AVIR - Image Resizing Algorithm (in C++)

Introduction

Me, Aleksey Vaneev, is happy to offer you an open source image resizing / scaling library which has reached a production level of quality, and is ready to be incorporated into any project. This library features routines for both down- and upsizing of 8- and 16-bit, 1 to 4-channel images. Image resizing routines were implemented in a portable, cross-platform, header-only C++ code, and have a high level of optimality. Beside resizing, this library offers a sub-pixel shift operation. Built-in sRGB gamma correction is available.

The resizing algorithm at first produces 2X upsized image (relative to the source image size, or relative to the destination image size if downsizing is performed) and then performs interpolation using a bank of sinc function-based fractional delay filters. At the last stage a correction filter is applied which fixes smoothing introduced at previous steps.

The resizing algorithm was designed to provide the best visual quality. The author even believes this algorithm provides the "ultimate" level of quality (for an orthogonal, non neural-network, resizing) which cannot be increased further: no math exists to provide a better frequency response, better anti-aliasing quality and at the same time having less ringing artifacts: these are 3 elements that define any resizing algorithm's quality; in AVIR practice these elements have a high correlation to each other, so they can be represented by a single parameter (AVIR offers several parameter sets with varying quality). Algorithm's time performance turned out to be very good as well (for the "ultimate" image quality).

An important element utilized by this algorithm is the so called Peaked Cosine window function, which is applied over sinc function in all filters. Please consult the documentation for more details.

Note that since AVIR implements orthogonal resizing, it may exhibit diagonal aliasing artifacts. These artifacts are usually suppressed by EWA or radial filtering techniques. EWA-like technique is not implemented in AVIR, because it requires considerably more computing resources and may produce a blurred image.

As a bonus, a much faster LANCIR image resizing algorithm is also offered as a part of this library. But the main focus of this documentation is the original AVIR image resizing algorithm.

AVIR is dedicated to women. Your digital photos can look good at any size!

P.S. Please credit the author of this library in your documentation in the following way: "AVIR image resizing algorithm designed by Aleksey Vaneev".

Affine and Non-Linear Transformations

AVIR does not offer affine and non-linear image transformations "out of the box". Since upsizing is a relatively fast operation in AVIR (required time scales linearly with the output image area), affine and non-linear transformations can be implemented in steps: 4- to 8-times upsizing, transformation via bilinear interpolation, downsizing (linear proportional affine transformations can probably skip the downsizing step). This should not compromise the transformation quality much as bilinear interpolation's problems will mostly reside in spectral area without useful signal, with a maximum of 0.7 dB high-frequency attenuation for 4-times upsizing, and 0.17 dB attenuation for 8-times upsizing. This approach is probably as time efficient as performing a high-quality transform over the input image directly (the only serious drawback is the increased memory requirement). Note that affine transformations that change image proportions should first apply proportion change during upsizing.

Requirements

C++ compiler and system with efficient "float" floating-point (24-bit mantissa) type support. This library can also internally use the "double" and SIMD floating-point types during resizing if needed. This library does not have dependencies beside the standard C library.

Usage Information

The image resizer is represented by the avir::CImageResizer<> class, which is a single front-end class for the whole library. Basically, you do not need to use nor understand any other classes beside this class.

• Documentation

The code of the library resides in the "avir" C++ namespace, effectively isolating it from all other code. The code is thread-safe. You need just a single resizer object per running application, at any time, even when resizing images concurrently.

To resize images in your application, simply add 3 lines of code (note that you may need to change ImageResizer( 8 ) here, to specify your image's true bit resolution, which may be 10 or even 16):

#include "avir.h"
avir :: CImageResizer<> ImageResizer( 8 );
ImageResizer.resizeImage( InBuf, 640, 480, 0, OutBuf, 1024, 768, 3, 0 );
(multi-threaded operation requires additional coding, see the documentation)

AVIR works with header-less "raw" image buffers. If you are not too familiar with the low-level "packed interleaved" image storage format, the InBuf is expected to be w*h*c elements in size, where w and h is the width and the height of the image in pixels, respectively, and c is the number of color channels in the image. In the example above, the size of the InBuf is 640*480*3=921600 elements. If you are working with 8-bit images, the buffer and the elements should have the uint8_t* type; if you are working with 16-bit images, they should have the uint16_t* type. Note that when processing 16-bit images, the value of 16 should be used in resizer's constructor. AVIR's algorithm does not discern between channel packing order (RGBA, ARGB, BGRA, etc.), so if the BGRA ordered elements were passed to it, the result will be also BGRA.

