July 20, 2018

Two Dimensional Phase Correlation as Neural Network Input for 3D Imaging

by Andrey Filippov

We uploaded an image set with 2D correlation data together with the import Python code for experiments with the neural networks and are now looking for collaboration with those who would love to apply their DL experience to the new kind of input data. More data will follow and we welcome feedback to make this data set more useful.

The application area we are interested in is an extremely long distance 3D scene reconstruction and ranging with the distance to baseline ratio of 1000:1 to 10,000:1 while preserving wide field of view. Earlier post describes aircraft distance and velocity measurements with up to 3,000:1 distance-to-baseline ratio and 60°(H)×45°(V) field of view.


Figure 1. Space-invariant 2D phase correlation data


Data set: source images, 2D correlation tiles, and X3D scene models

The data set contains 2D phase correlation output calculated from the 2592×1936 Bayer mosaic source images captured by the quad stereo camera, and Disparity Space Image (DSI) calculated from a pair of such cameras. Longer baseline provides higher range resolution and this DSI is serving as the ground truth for a single quad camera. The source images as well as all the used software is also provided under the GNU/GPLv3 license. DSI is organized as a 324×242 array – each sample is calculated from the corresponding 16×16 tile. Tiles are overlapping (as shown in Figure 3) with stride 8.

These data sets are provided together with the fully reconstructed X3D scene models, viewable in the browser (Wavefront OBJ files are also generated). The scene models are different from the raw DSI as the next software stages generate meshes, and that frequently leads to over-simplification of the original DSI (so most fronto parallel objects in the scene provide better range accuracy when probed near the bottom). Each scene is accompanied with the multi-layer TIFF file (*-DSI_COMBO.tiff) that allows to see the difference between the measured DSI and the one used in the rendered X3D model. File format and Python import software is documented in Oleg’s post “Reading quad stereo TIFF image stacks in Python and formatting data for TensorFlow”, the data files are directly viewable with ImageJ.

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May 6, 2018

Capturing Aircraft Position with the Long Range Quad Stereo Camera

by Andrey Filippov

Figure 1. Aircraft positions during descent captured with the quad stereo camera. Each animation frame corresponds to the available 3-D model.

While we continue to work on the multi-sensor stereo camera hardware (we plan to double the number of sensors to capture single-exposure HDR image sets) and develop code to get the ground truth data for the CNN training, we had some fun testing the camera for capturing aircraft position in 3-D space. Completely passive method, of course.

We found a suitable spot about 2.5 km from the beginning of the runway 34L of the Salt Lake City international airport (exact location is shown in the model viewer) so approaching aircraft would pass almost over our heads. With the 60°(H)×45°(V) field of view of the camera aircraft are visible when they are 270 m away horizontally.

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March 20, 2018

Dual Quad-Camera Rig for Capturing Image Sets

by Andrey Filippov

Figure 1. Dual quad-camera rig mounted on a car

Following the plan laid out in the earlier post we’ve built a camera rig for capturing training/testing image sets. The rig consists of the two quad cameras as shown in Figure 1. Four identical Sensor Front Ends (SFE) 10338E of each camera use 5 MPix MT9P006 image sensors, we will upgrade the cameras to 18 MPix SFE later this year, the circuit boards 103981 are in production now.

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February 5, 2018

High Resolution Multi-View Stereo: Tile Processor and Convolutional Neural Network

by Andrey Filippov

Figure 1. Multi-board setup for the TP+CNN prototype

Featured on Image Sensors World

This article describes our next steps that will continue the year-long research on high resolution multi-view stereo for long distance ranging and 3-D reconstruction. We plan to fuse the methods of high resolution images calibration and processing, already emulated functionality of the Tile Processor (TP), RTL code developed for its implementation and the Convolutional Neural Network (CNN). Compared to the CNN alone this approach promises over a hundred times reduction in the number of input features without sacrificing universality of the end-to-end processing. The TP part of the system is responsible for the high resolution aspects of the image acquisition (such as optical aberrations correction and image rectification), preserves deep sub-pixel super-resolution using efficient implementation of the 2-D linear transforms. Tile processor is free of any training, only a few hyperparameters define its operation, all the application-specific processing and “decision making” is delegated to the CNN.

