of pixels and the second plurality of pixels.
19. The system of claim 15 , wherein the second plurality of pixels is in the second two-dimensional slice of the image.
20. 16. The system of claim 15, wherein the first image processing server is further configured to interpolate the color information of the plurality of pixels of the first three-dimensional slice of the media plane by weighting and accumulating the color information of the first plurality of pixels and the color information of the second plurality of pixels located within a sample kernel space.