Claims Analysis
Total Claims: 27
Claim 1
Independent Claim
333 words
A method for generating a signal corresponding to a still, perceptible image representing a physical situation, comprising the steps of: a. using electromagnetic radiation, capturing a plurality of at least three images of said situation, each of said plurality having been captured at a distinct focal length, said focal lengths differing from each other and each of at least three overlapping images of said plurality sharing an overlap region that corresponds to the same portion of said situation: b. generating, for each of said plurality of images, an electromagnetic signal representing said image, resultina in at least three electromagnetic signals, each signal designated an overlap signal, each one of said overlap signals representing said overlap region of one of said three overlapping images: c. transforming each overlap signal so that it represents the respective image scaled to a common focal length and aligned to a common field of view, said transforming step comprising the steps of, for each said overlap signal: i. applying to said signal at least one affine transformation comprising the steps of: A. ordering said plurality of overlap signals in a sequence; B. for each sequentially adjacent pair of overlap signals in said sequence, determining a set of affine parameters substantially defining a transformation of the image represented by a first of said pair to the image represented by the second of said pair; C. for at least one of said plurality of overlap signals, combining a plurality of said sets of affine parameters into a composite set of affine parameters; and D. applying an affine transformation to said at least one overlap signal using said respective composite set of affine parameters; and ii. generating a signal that represents said transformed overlap signal; and d. combining each of said transformed overlap signals into a resultant signal that represents the combination of each of said scaled images into a single image of said situation of a single focal length using an aspect of each of said at least three overlap signals.
Claim 2
Independent Claim
333 words
A method for generating a signal corresponding to a still, perceptible image representing a physical situation, comprising the steps of: a. using electromagnetic radiation, capturing a plurality of at least three images of said situation, each of said plurality having been captured at a distinct focal length, said focal lengths differing from each other and each of at least three overlapping images of said plurality sharing an overlap region that corresponds to the same portion of said situation: b. generating, for each of said plurality of images, an electromagnetic signal representing said image, resultina in at least three electromagnetic signals, each signal designated an overlap signal, each one of said overlap signals representing said overlap region of one of said three overlapping images: c. transforming each overlap signal so that it represents the respective image scaled to a common focal length and aligned to a common field of view, said transforming step comprising the steps of, for each said overlap signal: i. applying to said signal at least one affine transformation comprising the steps of: A. ordering said plurality of overlap signals in a sequence; B. for each sequentially adjacent pair of overlap signals in said sequence, determining a set of affine parameters substantially defining a transformation of the image represented by a first of said pair to the image represented by the second of said pair; C. for at least one of said plurality of overlap signals, combining a plurality of said sets of affine parameters into a composite set of affine parameters; and D. applying an affine transformation to said at least one overlap signal using said respective composite set of affine parameters; and ii. generating a signal that represents said transformed overlap signal; and d. combining each of said transformed overlap signals into a resultant signal that represents the combination of each of said scaled images into a single image of said situation of a single focal length using an aspect of each of said at least three overlap signals.
Claim 3
Independent Claim
207 words
A method for generating a signal corresoonding to a still, perceptible image representing a physical situation, comprising the steps of: a. using electromagnetic radiation, capturing a plurality of at least three images of said situation, each of said plurality having been captured at a distinct focal length, said focal lengths differing from each other and each of at least three overlapping images of said plurality sharing an overlap region that corresoonds to the same portion of said situation; b. generating, for each of said plurality of images, an electromagnetic signal representing said image, resulting in at least three electromagnetic signals, each signal designated an overlap signal, each one of said overlap signals representing said overlap region of one of said three overlapping images: c. transforming each overlap signal so that it represents the respective image, scaled to a common focal length and aligned to a common field of view; d. combining each of said filtered, transformed overlap signals into a resultant signal that represents the combination of each of said scaled images into a single image of said situation of a single focal length by applying a temporal median filter to each transformed signal and using an aspect of each of said at least three overlap signals.
