# Patent

## Title
System and process for color-balancing a series of oblique images

## Abstract

An image processing system, comprising a computer running image processing software and selecting a series of color-balanced images to use as reference images. On an oblique image by image basis, the computer performs the following steps: (a) locate a portion(s) of a reference image(s) that overlaps the oblique image; (b) create multiple color-balancing transformations that approximately match a color distribution of the oblique image to a color distribution of overlapping portion(s) of the reference image(s); (c) transform pixels in the oblique image according to more than one of the multiple color-balancing transformations created for the oblique image; and (d) store the transformed pixel value in at least one of the oblique image or a copy of the oblique image.

## Background
CROSS-REFERENCE TO RELATED APPLICATIONS
This application is a continuation of U.S. Ser. No. 11/871,740, filed on Oct. 12, 2007, now U.S. Pat. No. 7,991,226 the entire contents of this application is hereby expressly incorporated herein by reference.


STATEMENT REGARDING FEDERALLY SPONSORED RESEARCH OR DEVELOPMENT
Not Applicable.
THE NAMES OF THE PARTIES TO A JOINT RESEARCH AGREEMENT
Not Applicable.
REFERENCE TO A “SEQUENCE LISTING,” A TABLE, OR A COMPUTER PROGRAM LISTING APPENDIX SUBMITTED ON A COMPACT DISC AND AN INCORPORATION-BY-REFERENCE OF THE MATERIAL ON THE COMPACT DISC (SEE §1.52(E)(5)). THE TOTAL NUMBER OF COMPACT DISCS INCLUDING DUPLICATES AND THE FILES ON EACH COMPACT DISC SHALL BE SPECIFIED
Not Applicable.
BACKGROUND OF THE INVENTION
In the remote sensing/aerial imaging industry, imagery is used to capture views of a geographic area and be able to measure objects and structures within the images as well as to be able to determine geographic locations of points within the image. These are generally referred to as “geo-referenced images” and come in two basic categories:
1. Captured Imagery—these images have the appearance as they were captured by the camera or sensor employed.
2. Projected Imagery—these images have been processed and converted such that they confirm to a mathematical projection.
All imagery starts as captured imagery, but as most software cannot geo-reference captured imagery, that imagery is then reprocessed to create the projected imagery. The most common form of projected imagery is the ortho-rectified image. This process aligns the image to an orthogonal or rectilinear grid (composed of rectangles). The input image used to create an ortho-rectified image is a nadir image—that is, an image captured with the camera pointing straight down.
In addition to capturing an image with the camera pointing straight down, it is possible to capture an image with the camera pointing at an oblique angle. The resulting imagery is generally referred to as an “oblique image” or as an “oblique aerial image.” The capture of oblique aerial images presents additional challenges compared to the capture of nadir images, generally due to the introduction of the oblique angle.
An example of a system that captures both nadir and oblique images is shown in FIG. 1. Airplane 10 is flying over the Earth 12 and capturing images utilizing three cameras 14a, 14b and 14c. FIG. 1 also illustrates the sun 16 positioned in a northern hemisphere orientation. The camera 14a is shown directed in a southern orientation generally towards the sun 16, the camera 14b is shown directed straight down, and the camera 14c is shown directed in a northern orientation generally away from the sun 16. The cameras 14a and 14c capture “oblique images”, while the camera 14b captures “nadir images”.
The oblique images present a more natural appearance than a nadir image because they show not just the roofs, as is the case of a nadir image, but also the sides of objects and structures. This is what we are most accustomed to seeing. In order to preserve this natural perspective, oblique images are generally presented without being ortho-rectified and instead left in the natural appearance that the camera captures. This practice makes it very easy for people to look at something in an oblique image and realize what that object is.
However, the sun/sky orientation when an oblique image is taken has a major impact on the color balance of the resulting photograph due to the reflections of light from the sun 16. There are two major types of reflection: diffuse and specular. Flat wall paint is a highly diffuse reflector—that is, light bounces nearly equally in all directions. A mirror is a highly specular reflector—that is, light bounces almost entirely in one direction off the mirror. There is nothing in nature that is a perfect specular or a perfect diffuse reflector—everything is some combination of the two. It is the specular nature of objects that presents a problem for color balancing oblique images.