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January 8, 2018

Efficient Complex Lapped Transform Implementation for the Space-Variant Frequency Domain Calculations of the Bayer Mosaic Color Images

by Andrey Filippov

This post continues discussion of the small tile space-variant frequency domain (FD) image processing in the camera, it demonstrates that modulated complex lapped transform (MCLT) of the Bayer mosaic color images requires almost 3 times less computational resources than that of the full RGB color data.

“Small Tile” and “Space Variant”

Why “small tile“? Most camera images have short (up to few pixels) correlation/mutual information span related to the acquisition system properties – optical aberrations cause a single scene object point influence a small area of the sensor pixels. When matching multiple images increase of the window size reduces the lateral (x,y) resolution, so many of the 3d reconstruction algorithms do not use any windows at all, and process every pixel individually. Other limitation on the window size comes from the fact that FD conversions (Fourier and similar) in Cartesian coordinates are shift-invariant, but are sensitive to scale and rotation mismatch. So targeting say 0.1 pixel disparity accuracy the scale mismatch should not cause error accumulation over window width exceeding that value. With 8×8 tiles (16×16 overlapped) acceptable scale mismatch (such as focal length variations) should be under 1%. That tolerance is reasonable, but it can not get much tighter.

What is “space variant“? One of the most universal operations performed in the FD is convolution (also related to correlation) that exploits convolution-multiplication property. Mathematically convolution applies the same operation to each of the points of the source data, so shifted object of the source image produces just a shifted result after convolution. In the physical world it is a close approximation, but not an exact one. Stars imaged by a telescope may have sharper images in the center, but more blurred in the peripheral areas. While close (angularly) stars produce almost the same shape images, the far ones do not. This does not invalidate convolution approach completely, but requires kernel to (smoothly) vary over the input images [12], makes it a space-variant kernel.

Figure 1. Complex Lapped Transform with DCT-IV/DST-IV: time-domain aliasing cancellation (TDAC) property. a) selection of overlapping input subsequences 2*N-long, multiplication by sine window; b) creating N-long sequences for DCT-IV (left) and DST-IV (right); c) (after frequency domain processing) extending N-long sequence using DCT-IV boundary conditions (DST-IV processing is similar); d) second multiplication by sine window; e) combining partial data

There is another issue related to the space-variant kernels. Fractional pixel shifts are required for multiple steps of the processing: aberration correction (obvious in the case of the lateral chromatic aberration), image rectification before matching that accounts for lens optical distortion, camera orientation mismatch and epipolar geometry transformations. Traditionally it is handled by the image rectification that involves re-sampling of the pixel values for a new grid using some type of the interpolation. This process distorts the signal data and introduces non-linear errors that reduce accuracy of the correlation, that is important for subpixel disparity measurements. Our approach completely eliminates resampling and combines integer pixel shift in the pixel domain and delegates the residual fractional pixel shift (±0.5 pix) to the FD, where it is implemented as a cosine/sine phase rotator. Multiple sources of the required pixel shift are combined for each tile, and then a single phase rotation is performed as a last step of pixel domain to FD conversion.