Claim 4
Independent Claim
207 words
A method for generating a signal corresoonding to a still, perceptible image representing a physical situation, comprising the steps of: a. using electromagnetic radiation, capturing a plurality of at least three images of said situation, each of said plurality having been captured at a distinct focal length, said focal lengths differing from each other and each of at least three overlapping images of said plurality sharing an overlap region that corresoonds to the same portion of said situation; b. generating, for each of said plurality of images, an electromagnetic signal representing said image, resulting in at least three electromagnetic signals, each signal designated an overlap signal, each one of said overlap signals representing said overlap region of one of said three overlapping images: c. transforming each overlap signal so that it represents the respective image, scaled to a common focal length and aligned to a common field of view; d. combining each of said filtered, transformed overlap signals into a resultant signal that represents the combination of each of said scaled images into a single image of said situation of a single focal length by applying a temporal median filter to each transformed signal and using an aspect of each of said at least three overlap signals.
Claim 5
Dependent Claim
27 words
The method of claim 2, said step of applying a temporal median filter comprising the step of applying a weighted temporal median filter to each transformed signal.
Claim 6
Dependent Claim
47 words
The method of claim 3, said weighted temporal median filter comprising a filter that assigns more weight to overlap signals that represent images that were produced at a longer focal length than to overlap signals that represent images that were produced at a relatively shorter focal length.
Claim 7
Independent Claim
353 words
A method for generating a signal corresponding to a still, perceptible image representing a physical situation, comprising the steps of: a. using electromagnetic radiation, capturing a plurality of at least three images of said situation, each of said plurality having been captured at a distinct focal length, said focal lengths differing from each other and each of at least three overlapping images of said plurality sharing an overlap region that corresoonds to the same portion of said situation: b. generating, for each of said plurality of images, an electromagnetic signal representing said image, resulting in at least three electromagnetic signals, each signal designated an overlap signal, each one of said overlap signals representing said overlap region of one of said three overlapping images; c. transforming each overlap signal so that it represents the respective image, scaled to a common focal length and aligned to a common field of view; and d. identifying differences between pairs of signals representing pairs of images, which signal differences are due to relative motions between pairs of images that are due to causes other than the fact that the two images were produced at different focal lengths said step of identifying differences between pairs of signals that are due to relative motions comprising the steps of: A. estimating a first relative motion of a first pattern portion of both signals of a pair; A. using said estimated first motion to determine a second relative motion of a second pattern portion of both signals; C. repeating the following steps until a desired resolution of relative motion is achieved: α. using said second relative motion to specify more precisely said first relative motion of said first pattern portion; and β. using said more precise specification of said first relative motion to specify more precisely said second relative motion of said second pattern portion; and e. combining each of said transformed overlap signals into a resultant signal that represents the combination of each of said scaled images into a single image of said situation of a single focal length using an aspect of each of said at least three overlap signals.
Claim 8
Independent Claim
353 words
A method for generating a signal corresponding to a still, perceptible image representing a physical situation, comprising the steps of: a. using electromagnetic radiation, capturing a plurality of at least three images of said situation, each of said plurality having been captured at a distinct focal length, said focal lengths differing from each other and each of at least three overlapping images of said plurality sharing an overlap region that corresoonds to the same portion of said situation: b. generating, for each of said plurality of images, an electromagnetic signal representing said image, resulting in at least three electromagnetic signals, each signal designated an overlap signal, each one of said overlap signals representing said overlap region of one of said three overlapping images; c. transforming each overlap signal so that it represents the respective image, scaled to a common focal length and aligned to a common field of view; and d. identifying differences between pairs of signals representing pairs of images, which signal differences are due to relative motions between pairs of images that are due to causes other than the fact that the two images were produced at different focal lengths said step of identifying differences between pairs of signals that are due to relative motions comprising the steps of: A. estimating a first relative motion of a first pattern portion of both signals of a pair; A. using said estimated first motion to determine a second relative motion of a second pattern portion of both signals; C. repeating the following steps until a desired resolution of relative motion is achieved: α. using said second relative motion to specify more precisely said first relative motion of said first pattern portion; and β. using said more precise specification of said first relative motion to specify more precisely said second relative motion of said second pattern portion; and e. combining each of said transformed overlap signals into a resultant signal that represents the combination of each of said scaled images into a single image of said situation of a single focal length using an aspect of each of said at least three overlap signals.