Color balancing nadir aerial images is known in the art. However, color balancing oblique aerial images presents unique challenges. When collecting nadir images (images captured with camera 14b pointing straight down), every image has a consistent orientation with respect to the sun 16. However, when collecting oblique images (images captured with the cameras 14a and 14c pointing at an oblique angle relative to the horizon) different images have different orientations with respect to the sun 16. For instance, in the northern hemisphere, a camera aimed to the north (camera 14c) points away from the sun 16, while a camera aimed to the south (camera 14a) points toward the sun 16.
Specular reflections bounce off a surface and leave the surface at roughly the same angle with which they hit the surface—like a ball bouncing off a flat surface. When the camera 14a is pointing towards the sun 16, the camera 14a picks up specular reflections from the sun 16 and therefore any images captured with that camera pick up a strong yellow/red tint to the captured scene. The camera 14c, on the other hand, is pointing away from the sun 16 and picks up specular reflections from the sky and therefore any images captured with that camera pick up a strong blue tint to the scene. When these two images are viewed side by side, the difference can be very noticeable and distracting to the overall image appearance. It is desirable to color balance the oblique images such that they have a substantially consistent color tone.
Shown in FIG. 2 is a diagrammatic view of the capturing of three different overlapping images of a same scene from three different positions. The three different positions are labeled as Position A, Position B and Position C for purposes of clarity. The scene is positioned in the northern hemisphere, and thus, the image captured from Position A is taken with the camera positioned in a southern orientation toward the sun 16, while the image captured from Position C is taken with the camera positioned in a northern orientation away from the sun 16. The image captured from Position B is taken with the camera positioned directly above the scene. In this example, the image captured from Position A has a yellow/reddish tint due to the strong specular reflections from the sun 16, the image captured from Position B has a neutral tint due to roughly equal specular reflections from the sun 16 and sky, and the image captured from Position C has a bluish tint due to the strong specular reflections from the sky.
Referring to FIG. 3, shown therein is a diagrammatic view of the capturing of an oblique image of the Earth 12 where a field of view of the camera is designated with the lines P1 and P2. The lines P1 and P2 represent path lengths, i.e., the distance the light travels from a scene on the Earth 12 to the camera. In an oblique image, the path lengths P1 and P2 are significantly different and this presents a second challenge to color balancing oblique images: the top of the image goes through significantly more atmosphere than the bottom of the image. In a nadir image, path length (the distance the light must travel from a scene on the Earth 12 to the camera) at the edges of the useable image are typically not all that much different than the path length to the nadir point. For instance, lines P3 and P4 represent the path lengths for a typical camera/lens configuration, the difference between the shortest path length (straight down) and the longest path length (to the far corner) is only about 6%.
But with oblique images, because of the nature of trigonometry, when the field of view angle is added to the oblique camera axis angle, the path lengths P1 and P2 are very different. To illustrate an extreme, if the top of the camera is pointed above the horizon then the path length P1 is infinite—clearly much longer than the path length P2 at the front of the image. In a typical camera/lens configuration and at a typical oblique angle, the difference between the shortest path length (to the middle front of the image) and the longest path length (to the far back corner of the image) is about 87%—nearly twice as long.
The challenge this difference in path length presents is that the light from the scene captured by the top of the camera travels through a lot more atmosphere than the light from the scene captured by the bottom of the camera. This results in more tinting or scattering, an increased introduction of blue sky light, an increase in blurriness, and a decrease in clarity due to smog or haze. Thus, if the image is color balanced based upon the tinting in the top of the image then the color balancing of the bottom of the image will be incorrect. Likewise, if the image is color-balanced based upon the tinting in the bottom of the image then the color-balancing of the top of the image will be incorrect. One could color-balance based upon the tinting in the middle of the image, but then the color-balancing of the top and bottom of the image would be incorrect.
In light of the foregoing, there is a need for a system and process for color-balancing oblique images that overcomes the challenges discussed above. It is to such a system and process that the present invention is directed.