Frequency Domain Conversion with the Modulated Complex Lapped Transform

Modulated Complex Lapped Transform (MCLT)[3] can be used to split input sequence into overlapping fractions, processed separately and then recombined without block artifacts. Popular application is the signal compression where “processed separately” means compressed by the encoder (may be lossy) and then reconstructed by the decoder. MCLT is similar to the MDCT that is implemented with DCT-IV, but it additionally preserves and allows frequency domain modification of the signal phase. This feature is required for our application (fractional pixel shifts and asymmetrical lens aberrations modify phase), and MCLT includes both MDCT and MDST (that use DCT-IV and DST-IV respectively). For the image processing (2d conversion) four sub-transforms are needed:

  • horizontal DCT-IV followed by vertical DCT-IV
  • horizontal DST-IV followed by vertical DCT-IV
  • horizontal DCT-IV followed by vertical DST-IV
  • horizontal DST-IV followed by vertical DST-IV

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December 3, 2017

Drupal, WordPress, Mediawiki, Mail Archive, Gitlab – all in one web site

by Andrey Filippov and Oleg Dzhimiev

Multiple Subdomains for the Same Web Site

It is a common case when a company or organization uses multiple content management systems (CMS) and specialized web application to organize its web presence. We describe here how Elphel handles such CMS variety and provide the source code that can be customized for other similar sites. (more…)

September 20, 2017

Long range multi-view stereo camera with 4 sensors

by Andrey Filippov

Figure 1. Four sensor stereo camera

Four-camera stereo rig prototype is capable of measuring distances thousands times exceeding the camera baseline over wide (60 by 45 degrees) field of view. With 150 mm distance between lenses it provides ranging data at 200 meters with 10% accuracy, production units will have higher accuracy. Initial implementation uses software post-processing, but the core part of the software (tile processor) is designed as FPGA simulation and will be moved to the actual FPGA of the camera for the real time applications. Scroll down or just hyper-jump to Scene viewer for the links to see example images and reconstructed scenes. (more…)

January 19, 2017

Lapped MDCT-based image conditioning with optical aberrations correction, color conversion, edge emphasis and noise reduction

by Andrey Filippov

Fig.1. Image comparison of the different processing stages output

Results of the processing of the color image

Previous blog post “Lens aberration correction with the lapped MDCT” described our experiments with the lapped MDCT[1] for optical aberration corrections of a single color channel and separation of the asymmetrical kernel into a small asymmetrical part for direct convolution and a larger symmetrical one to be applied in the frequency domain of the MDCT. We supplemented this processing chain with additional steps of the image conditioning to evaluate the overall quality of the of the results and feasibility of the MDCT approach for processing in the camera FPGA. Image comparator in Fig.1 allows to see the difference between the images generated from the results of the several stages of the processing. It makes possible to compare any two of the image layers by either sliding the image separator or by just clicking on the image – that alternates right/left images. Zoom is controlled by the scroll wheel (click on the zoom indicator fits image), pan – by dragging. Original image was acquired with Elphel model 393 camera with 5 Mpix MT9P006 image sensor and Sunex DSL227 fisheye lens, saved in jp4 format as a raw Bayer data at 98% compression quality. Calibration was performed with the Java program using calibration pattern visible in the image itself. The program is designed to work with the low-distortion lenses so fisheye was a stretch and the calibration kernels near the edges are just replicated from the ones closer to the center, so aberration correction is only partial in those areas. First two layers differ just by added annotations, they both show output of a simple bilinear demosaic processing, same as generated by the camera when running in JPEG mode. Next layers show different stages of the processing, details are provided later in this blog post. (more…)

January 7, 2017

Lens aberration correction with the lapped MDCT

by Andrey Filippov

Modern small-pixel image sensors exceed resolution of the lenses, so it is the optics of the camera, not the raw sensor “megapixels” that define how sharp are the images, especially in the off-center areas. Multi-sensor camera systems that depend on the tiled images do not have any center areas, so overall system resolution may be as low as that of is its worst part.
Fig. 1. Lateral chromatic aberration and Bayer mosaic: a) monochrome (green) PSF, b) composite color PSF, c) Bayer mosaic of the sensor (direction of aberration shown), d) distorted mosaic matching chromatic aberration in b).

Fig. 1. Lateral chromatic aberration and Bayer mosaic: a) monochrome (green) PSF, b) composite color PSF, c) Bayer mosaic of the sensor, d) distorted mosaic for the chromatic aberration of b).