If the graphics library you are using returns a uint32_t* pointer to a raw 4-channel packed pixel data, you will need to cast both the input and output pointers to the uint8_t* type when supplying them to the resizing function, and set the ElCount to 4.

For low-ringing performance:

avir :: CImageResizer<> ImageResizer( 8, 0, avir :: CImageResizerParamsLR() );

To use the built-in gamma correction, which is disabled by default, an object of the avir::CImageResizerVars class with its variable UseSRGBGamma set to true should be supplied to the resizeImage() function. Note that, when enabled, the gamma correction is applied to all channels (e.g. alpha-channel) in the current implementation.

avir :: CImageResizerVars Vars;
Vars.UseSRGBGamma = true;

Dithering (error-diffusion dither which is perceptually good) can be enabled this way:

typedef avir :: fpclass_def< float, float,
    avir :: CImageResizerDithererErrdINL< float > > fpclass_dith;
avir :: CImageResizer< fpclass_dith > ImageResizer( 8 );

The library is able to process images of any bit depth: this includes 8-bit, 16-bit, float and double types. Larger integer and signed integer types are not supported. Supported source and destination image sizes are only limited by the available system memory. Note that the resizing function applies clipping to integer output only; floating-point output will not be clipped to [0; 1] range.

The code of this library was commented in the Doxygen style. To generate the documentation locally you may run the doxygen ./other/avirdoxy.txt command from the library's directory. Note that the code was suitably documented allowing you to make modifications, and to gain full understanding of the algorithm.

Preliminary tests show that this library (compiled with Intel C++ Compiler 18.2 with AVX2 instructions enabled, without explicit SIMD resizing code) can resize 8-bit RGB 5184x3456 (17.9 Mpixel) 3-channel image down to 1920x1280 (2.5 Mpixel) image in 245 milliseconds, utilizing a single thread, on Intel Core i7-7700K processor-based system without overclocking. This scales down to 74 milliseconds if 8 threads are utilized.

Multi-threaded operation is not provided by this library "out of the box". The multi-threaded (horizontally-threaded) infrastructure is available, but requires additional system-specific interfacing code for engagement.

SIMD Usage Information

This library is capable of using SIMD floating-point types for internal variables. This means that up to 4 color channels can be processed in parallel. Since the default interleaved processing algorithm itself remains non-SIMD, the use of SIMD internal types is not practical for 1- and 2-channel image resizing (due to overhead). SIMD internal type can be used this way:

#include "avir_float4_sse.h"
avir :: CImageResizer< avir :: fpclass_float4 > ImageResizer( 8 );

For 1-channel and 2-channel image resizing when AVX instructions are allowed it may be reasonable to utilize de-interleaved SIMD processing algorithm. While it gives no performance benefit if the "float4" SSE processing type is used, it offers some performance boost if the "float8" AVX processing type is used (given dithering is not performed, or otherwise performance is reduced at the dithering stage since recursive dithering cannot be parallelized). The internal type remains non-SIMD "float". De-interleaved algorithm can be used this way:

#include "avir_float8_avx.h"
avir :: CImageResizer< avir :: fpclass_float8_dil > ImageResizer( 8 );

It's important to note that on the latest Intel processors (i7-7700K and probably later) the use of the aforementioned SIMD-specific resizing code may not be justifiable, or may be even counter-productive due to many factors: memory bandwidth bottleneck, increased efficiency of processor's circuitry utilization and out-of-order execution, automatic SIMD optimizations performed by the compiler. This is at least true when compiling 64-bit code with Intel C++ Compiler 18.2 with /QxSSE4.2, or especially with the /QxCORE-AVX2 option. SSE-specific resizing code may still be a little bit more efficient for 4-channel image resizing.

