It has been known since the early 1960s that hexagonal sampling is the optimal sampling approach for isotropically
band-limited images, providing a 13.4% improvement in sampling efficiency over rectangular sampling. Despite
this fact and other significant advantages of hexagonal sampling, rectangular sampling is still used for virtually
all modern digital image processing systems. This is arguably due to the lack of an efficient addressing system for
hexagonal grids. Array set addressing (ASA) is a recent advance in addressing hexagonal grids that allows image
processing techniques to be performed efficiently on hexagonally sampled images. This paper will describe ASA
and discuss its advantages. With ASA, a renewed interest in sensors that sample hexagonally is occurring. We
will describe a new visible imager that simultaneously samples both hexagonally and rectangularly. This novel
research tool has the ability to provide real imagery that can be used to quantitatively compare the performance
of an image processing operation on both hexagonally sampled and rectangularly sampled images. We will also
describe current efforts and plans for future visible sensors that sample hexagonally. The advantages of hexagonal
sampling are not limited to the visible domain and should be equally realizable in the infrared domain. This
paper will discuss considerations for developing infrared sensors that sample hexagonally. On-focal plane array
(FPA) processing, readout architectures, detector materials, and bump-bonding are among the topics to be
It has long been known that there are numerous advantages to sampling images hexagonally rather than rectangularly. However, due to various shortcomings of the addressing schemes, hexagonal sampling for digital images has not been embraced by the mainstream digital imaging community. The idea of using hexagonal sampling for digital imaging applications has been around since the early 1960s, yet no efficient addressing method for hexagonal grids has been developed in that time. This paper introduces a new hexagonal addressing approach, called array set addressing (ASA), that solves the problems exhibited by other addressing methods. The ASA approach uses three coordinates to represent the hexagonal grid as a pair of rectangular arrays. This representation supports efficient linear algebra and image processing manipulation. ASA-based implementations of several basic image processing operations are presented and shown to be efficient. A hexagonal fast Fourier transform, based on the fact that the Fourier kernel becomes separable when using ASA coordinates, is also presented.
It has been shown through various research efforts over the past few decades that there are numerous advantages
to sampling images hexagonally rather than rectangularly. Despite the advantages, hexagonal imaging has not
been generally accepted as being advantageous due to the lack of sensors that sample hexagonally, lack of
displays for hexagonal images, and lack of an elegant addressing scheme. The advantages gained by sampling
hexagonally are offset by the additional processing required to deal with the problems that are inherent with the
previously proposed addressing schemes. Hence, there is insufficient motivation to develop sensors and displays
that operate in the hexagonal domain. This paper introduces an addressing scheme, array set addressing, that
solves the problems exhibited by other approaches. This new approach represents the hexagonal grid with a pair
of rectangular arrays, supporting efficient linear algebra and image processing manipulation. Early results have
shown that image processing techniques such as convolution, downsampling, calculating Euclidean distances, and
vector arithmetic can be done with no more complexity than is required for processing rectangularly sampled
In our previous papers, the FPGA-based processing package and the co-processor board have been introduced for numerous commercial and military applications including motion detection, optical flow, background velocimetry, and target tracking. The processing package is being continually upgraded by new point- and area-applied algorithms for a variety of real-time digital video camera systems including foveal sensors based on Nova's Variable Acuity Superpixel Imager (VASITM) and Large Format VASITM (LVASITM) technologies. This paper demonstrates the FPGA-based processor for high frame-rate target detection in a cluttered background using variable acuity sensors. For the 1024 x 1024 pixel LVASITM Focal Plane Array (FPA), the proposed target-detection algorithm increases the frame rate from 4 Hz for the full resolution mode up to 450 Hz for the foveal mode while maintaining full field of view and target-detection performances on cluttered backgrounds that are comparable with detection performances at the full resolution mode.
With the recent introduction of infrared cameras that have the ability to produce variable acuity imagery, it has become necessary to develop methods for bad pixel replacement and non-uniformity correction within superpixels. Since a superpixel is formed by averaging a group of smaller pixels on chip prior to readout, producing a single value, we cannot apply gains and offsets to the individual pixels that contribute to the superpixel value, nor can we replace bad pixels within a superpixel before they corrupt the aggregate intensity of the superpixel. Without new superpixel correction methods, the imagery produced by this exciting technology is less appealing to human observers and corrupted superpixel intensities lead to problems with the algorithms that process the imagery to perform useful automated tasks, such as "hot-spot" tracking. This paper will introduce a method for performing the non-uniformity and bad pixel corrections in superpixels and demonstrate the performance.
A wide variety of imaging applications exist for 1K x 1K midwave infrared (MWIR) imagers and Nova's Variable Acuity Superpixel Imager (VASTM) technology1,2 has now progressed to this image format. This paper will demonstrate a variety of imagery from MWIR cameras using this large format "LVASI" device; the in-pixel processing used by the LVASI cameras represents the state-of-the-art for image size, total field of view, high frame rates, low data bandwidths and real-time spatial reprogrammability of focal plane arrays (FPAs). Using these devices, imaging systems may now be implemented that permit the operator to "zoom in" to regions of interest with very high spatial resolution, while covering the remainder of the total field of view (TFOV) at conventional resolutions. The bandwidth compression attainable using these sensors helps to make possible systems that can transmit their high resolution imagery through wireless interconnected networks.
We present recent infrared image data that highlight numerous applications including missile detection/tracking, search/rescue and remote surveillance applications.
Infrared detectors operating in two or more wavebands can be used to obtain emissivity-area, temperature, and related parameters. While the cameras themselves may not collect data in the two bands simultaneously in space or time, the algorithms used to calculate such parameters rely on spatial and temporal alignment of the true optical data in the two bands. When such systems are tested in a hardware-in-the-loop (HWIL) environment, this requirement for alignment is in turn imposed on the projection systems used for testing. As has been discussed in previous presentations to this forum, optical distortion and misalignment can lead to significant band-to-band and band-to-truth simulation errors. This paper will address the potential impact of techniques to remove these errors on typical two-color estimation algorithms, as well as improvements obtained using distortion removal techniques applied to HWIL data collected at the Kinetic Kill Vehicle Hardware-in-the-Loop Simulator (KHILS) facility.