De-mosaic processing and chromatic aberrations

Our current cameras role is to preserve the raw sensor data while providing some moderate compression, all the image correction is applied during post-processing. Handling the lens aberration has to be done before color conversion (or de-mosaicing). When converting Bayer data to color images most cameras start with the calculation of the “missing” colors in the RG/GB pattern using 3×3 or 5×5 kernels, this procedure relies on the specific arrangement of the color filters. Each of the red and blue pixels has 4 green ones at the same distance (pixel pitch) and 4 of the opposite (R for B and B for R) color at the equidistant diagonal locations. Fig.1. shows how lateral chromatic aberration disturbs these relations. Fig.1a is the point-spread function (PSF) of the green channel of the sensor. The resolution of the PSF measurement is twice higher than the pixel pitch, so the lens is not that bad – horizontal distance between the 2 greens in Fig.1c corresponds to 4 pixels of Fig.1a. It is also clearly visible that the PSF is elongated and the radial resolution in this part of the image is better than the tangential one (lens center is left-down). Fig.1b shows superposition of the 3 color channels: blue center is shifted up-and-right by approximately 2 PSF pixels (so one actual pixel period of the sensor) and the red one – half-pixel left-and-down from the green center. So the point light of a star, centered around some green pixel will not just spread uniformly to the two “R”s and two “B”s shown connected with lines in Fig.1c, but the other ones and in different order. Fig.1d illustrates the effective positions of the sensor pixels that match the lens aberration. (more…)

December 17, 2016

DCT type IV implementation

by Andrey Filippov

As we finished with the basic camera functionality and tested the first Eyesis4π built with the new 10393 system boards (it is smaller, requires less power and, is faster) we are moving forward with the in-camera image processing. We plan to combine our current camera calibration methods that require off-line post processing and the real-time image correction using the camera own FPGA resources. This project development will require switching between the actual FPGA coding and the software implementation of the same algorithms before going to the next step – software is still easier to design. The first part was in FPGA realm – it was to implement the fundamental image processing block that we already know we’ll be using and see how much of the resources it needs.

DCT type IV as a building block for in-camera image processing

We consider a small (8×8 pixel) DCT-IV to be a universal block for conditioning of the raw acquired images. Such operations as lens optical aberrations correction, color conversion (de-mosaic) in the presence of the lateral chromatic aberration, image rectification (de-warping) are easier to perform in the frequency domain using convolution-multiplication property and other algorithms. In post-processing we use DFT (Discrete Fourier Transform) over rather large (64×64 to 512×512) tiles, but that would be too much for the in-camera processing. First is the tile size – for good lenses we do not need that large convolution kernels. Additionally we plan to combine several processing steps into one (based on our off-line post-processing experience) and so we do not need to sub-sample images – in our current software we double resolution of the raw images at the beginning and scale back the final result to reduce image degradation caused by re-sampling. The second area where we plan to reduce computations is the replacement of the DFT with the DCT that is designed to be fed with the pure real data and so requires less arithmetic operations than DFT that processes complex input values.

Why “type IV” of the DCT?

Fig.1. Signal flow graph for DCT-IV

Fig.1. Signal flow graph for DCT-IV

We already have DCT type II implemented for the JPEG/JP4 compression, and we still needed another one. Type IV is used in audio compression because it can be converted to a modified discrete cosine transform (MDCT) – a procedure when multiple overlapped windows are processed one at a time and the results are seamlessly combined without any block artifacts that are familiar for the JPEG with low settings of the compression quality. We too need lapped transform to process large images with relatively small (much smaller than the image itself) convolution kernels, and DCT-IV is a perfect fit. 8-point DCT-IV allows to implement transformation of 16-point segments with 8-point overlap in a reversible manner – the inverse transformation of 8-point data may be converted to 16-point overlapping segments, and being added together these segments result in the original data. (more…)
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