Notes

This library was tested for compatibility with GNU C++, Microsoft Visual C++, LLVM, and Intel C++ compilers, on 32- and 64-bit Windows, macOS, and CentOS Linux. The code was also tested with Dr.Memory/Win32 for the absence of uninitialized or unaddressable memory accesses.

All code is fully "inline", without the need to compile any source files. The memory footprint of the library itself is very modest, except that the size of the temporary image buffers depends on the input and output image sizes, and is proportionally large.

The "heart" of resizing algorithm's quality resides in the parameters defined via the avir::CImageResizerParams structure. While the default set of parameters that offers a good quality was already provided, there is (probably) still a place for improvement exists, and the default parameters may change in a future update. If you need to recall an exact set of parameters, simply save them locally for a later use.

When the algorithm is run with no resizing applied (k=1), the result of resizing will not be an exact, but a very close copy of the source image. The reason for such inexactness is that the image is always low-pass filtered at first to reduce aliasing during subsequent resizing, and at last filtered by a correction filter. Such approach allows algorithm to maintain a stable level of quality regardless of the resizing "k" factor used.

This library includes a binary command line tool "imageresize" for some desktop platforms. This tool was designed to be used as a demonstration of library's performance, and as a reference, it is multi-threaded (the -t switch can be used to control the number of threads utilized). This tool uses plain "float" processing (no explicit SIMD) and relies on automatic compiler optimizations. This tool uses the following libraries:

• turbojpeg Copyright (c) 2009-2013 D. R. Commander
• libpng Copyright (c) 1998-2013 Glenn Randers-Pehrson
• zlib Copyright (c) 1995-2013 Jean-loup Gailly and Mark Adler

Note that you can enable gamma-correction with the -g switch. However, sometimes gamma-correction produces "greenish/reddish/bluish haze" since low-amplitude oscillations produced by resizing at object boundaries are amplified by gamma correction. This can also have an effect of reduced contrast.

Interpolation Discussion

The use of certain low-pass filters and 2X upsampling in this library is hardly debatable, because they are needed to attain a certain anti-aliasing effect and keep ringing artifacts low. But the use of sinc function-based interpolation filter that is 18 taps-long (may be higher, up to 36 taps in practice) can be questioned, because such interpolation filter requires 18 multiply-add operations. Comparatively, an optimal Hermite or cubic interpolation spline requires 8 multiply and 11 add operations.

One of the reasons 18-tap filter is preferred, is because due to memory bandwidth limitations using a lower-order filter does not provide any significant performance increase (e.g. 14-tap filter is less than 5% more efficient overall). At the same time, in comparison to cubic spline, 18-tap filter embeds a low-pass filter that rejects signal above 0.5*pi (provides additional anti-aliasing filtering), and this filter has a consistent shape at all fractional offsets. Splines have a varying low-pass filter shape at different fractional offsets (e.g. no low-pass filtering at 0.0 offset, and maximal low-pass filtering at 0.5 offset). 18-tap filter also offers a superior stop-band attenuation which almost guarantees absence of artifacts if the image is considerably sharpened afterwards.

Why 2X upsizing in AVIR?

Classic approaches to image resizing do not perform an additional 2X upsizing. So, why such upsizing is needed at all in AVIR? Indeed, image resizing can be implemented using a single interpolation filter which is applied to the source image directly. However, such approach has limitations:

First of all, speaking about non-2X-upsized resizing, during upsizing the interpolation filter has to be tuned to a frequency close to pi (Nyquist) in order to reduce high-frequency smoothing: this reduces the space left for filter optimization. Beside that, during downsizing, a filter that performs well and predictable when tuned to frequencies close to the Nyquist frequency, may become distorted in its spectral shape when it is tuned to lower frequencies. That is why it is usually a good idea to have filter's stop-band begin below Nyquist so that the transition band's shape remains stable at any lower-frequency setting. At the same time, this requirement complicates a further corrective filtering, because correction filter may become too steep at the point where the stop-band begins.