BRIEF DESCRIPTION OF THE DRAWINGS
So that the above recited features and advantages of the present invention can be understood in detail, a more particular description of the invention, briefly summarized above, may be had by reference to the embodiments thereof that are illustrated in the appended drawings. It is to be noted, however, that the appended drawings illustrate only typical embodiments of this invention and are therefore not to be considered limiting of its scope, for the invention may admit to other equally effective embodiments.
FIG. 1 is a diagrammatic view of an airplane flying over the Earth and capturing images utilizing three cameras.
FIG. 2 is a diagrammatic view of the capturing of three different overlapping images of a same scene from three different positions.
FIG. 3 is a diagrammatic view of the capturing of an oblique image of the Earth 12 where a field of view of an oblique aerial camera is designated utilizing the path lengths P1 and P2, i.e., the distance the light travels from a scene on the Earth to the camera, and a field of view of a nadir aerial camera is designated utilizing path lengths P3 and P4.
FIG. 4 is a schematic view of an image processing system constructed in accordance with the present invention.
FIG. 5 is a schematic view of an oblique image that has been sectioned in accordance with the present invention.
FIG. 6 is a schematic view of another example of an oblique image that has been sectioned in accordance with the present invention.
FIG. 7 is a histogram of a color distribution for a red color band of an oblique image in accordance with the present invention.
FIG. 8 is a histogram of a color distribution of a blue color band of an oblique image in accordance with the present invention.
FIG. 9 is a portion of a color oblique image captured by a camera angled away from the sun.
FIG. 10 is a portion of a color oblique image of the same area depicted in FIG. 9 but captured by a camera angled toward the sun.