Claim 9
Independent Claim
233 words
A method for generating a signal corresponding to a still, perceptible image of a physical situation, comprising the steps of: a. using electromagnetic radiation, capturing a plurality of images of said situation, each of said plurality having been produced covering a distinct field of view, said fields of view differing from each other and being members of an overall field of view, each field of view overlapping at least one other field of view, each pair of overlapping images of said plurality sharing an overlap region that corresponds to the same portion of said situation, and said overall field of view corresponding to a greater extent of said situation than any single image of said plurality; b. generating, for each of an overlapping pair of said plurality of images, an electromagnetic signal representing said image, each signal designated an overlap signal; c. transforming each overlap signal so that it represents the respective image aligned to said overall field of view, said transformation being conducted without reference to the locations of features relative to said overall field of view or said physical situation; and d. combining each of said transformed overlap signals into a resultant signal that represents the combination of each of said aligned images into a single image of said situation of said overall field of view by applying a temporal median filter to said transformed overlap signals representing said aligned images.
Claim 10
Independent Claim
233 words
A method for generating a signal corresponding to a still, perceptible image of a physical situation, comprising the steps of: a. using electromagnetic radiation, capturing a plurality of images of said situation, each of said plurality having been produced covering a distinct field of view, said fields of view differing from each other and being members of an overall field of view, each field of view overlapping at least one other field of view, each pair of overlapping images of said plurality sharing an overlap region that corresponds to the same portion of said situation, and said overall field of view corresponding to a greater extent of said situation than any single image of said plurality; b. generating, for each of an overlapping pair of said plurality of images, an electromagnetic signal representing said image, each signal designated an overlap signal; c. transforming each overlap signal so that it represents the respective image aligned to said overall field of view, said transformation being conducted without reference to the locations of features relative to said overall field of view or said physical situation; and d. combining each of said transformed overlap signals into a resultant signal that represents the combination of each of said aligned images into a single image of said situation of said overall field of view by applying a temporal median filter to said transformed overlap signals representing said aligned images.
Claim 11
Independent Claim
359 words
A method for generating a signal corresponding to a still, perceptible image of a physical situation, comprising the steps of: a. using electromagnetic radiation, capturing a plurality of images of said situation, each of said plurality having been produced covering a distinct field of view, said fields of view differing from each other and being members of an overall field of view, each field of view overlapping at least one other field of view, each pair of overlapping images of said plurality sharing an overlap region that corresponds to the same portion of said situation, and said overall field of view corresponding to a greater extent of said situation than any single image of said plurality; b. generating, for each of an overlapping pair of said plurality of images, an electromagnetic signal representing said image, each signal designated an overlap signal; c. without reference to the locations of features reletive to said overall field of view or said physical situation, transforming each overlap signal so that it represents the respective image aligned to said overall field of view, said transformation being conducted by the steps of, for each said overlap signal: i. applying to said overlap signal at least one affine transformation by conducting the steps of; A. ordering said plurality of overlap signals in a sequence; B. for each sequentially adjacent pair of overlap signals in said sequence, determining a set of affine parameters substantially defining a transformation of said image represented by a first of said pair of overlap signals to the image represented by the second of said pair of signals; C. for at least one of said plurality of overlap signals, combining a plurality of said sets of affine parameters into a composite set of affine parameters; and D. applying an affine transformation to said at least one overlap signal using said respective composite set of affine parameters; and ii. generating a signal that represents said transformed overlap signal; and d. combining each of said transformed overlap signals into a resultant signal that represents the combination of each of said aligned images into a single image of said situation of said overall field of view.
Claim 12
Independent Claim
359 words
A method for generating a signal corresponding to a still, perceptible image of a physical situation, comprising the steps of: a. using electromagnetic radiation, capturing a plurality of images of said situation, each of said plurality having been produced covering a distinct field of view, said fields of view differing from each other and being members of an overall field of view, each field of view overlapping at least one other field of view, each pair of overlapping images of said plurality sharing an overlap region that corresponds to the same portion of said situation, and said overall field of view corresponding to a greater extent of said situation than any single image of said plurality; b. generating, for each of an overlapping pair of said plurality of images, an electromagnetic signal representing said image, each signal designated an overlap signal; c. without reference to the locations of features reletive to said overall field of view or said physical situation, transforming each overlap signal so that it represents the respective image aligned to said overall field of view, said transformation being conducted by the steps of, for each said overlap signal: i. applying to said overlap signal at least one affine transformation by conducting the steps of; A. ordering said plurality of overlap signals in a sequence; B. for each sequentially adjacent pair of overlap signals in said sequence, determining a set of affine parameters substantially defining a transformation of said image represented by a first of said pair of overlap signals to the image represented by the second of said pair of signals; C. for at least one of said plurality of overlap signals, combining a plurality of said sets of affine parameters into a composite set of affine parameters; and D. applying an affine transformation to said at least one overlap signal using said respective composite set of affine parameters; and ii. generating a signal that represents said transformed overlap signal; and d. combining each of said transformed overlap signals into a resultant signal that represents the combination of each of said aligned images into a single image of said situation of said overall field of view.