Secondly, speaking about non-2X-upsized resizing, filter has to be very short (with a base length of 5-7 taps, further multiplied by the resizing factor) or otherwise the ringing artifacts will be very strong: it is a general rule that the steeper the filter is around signal frequencies being removed the higher the ringing artifacts are. That is why it is preferred to move steep transitions into the spectral area with a quieter signal. A short filter also means it cannot provide a strong "beyond-Nyquist" stop-band attenuation, so an interpolated image will look a bit edgy or not very clean due to stop-band artifacts.

To sum up, only additional controlled 2X upsizing provides enough spectral space to design interpolation filter without visible ringing artifacts yet providing a strong stop-band attenuation and stable spectral characteristics (good at any resizing "k" factor). Moreover, 2X upsizing becomes very important in maintaining a good resizing quality when downsizing and upsizing by small "k" factors, in the range 0.5 to 2: resizing approaches that do not perform 2X upsizing usually cannot design a good interpolation filter for such factors just because there is not enough spectral space available.

Why Peaked Cosine in AVIR?

First of all, AVIR is a general solution to image resizing problem. That is why it should not be directly compared to "spline interpolation" or "Lanczos resampling", because the latter two are only means to design interpolation filters, and they can be implemented in a variety of ways, even in sub-optimal ways. Secondly, with only a minimal effort AVIR can be changed to use any existing interpolation formula and any window function, but this is just not needed.

An effort was made to compare Peaked Cosine to Lanczos window function, and here is the author's opinion. Peaked Cosine has two degrees of freedom whereas Lanczos has one degree of freedom. While both functions can be used with acceptable results, Peaked Cosine window function used in automatic parameter optimization really pushes the limits of frequency response linearity, anti-aliasing strength (stop-band attenuation) and low-ringing performance which Lanczos cannot usually achieve. This is true at least when using a general-purpose downhill simplex optimization method. Lanczos window has good (but not better) characteristics in several special cases (certain "k" factors) which makes it of limited use in a general solution such as AVIR.

Among other window functions (Kaiser, Gaussian, Cauchy, Poisson, generalized cosine windows) there are no better candidates as well. It looks like Peaked Cosine function's scalability (it retains stable, almost continously-variable spectral characteristics at any window parameter values), and its ability to create "desirable" pass-band ripple in the frequency response near the cutoff point contribute to its better overall quality. Somehow Peaked Cosine window function optimization manages to converge to reasonable states in most cases (that is why AVIR library comes with a set of equally robust, but distinctive parameter sets) whereas all other window functions tend to produce unpredictable optimization results.

The only disadvantage of Peaked Cosine window function is that usable filters windowed by this function tend to be longer than "usual" (with Kaiser window being the "golden standard" for filter length per decibel of stop-band attenuation). This is a price that should be paid for stable spectral characteristics.

This waterfall graph depicts the windowing function, at varying Alpha values.

Note that since mathematical formulas cannot be patented nor copyrighted, you are free to adopt this windowing function in your applications and research. Just consider giving it a proper credit.

LANCIR

As a part of AVIR library, the CLancIR class is also offered which is an optimal implementation of Lanczos image resizing filter. This class has a similar programmatic interface to AVIR, but it is not thread-safe: each executing thread should have its own CLancIR object. This class was designed for cases of batch processing of same-sized frames like in video encoding, or for just-in-time resizing of an application's assets. This Lanczos implementation is likely one of the fastest available for CPUs; it features radical AVX, SSE2, and NEON optimizations.

LANCIR offers up to three times faster image resizing in comparison to AVIR. The quality difference is, however, debatable. Note that while LANCIR can take 8- and 16-bit and float image buffers, its precision is limited to 8-bit resizing.

LANCIR should be seen as a bonus and as an "industrial standard" reference for comparison. By default, LANCIR uses Lanczos filter's a parameter equal to 3 which is similar to AVIR's default setting.

Comparison

This graph displays a comparison of AVIR 2.9 (default parameters) and Lanczos-3 image resizing algorithm in the area of frequency response. The methodology can be seen in the other/frtest.cpp file. This graph displays an average frequency response over a set of resizing factors. It is similar but not equal to Fourier analysis as any errors and aliasing artifacts are integrated into the response. As you can see, AVIR offers a visibly better frequency response linearity. The horizontal scale displays a normalized frequency scale, where 0 is DC frequency and 1 is Nyquist frequency. In common terms, 1 corresponds to 1-pixel image features, 0.5 corresponds to 2-pixel features while 0.25 corresponds to 4-pixel features, etc. The vertical scale is in decibel.