DETAILED DESCRIPTION OF THE INVENTION
Before explaining at least one embodiment of the invention in detail, it is to be understood that the invention is not limited in its application to the details of construction, experiments, exemplary data, and/or the arrangement of the components set forth in the following description or illustrated in the drawings. The invention is capable of other embodiments or of being practiced or carried out in various ways. Also, it is to be understood that the phraseology and terminology employed herein is for purpose of description and should not be regarded as limiting.
The processes described in this patent provide a means for color balancing oblique images so that they take on a consistent color tone. The principal behind these processes is to select a set of color-balanced images to use as reference images to create color-balance transformations for a series of oblique images so that the resulting color-balanced oblique images will have a color tone similar to the reference images. Because they typically have a consistent sun/sky orientation, nadir images are often the best choice for the reference images; however, this is not required. It is recommended that the reference images be from a consistent sun/sky orientation, so, for instance, instead of the nadir images, the north-looking oblique images could be used as the reference images and the remaining oblique images transformed to match their color tone.
The consistent color tone for the reference images can be achieved in a variety of manners, such as by having images that are naturally balanced, i.e., captured under similar conditions and/or orientations and therefore already have a consistent color tone, or by color-balancing the images to each other after they are captured so that they have a consistent color tone. Or nadir images captured under different conditions can first be color-balanced to each other to produce a consistent color tone. There are numerous methods for color-balancing nadir images described in remote sensing textbooks—basically any method that produces a consistent color tone for a set of similar images will work. As these methods for nadir images are known in the art, they are not discussed here.
Once the reference images have been selected, the oblique images can be color balanced to match. This is accomplished by finding one or more portion(s) of reference image(s) that correspond to the same area of the scene contained within the oblique image—in other words, finding their areas of overlap.
In a preferred embodiment, the reference images and the oblique images are geo-referenced so that finding the portions of the references image(s) corresponding to the same area of the scene contained within the oblique images can be accomplished with a computer and thereby automated.
Thus, in the preferred embodiment, the logic of the process described herein is executed by a computer to provide an automated process for color-balancing a series of oblique images.
Referring now to the drawings, and in particular to FIG. 4, shown therein and designated by a reference numeral 20 is an image processing system constructed in accordance with the present invention. In general, the image processing system 20 is provided with a computer 22, and a camera system 24. As will be described in more detail below, the image processing system 20 is adapted to color balance the series of oblique images captured from one or more positions and from one or more orientations so that such oblique images are provided with a substantially consistent color balance thereby reducing or even eliminating the unwanted yellowish/reddish or bluish tinting described above.
In general, the computer 22 receives a series of reference images, and a series of oblique images from the camera system 24. The reference images and the oblique images can be received by the computer system 22 either directly or indirectly from the camera system 24, and can be passed from the camera system 24 either in batches, in real-time with the capturing of the reference images and/or the oblique images, or at a period of time substantially after the capturing of the reference images and the oblique images. For example, the reference images and/or the oblique images can be transmitted or transferred from the camera system 24 to the computer system 22 days and/or weeks and/or years after the capturing of the reference images and the oblique images from the camera system 24.
The computer 22 preferably runs image processing software (or firmware) adapted to perform the functions described herein, and the resulting images and data are stored on one or more computer readable mediums. Examples of a computer readable medium include an optical storage device, a magnetic storage device, an electronic storage device or the like. The term “Computer” as used herein means a system or systems that are able to embody and/or execute the logic of the processes described herein. The logic embodied in the form of software instructions or firmware may be executed on any appropriate hardware which may be a dedicated system or systems, or a general purpose computer system, a personal computer system or distributed processing computer system, all of which are well understood in the art, and a detailed description of how to make or use such computer systems is not deemed necessary herein. When the computer 22 is used to execute the logic of the processes described herein, such computer(s) and/or execution can be conducted at a same geographic location or multiple different geographic locations. Furthermore, the execution of the logic can be conducted continuously or at multiple discrete times. Further, such logic can be performed about simultaneously with the capture of the images, or thereafter or combinations thereof.
The image capture system 24 is typically used for capturing aerial images as shown in FIGS. 1-3. Suitable image capture systems are shown and described in a provisional patent application identified by U.S. Ser. No. 60/901,444, the entire content of which is hereby incorporated herein by reference. Typically, the image capture system 24 is provided with, one or more image capture devices, one or more monitoring systems, one or more event multiplexer systems, and one or more data storage units or computer systems. In the examples depicted in FIGS. 1-3 of U.S. Ser. No. 60/901,444, the “image capture system 10” is provided with four image capture devices mounted in a sweep pattern (see FIG. 1 of U.S. Ser. No. 60/901,444); five image capture devices mounted in a 360 pattern having image capture devices pointing fore, aft, port, starboard and straight down (see FIG. 2 of U.S. Ser. No. 60/901,444); or four image capture devices mounted in separate directions generally aligned with respective parts of streets (see FIG. 3 of U.S. Ser. No. 60/901,444).
In certain embodiments, the image capture devices of the image capture system 24 can be mounted to a moving platform such as a manned airplane, an unmanned airplane, a train, an automobile such as a van, a boat, a four wheeler, a motor cycle, a tractor, a robotic device or the like.
As discussed above, the computer 22 executes instructions to effect the color-balancing of the series of oblique images captured from one or more positions and from one or more orientations. On an oblique image by oblique image basis, the computer 22 is programmed with instructions to locate one or more portions of one or more reference images that overlap the oblique image, and then create a color balancing transformation that approximately matches the color distribution of the oblique image to the color distribution of the overlapping portions of the reference images. Then, the computer 22 transforms pixels in the oblique image according to the color balancing transformation created for that oblique image, and then preferably stores the transform pixel values in the oblique image or a copy of the oblique image. The oblique images having the transformed pixel values are referred to herein after as “color-balanced oblique images”.