Claim 13
Independent Claim
233 words
An apparatus for generating a signal corresponding to a still, perceptible image of a situation comprising: a. means for capturing a plurality of images of said situation, using electromagnetic radiation, each of said plurality having been produced at a distinct field of view, said fields of view differing from each other and being members of an overall field of view, each field of view overlapping at least one other field of view, each pair of overlapping images of said plurality sharing an overlap region that corresponds to the same portion of said situation, and said overall field of view corresponding to a greater extent of said situation than any single image of said plurality; b. transducer means for transducing each of said images into an electromagnetic signal representative of said image, each signal so transduced designated an overlap signal; c. signal processing means for transforming each overlap signal so that it represents the respective image aligned to said overall field of view, without reference to said overall field of view or said physical situation; and d. signal processing means for combining each of said transformed overlap signals into a resultant signal that represents the combination of each of said aligned images into a single image of said situation of said overall field of view, said signal processing means comprising means for applying a temporal median filter to each of said transformed overlap signals.
Claim 14
Independent Claim
233 words
An apparatus for generating a signal corresponding to a still, perceptible image of a situation comprising: a. means for capturing a plurality of images of said situation, using electromagnetic radiation, each of said plurality having been produced at a distinct field of view, said fields of view differing from each other and being members of an overall field of view, each field of view overlapping at least one other field of view, each pair of overlapping images of said plurality sharing an overlap region that corresponds to the same portion of said situation, and said overall field of view corresponding to a greater extent of said situation than any single image of said plurality; b. transducer means for transducing each of said images into an electromagnetic signal representative of said image, each signal so transduced designated an overlap signal; c. signal processing means for transforming each overlap signal so that it represents the respective image aligned to said overall field of view, without reference to said overall field of view or said physical situation; and d. signal processing means for combining each of said transformed overlap signals into a resultant signal that represents the combination of each of said aligned images into a single image of said situation of said overall field of view, said signal processing means comprising means for applying a temporal median filter to each of said transformed overlap signals.
Claim 15
Dependent Claim
18 words
The apparatus of claim 8, said means for capturing a plurality of images comprising a video recording device.
Claim 16
Independent Claim
187 words
A method for generating a signal that represents a still, perceptible image of a physical situation comprising the steps of: a. establishing a plurality of different sampling lattices bearing no predetermined spatial relationship to one another; b. using electromagnetic radiation, capturing a plurality of images of said situation, each of said plurality having been captured at a distinct time with a different of said plurality of different sampling lattices, a region of each of said plurality of images constituting an image of the same portion of said situation as is captured by at least one other of said images; c. generating, for each of said images, an electromagnetic signal representative of said image; d. transforming each signal so that it represents the respective image, aligned to a common field of view; and e. combining at least two of said transformed signals, using a sampling lattice of higher resolution than any sampling lattice of any image of said plurality into a resultant signal that represents the combination of at least two of said images into a single image having an enhanced resolution over any of said original images.
Claim 17
Independent Claim
187 words
A method for generating a signal that represents a still, perceptible image of a physical situation comprising the steps of: a. establishing a plurality of different sampling lattices bearing no predetermined spatial relationship to one another; b. using electromagnetic radiation, capturing a plurality of images of said situation, each of said plurality having been captured at a distinct time with a different of said plurality of different sampling lattices, a region of each of said plurality of images constituting an image of the same portion of said situation as is captured by at least one other of said images; c. generating, for each of said images, an electromagnetic signal representative of said image; d. transforming each signal so that it represents the respective image, aligned to a common field of view; and e. combining at least two of said transformed signals, using a sampling lattice of higher resolution than any sampling lattice of any image of said plurality into a resultant signal that represents the combination of at least two of said images into a single image having an enhanced resolution over any of said original images.
Claim 18
Dependent Claim
37 words
The method of claim 10, said step of transforming each of said signals comprising the steps of: a. applying to said signal at least one affine transformation; and b. generating a signal that represents said transformed signal.