The following graph displays a comparison of an average dynamic range over a set of resizing factors. The dynamic range is estimated by performing two-way resizing, followed by deviation/error estimation relative to the original image. As you can see here, aliasing artifacts visibly reduce dynamic range above 0.5*Nyquist. An interesting aspect of this measurement method is that it reflects modes of visual ringing very well: they correspond to the points on frequency response where differential approaches zero.

Note that on downsizing the response graphs look similar to these.

Users

This library is used by:

• Contaware.com
• Pretext contact maps
• LVC Audio
• Trainz
• MLV App

This video was "unsqueezed" with AVIR by a factor of 3 from ML RAW video, and at the final stage was downsampled to 4K resolution.

Please drop me a note at aleksey.vaneev@gmail.com and I will include a link to your software product to the list of users. This list is important at maintaining confidence in this library among the interested parties.

Change Log

Version 3.0:

• Improved speed by 10-25% on upsizing by utilizing a special resizing function together with filter-less 2X upsizing. Does not apply to the de-interleaved (AVX) resizing.
• Minor LANCIR optimization.

Version 2.9:

• Removed a rarely-used half-band resizing step completely since it offers no practical performance nor quality benefits.
• Optimized filter generation function (removed divisions by a constant) as filters are always post-normalized anyway. This may reduce overhead when creating thumbnail-sized images.

Version 2.8:

• Fixed regression with the copy-constructor of CImageResizeVars class (previously it caused uninitialized accesses).
• Removed filter length optimization as it did not reduce overhead measurably.
• Optimized "peaked cosine" window function generator (removed division).
• Added "unbiasing" to resizer - an unconventional approach which reduces peak error significantly, at the expense of 5% increased overhead.
• Reoptimized filter parameters, now yielding an unprecedented quality.

Version 2.7:

• Added normalization of individual fractional delay filters. This reduced peak error by 3 dB, which is substantial for image resizing.
• Reoptimized all filter parameters resulting in better frequency response linearity.
• Added AVIR_NOCTOR macro to avoid copy-constructing and copying objects of some classes via a default copy function.
• Added copy-constructor and assignment operator to the CImageResizerVars class, to avoid uninitialized memory copying.
• Corrected automatic image offseting and "k" factor on image upsizing.

Version 2.6:

• A minor fix to sRGB gamma approximation functions.
• LANCIR: fixed a rare access violation crash.

Version 2.5:

• Surrounded memcpy calls with length checks to conform to memcpy specification which does not allow NULL pointers even with zero copy length.

Version 2.4:

• Removed outdated _mm_reset() function calls from the SIMD code.
• Changed float4 round() to use SSE2 rounding features, avoiding use of 64-bit registers.

Version 2.3:

• Implemented CLancIR image resizing algorithm.
• Fixed a minor image offset on image upsizing.

Version 2.2:

• Released AVIR under a permissive MIT license agreement.

Version 2.1:

• Fixed error-diffusion dither problems introduced in the previous version.
• Added the -1 switch to the imageresize to enable 1-bit output for dither's quality evaluation (use together with the -d switch).
• Added the --algparams= switch to the imageresize to control resizing quality (replaces the --low-ring switch).
• Added avir :: CImageResizerParamsULR parameter set for lowest-ringing performance possible (not considerably different to avir :: CImageResizerParamsLR, but a bit lower ringing).

Version 2.0:

• Minor inner loop optimizations.
• Lifted the supported image size constraint by switching buffer addressing to size_t from int, now image size is limited by the available system memory.
• Added several useful switches to the imageresize utility.
• Now imageresize does not apply gamma-correction by default.
• Fixed scaling of bit depth-reduction operation.
• Improved error-diffusion dither's signal-to-noise ratio.
• Compiled binaries with AVX2 instruction set (SSE4 for macOS).