In a preferred embodiment, the reference images are geo-referenced to aid in the location of the overlapping portion(s), and also color-balanced. The reference images can be color-balanced either naturally because they are captured from a consistent orientation, or they can be color-balanced using well-known practices. In a preferred embodiment, the reference images are nadir images.
In a preferred embodiment, the overlapping portions of the reference images and the oblique images have a similar scene—because it is expected that the scenes will be somewhat different. For example, assuming that the scene includes a building, the oblique images will show the sides of the building while the nadir images will not. Typically, the closer the scene contents in the overlapping portion(s) match (Leaf-on, leaf off, flooding, snow, or the like) the better the results. Ideally, the reference images and the oblique images will be taken during the same photo shoot to enhance the similarity of the lighting and scene content.
Preferably, one or more color balancing transformation is created for each of the oblique images in the series of oblique images. However, it should be understood that the one or more color balancing transformations do not have to be made for each of the oblique images in the series. In other words, not all of the oblique images in the series of oblique images must be color-balanced in accordance with the present invention. In addition, while all of the pixels in the oblique image are preferably transformed according to the one or more color balancing transformation created for that particular oblique image, it should be understood that less than all of the pixels can be transformed. For example, the pixels in the oblique image can be organized into groups, and then a certain percentage of such pixels (such as 60-90%) can be transformed.
In general, the automated process preferably (1) divides each oblique image in the series into a plurality of sections, (2) identifies a portion of a reference image overlapping the section, and then (3) creates a color-balancing transformation. Preferably a color-balancing transformation for each color band in the color space is created and for each section in the oblique image approximating the color distribution of the overlapping section in the one or more reference images. For example, assuming an RGB color space, a histogram of the color distribution for each color band, i.e., red, green and blue in each section of the oblique image and the overlapping portion of the same scene in the nadir image (develop two histograms for each section) is created. Exemplary histograms for the red and blue color bands are shown in FIGS. 7 and 8. The color space can be any suitable color space, such as RGB, XYZ, LUV, CMYK, or false color IR.
The color distribution histogram of an image shows the number of pixels for each pixel value within the range of the image. If the minimum value of the image is 0 and the maximum value of the image is 255, the histogram of the image shows the number of pixels for each value ranging between and including 0 and 255. Peaks in the histogram represent more common values within the image that usually consist of nearly uniform regions. Valleys in the histogram represent less common values. Empty regions within the histogram indicate that no pixels within the image contain those values. The solid lines shown in the histograms in FIGS. 7 and 8 show exemplary values of an aerial oblique image that has not yet been color-balanced while the dashed lines shown in the histograms show exemplary values of the same aerial oblique image that has been color-balanced utilizing the process described herein.
The solid line in the histogram of FIG. 7 shows the color distribution of the red band for an oblique image that was captured by a camera pointing in a generally south direction and that has a reddish tint due to the specular reflections from the sun 16, while the dashed line shows a reduction in the red pixel values in the color-balanced image. Similarly, the solid line in the histogram of FIG. 8 shows the color distribution of the blue band for an oblique image that was captured by a camera pointing in a generally north direction and that has a bluish tint due to the specular reflections from the sky. The dashed line in FIG. 8 shows a reduction in the blue pixel values in the color-balanced image.
To color-balance the series of oblique images, each of the oblique images are preferably divided into a plurality of sections. For example, an oblique image 30 shown in FIG. 5 has been divided into nine sections 32a-i, and the oblique image 34 shown in FIG. 6 has been divided into 6 sections 36a-f. Any number of sections can be used, but dividing the oblique image 30 into more sections decreases the likelihood of variability in the image. For example, oblique images can change color depending upon their orientation and the distance that the scene is away from the camera. Images taken in a direction away from the sun 16 are usually bluer at the top, while images taken in a direction toward the sun 16 have a reddish-orange cast. The number, size and location of the sections within the oblique images can be predetermined or randomly determined.
Once the oblique image has been divided into sections, then, on a section by section basis one or more portions of a reference image is located that overlaps the oblique image section. Then, a color-balancing transformation is created that approximately matches the color distribution of the oblique image section to the color distribution of the overlapping reference portion(s). This can be accomplished using any suitable algorithm or technique, such as histogram equalization. Histogram equalization is a well known algorithm, so no further comments are deemed necessary to teach one skilled in the art how to make and use histogram equalization. For the oblique image 30 that has been divided into nine oblique image sections 32a-i, this process occurs nine times.
For each section, at least three histograms (color distribution for the overlapping reference portion, color distribution for the oblique image section, and color balancing transformation for the oblique image section) are created for each color band in the color space.
Then, pixel values for each color band in each of the oblique images are color-balanced and blended to provide a substantially consistent color tone. This can be accomplished by using a combination of the color-balancing transformations (e.g., histograms) for the oblique image. The blending may be accomplished through bi-linear interpolation, linear interpolation, cubics, splines and/or the like. Alternatively, one transform may be used for the entire image.
In a preferred embodiment, the color-balancing and blending is accomplished as follows. First, on a pixel by pixel basis, for the oblique image to be color-balanced, one or more oblique image sections are selected which apply to the particular pixel. Then, for each color band, the pixel value is calculated independently (or transformed) using the color balancing transformation for each selected oblique image section yielding a transformed pixel value for each selected oblique image section. Then, the transformed pixel values are blended into a single resulting pixel value using any suitable algorithm, such as bi-linear interpolation, linear interpolation, cubics, splines or the like. Then, the resulting pixel value is stored in the oblique image or a copy (such as a memory copy) of the oblique image. This process is preferably repeated for every pixel in the oblique image. However, it should be understood that this process could only be repeated for a subset of the pixels.
In general, the process described above may be performed on a continuous or intermittent basis. For example, once the section color balancing transformations are created, such section color balancing transformations can be stored, and then applied on a pixel by pixel basis at a later time to color-balance the oblique image. For example, the color-balancing transformations can be stored with the oblique image and then utilized to color-balance the oblique image when it is retrieved or displayed.
Set forth hereinafter is pseudo-code for one embodiment of the present invention:















Select oblique images to adjust



Select reference images



For( each image to be color-balanced ){



  Divide image into sections



  For( each image section used ){



    Choose one or more overlapping reference images



    If ( only one reference image is chosen ) {



      Create section color-balancing transformation from



      chosen reference image



    }



    Else {



      Create empty section color-balancing transformation



      For ( each chosen reference image ){



        Create  temporary  color-balancing



        transformation for this chosen reference image



        Combine  temporary  color-balancing



        transformation into section color-balancing



        transformation



      }



    }



  }



  For (each pixel to be transformed){



    Create empty final pixel value



    For (each image section used){



      If (section is applicable to pixel){



        Compute transformed pixel value from section



        color-balancing transformation



        Blend transformed pixel value into final pixel



        value



      }



    }



    Store final pixel value



  }



}










For RGB color images, the above process is repeated three times, once for each color pixel component, i.e. the red pixels, the green pixels, and the blue pixels, each with its own color-balancing transformation.
Although the foregoing invention has been described in some detail by way of illustration and example for purposes of clarity of understanding, it will be obvious to those skilled in the art that certain changes and modifications may be practiced without departing from the spirit and scope thereof, as described in this specification and as defined in the appended claims below. The term “comprising” within the claims is intended to mean “including at least” such that the recited listing of elements in a claim are an open group. “A,” “an” and other singular terms are intended to include the plural forms thereof unless specifically excluded.

## Claims

1. An image processing system, comprising:
a computer running image processing software to:
select a series of color-balanced images to use as reference images;
on an oblique image by image basis performing the following steps:
locate a portion(s) of a reference image(s) that overlaps the oblique image;
create multiple color-balancing transformations that approximately match a color distribution of the oblique image to a color distribution of overlapping portion(s) of the reference image(s);
transform pixels in the oblique image according to more than one of the multiple color-balancing transformations created for the oblique image; and

store the transformed pixel value in at least one of the oblique image or a copy of the oblique image.

2. An image processing system, comprising:
a computer running image processing software to:
select a series of color-balanced reference images;

on an oblique image by image basis performing the following steps:
locate a portion(s) of a reference image(s) that overlaps the oblique image;
create multiple color-balancing transformations that approximately match a color distribution of the oblique image to a color distribution of overlapping portion(s) of the reference image(s); and
transform pixels in the oblique image according to more than one of the color-balancing transformations created for that oblique image.

3. An image processing system, comprising:
a computer running image processing software to:
a. select a series of color-balanced images to use as reference images;
on an oblique image by oblique image basis, performing the steps of:
b. divide the oblique image into a plurality of oblique image sections;
on a section by section basis performing the steps of:
c. locate a portion(s) of a reference image(s) that overlaps the oblique image section; and
d. create a color-balancing transformation that approximately matches a color distribution of the oblique image section to a color distribution of the overlapping reference portion(s);

on a pixel by pixel basis for the oblique image, performing the steps of:
e. select the oblique image section(s) that apply to the pixel;
f. transform the pixel by the color balancing transformation for that selected oblique image section yielding a transformed pixel value for each selected oblique image section;
g. blend the transformed pixel values into a single resulting pixel value; and
h. store the resulting pixel value in at least one of the oblique image and a copy of the oblique image.

4. The image processing system of claim 3, wherein the computer performs steps d, e, f, g, and h independently for multiple different pixel color values.

5. The image processing system of claim 4, wherein the computer performs step g, which is further defined as blending the transformed pixel values into a single resulting pixel value using bi-linear interpolation.

6. The image processing system of claim 3, wherein, after the computer performs steps a-d, the computer performs the step of d1: storing the color balancing transformations for the sections so that they can be applied at a later time.

7. The image processing system of claim 6, wherein the computer performs steps a-d and d1 at one time, and performs steps e-h at a later time using the color balancing transformations stored in step d1.

8. The image processing system of claim 3, wherein the computer performs step g, which is defined as blending the transformed pixel values into a single resulting pixel value using bi-linear interpolation.

9. The image processing system of claim 3, wherein the oblique images are aerial oblique images and the reference images are aerial nadir images.

10. The image processing system of claim 9, wherein the computer performs steps d, e, f, g, and h independently for multiple different pixel color values.

11. The image processing system of claim 10, wherein the computer, after performing steps a-d,
d1. storing the color balancing transformations so that they can be applied at a later time.

12. The image processing system of claim 11, wherein the computer performs steps a-d and d1 at one time, and perform steps e-h at a later time using the color balancing transformations stored in step d1.

13. The image processing system of claim 3, wherein the computer performs step g, which is defined as blending the transformed pixel values into a single resulting pixel value using bi-linear interpolation.