Claim 19
Dependent Claim
55 words
The method of claim 11, said step of applying at least one affine transformation comprising the step of generating a plurality of signals that represent a sequence of modified image frames which have been reduced in resolution and sampling, and applying to said plurality of signals representing said modified frames at least one affine transformation.
Claim 20
Dependent Claim
108 words
The method of claim 11, said step of applying at least one affine transformation comprising the steps of: a. ordering said plurality of signals in a sequence; b. for each pair of signals in said sequence, determining a set of affine parameters substantially defining a transformation of the image represented by a first of said pair to the image represented by a second of said pair; c. for each of said plurality of signals, combining a plurality of said sets of affine parameters into a composite set of affine parameters; and d. applying an affine transformation to each said signal using said respective composite set of affine parameters.
Claim 21
Dependent Claim
26 words
The method of claim 13, said step of combining comprising the steps of applying a temporal median filter to the corresponding signal representing each aligned image.
Claim 22
Independent Claim
150 words
A method for generating a signal representing a still, perceptible image of a physical situation comprising the steps of: a. establishing a plurality of different space time sampling lattices bearing no predetermined space time relationship to one another: b. using electromagnetic radiation, capturing a plurality of images, each of said plurality having been captured at a distinct and different space time coordinate with a different one of said plurality of different space time sampling lattices; c. generating, for each of said images, an electromagnetic signal representative of said image; d. transforming each signal so that it represents the respective image, aligned to a common field of view; and e. combining each of said transformed signals into a resultant signal that represents the combination of each of said images into a single image of a common field of view having a higher resolution than any of the original plurality of images.
Claim 23
Independent Claim
150 words
A method for generating a signal representing a still, perceptible image of a physical situation comprising the steps of: a. establishing a plurality of different space time sampling lattices bearing no predetermined space time relationship to one another: b. using electromagnetic radiation, capturing a plurality of images, each of said plurality having been captured at a distinct and different space time coordinate with a different one of said plurality of different space time sampling lattices; c. generating, for each of said images, an electromagnetic signal representative of said image; d. transforming each signal so that it represents the respective image, aligned to a common field of view; and e. combining each of said transformed signals into a resultant signal that represents the combination of each of said images into a single image of a common field of view having a higher resolution than any of the original plurality of images.
Claim 24
Independent Claim
330 words
A method for generating a signal corresoonding to a still, oerceotible image representing a physical situation, comprising the steps of: a. using electromagnetic radiation, capturing a plurality of at least three images of said situation, each of said plurality having been captured at a distinct focal length, said focal lengths differing from each other and each of at least three overlapping images of said plurality sharing an overlap region that corresponds to the same portion of said situation; b. ⊙ generating, for each of said plurality of images, an electromagnetic signal representing said image, resulting in at least three electromagnetic signals, each signal designated an overlap signal, each one of said overlap signals representing said overlap region of one of said three overlapping images; c. transforming each overlap signal so that it represents the resoective image, scaled to a common focal length and aligned to a common field of view, said transforming step comprising the steps of: i. ordering said plurality of overlap signals into a sequence; ii. for at least two of said overlap signals, applying to said at least two signals at least one affine transformation; iii. wherein for at least one of said at least two of said overlap signals, said at least one affine transformation transforms said signal so that it represents the respective image aligned to a common field of view with an image of said sequence that is distant from said respective image in said sequence; and iv. generating a signal that represents said transformed overlap signal; and d. combining each of said transformed overlap signals into a resultant signal that represents the combination of each of said scaled images into a single image of said situation of a single focal length, said single image being arranged according to a combination sampling lattice that defines a plurality of pixels, using an aspect of each of said at least three overlap signals at each pixel of said single image that represents said combined overlap signals.
Claim 25
Independent Claim
330 words
A method for generating a signal corresoonding to a still, oerceotible image representing a physical situation, comprising the steps of: a. using electromagnetic radiation, capturing a plurality of at least three images of said situation, each of said plurality having been captured at a distinct focal length, said focal lengths differing from each other and each of at least three overlapping images of said plurality sharing an overlap region that corresponds to the same portion of said situation; b. ⊙ generating, for each of said plurality of images, an electromagnetic signal representing said image, resulting in at least three electromagnetic signals, each signal designated an overlap signal, each one of said overlap signals representing said overlap region of one of said three overlapping images; c. transforming each overlap signal so that it represents the resoective image, scaled to a common focal length and aligned to a common field of view, said transforming step comprising the steps of: i. ordering said plurality of overlap signals into a sequence; ii. for at least two of said overlap signals, applying to said at least two signals at least one affine transformation; iii. wherein for at least one of said at least two of said overlap signals, said at least one affine transformation transforms said signal so that it represents the respective image aligned to a common field of view with an image of said sequence that is distant from said respective image in said sequence; and iv. generating a signal that represents said transformed overlap signal; and d. combining each of said transformed overlap signals into a resultant signal that represents the combination of each of said scaled images into a single image of said situation of a single focal length, said single image being arranged according to a combination sampling lattice that defines a plurality of pixels, using an aspect of each of said at least three overlap signals at each pixel of said single image that represents said combined overlap signals.
Claim 26
Independent Claim
406 words
A method for generating a signal corresponding to a still, perceptible image representing a physical situation, comprising the steps of: a. using electromagnetic radiation, capturing a plurality of at least three images of said situation, each of said plurality having been captured at a distinct focal length, said focal lengths differing from each other and each of at least three overlapping images of said plurality sharing an overlap region that corresponds to the same portion of said situation: b. generating, for each of said plurality of images, an electromagnetic signal representing said image, resulting in at least three electromagnetic signals, each signal designated an overlap signal, each one of said overlap signals representing said overlap region of one of said three overlapping images; c. transformina each overlap signal so that it represents the respective image, scaled to a common focal length and aligned to a common field of view, said transforming step comprising the steps of, for each said overlap signal; i. applying to said signal at least one affine transformation comprising the steps of: A. ordering said plurality of overlap signals in a sequence; B. for each sequentially adjacent pair of overlap signals in said sequence, determining a set of affine parameters substantially defining a transformation of the image represented by a first of said pair to the image represented by the second of said pair; C. for at least one of said plurality of overlap signals, applying a fixst affine transformation to said at least one overlap signal using said affine parameters determined with respect to said overlap signal as the first of a pair and an adjacent overlap signal as the second of said pair to generate a first transformed overlap signal; and D. applying to said first transformed overlap signal a second affine transformation using said affine parameters determined with respect to a second pair of overlap signals that comprise: α. said adjacent overlap signal as the first signal of said second pair; and β. another overlap signal, different from said at least one overlap signal, as the second signal of said second pair; and ii. generating a signal that represents said transformed overlap signal; and d. combining each of said transformer overlap signals into a resultant signal that represents the combination of each of said scaled images into a sinale image of said situation of a single focal length using an aspect of each of said at least three overlap signals.
Claim 27
Independent Claim
406 words
A method for generating a signal corresponding to a still, perceptible image representing a physical situation, comprising the steps of: a. using electromagnetic radiation, capturing a plurality of at least three images of said situation, each of said plurality having been captured at a distinct focal length, said focal lengths differing from each other and each of at least three overlapping images of said plurality sharing an overlap region that corresponds to the same portion of said situation: b. generating, for each of said plurality of images, an electromagnetic signal representing said image, resulting in at least three electromagnetic signals, each signal designated an overlap signal, each one of said overlap signals representing said overlap region of one of said three overlapping images; c. transformina each overlap signal so that it represents the respective image, scaled to a common focal length and aligned to a common field of view, said transforming step comprising the steps of, for each said overlap signal; i. applying to said signal at least one affine transformation comprising the steps of: A. ordering said plurality of overlap signals in a sequence; B. for each sequentially adjacent pair of overlap signals in said sequence, determining a set of affine parameters substantially defining a transformation of the image represented by a first of said pair to the image represented by the second of said pair; C. for at least one of said plurality of overlap signals, applying a fixst affine transformation to said at least one overlap signal using said affine parameters determined with respect to said overlap signal as the first of a pair and an adjacent overlap signal as the second of said pair to generate a first transformed overlap signal; and D. applying to said first transformed overlap signal a second affine transformation using said affine parameters determined with respect to a second pair of overlap signals that comprise: α. said adjacent overlap signal as the first signal of said second pair; and β. another overlap signal, different from said at least one overlap signal, as the second signal of said second pair; and ii. generating a signal that represents said transformed overlap signal; and d. combining each of said transformer overlap signals into a resultant signal that represents the combination of each of said scaled images into a sinale image of said situation of a single focal length using an aspect of each of said at least three overlap signals.