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Image pyramid generation specialized for connectomics data types and procedures.

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Image pyramid generation specialized for connectomics data types and procedures. If your brain wasn't tiny before, it will be now.

import tinybrain 

img = load_3d_em_stack()

# 2x2 and 2x2x2 downsamples are on a fast path.
# e.g. (2,2), (2,2,1), (2,2,1,1), (2,2,2), (2,2,2,1)
img_pyramid = tinybrain.downsample_with_averaging(img, factor=(2,2,1), num_mips=5, sparse=False)

labels = load_3d_labels()
label_pyramid = tinybrain.downsample_segmentation(labels, factor=(2,2,1), num_mips=5, sparse=False))


pip install numpy
pip install tinybrain


Image hierarchy generation in connectomics uses a few different techniques for visualizing data, but predominantly we create image pyramids of uint8 grayscale images using 2x2 average pooling and of uint8 to uint64 segmentation labels using 2x2 mode pooling. When images become very large and people wish to visualze upper mip levels using three axes at once, it becomes desirable to perform 2x2x2 downsamples to maintain isotropy.

It's possible to compute both of these using numpy, however as multiple packages found it useful to copy the downsample functions, it makes sense to formalize these functions into a seperate library located on PyPI.

Given the disparate circumstances that they will be used in, these functions should work fast as possible with low memory usage and avoid numerical issues such as integer truncation while generating multiple mip levels.

Considerations: downsample_with_averaging

It's advisable to generate multiple mip levels at once rather than recursively computing new images as for integer type images, this leads to integer truncation issues. In the common case of 2x2x1 downsampling, a recursively computed image would lose 0.75 brightness per a mip level. Therefore, take advantage of the num_mips argument which strikes a balance that limits integer truncation loss to once every 4 mip levels. This compromise allows for the use of integer arithmatic and no more memory usage than 2x the input image including the output downsamples. If you seek to eliminate the loss beyond 4 mip levels, try promoting the type before downsampling. 2x2x2x1 downsamples truncate every 8 mip levels.

A C++ high performance path is triggered for 2x2x1x1 and 2x2x2x1 downsample factors on uint8, uint16, float32, and float64 data types in Fortran order. Other factors, data types, and orderings are computed using a numpy pathway that is much slower and more memory intensive.

We also include a sparse mode for downsampling 2x2x2 patches, which prevents "ghosting" where one z-slice overlaps a black region on the next slice and becomes semi-transparent after downsampling. We deal with this by neglecting the background pixels from the averaging operation.

Example Benchmark

On a 1024x1024x100 uint8 image I ran the following code. PIL and OpenCV are actually much faster than this benchmark shows because most of the time is spent writing to the numpy array. tinybrain has a large advantage working on 3D and 4D arrays. Of course, this is a very simple benchmark and it may be possible to tune each of these approaches. On single slices, Pillow was faster than tinybrain.

img = np.load("image.npy")

s = time.time()
downsample_with_averaging(img, (2,2,1))
print("Original ", time.time() - s)

s = time.time()
out = tinybrain.downsample_with_averaging(img, (2,2,1))
print("tinybrain ", time.time() - s)

s = time.time()
out = np.zeros(shape=(512,512,100))
for z in range(img.shape[2]):
  out[:,:,z] = cv2.resize(img[:,:,z], dsize=(512, 512) )
print("OpenCV ", time.time() - s)

s = time.time()
out = np.zeros(shape=(512,512,100))
for z in range(img.shape[2]):
  pilimg = Image.fromarray(img[:,:,z])
  out[:,:,z] = pilimg.resize( (512, 512) )
print("Pillow ", time.time() - s)

# Method     Run Time             Rel. Perf.
# Original   1820 ms +/- 3.73 ms    1.0x
# tinybrain    67 ms +/- 0.40 ms   27.2x 
# OpenCV      469 ms +/- 1.12 ms    3.9x
# Pillow      937 ms +/- 7.63 ms    1.9x

Here's the output from on an Apple Silicon 2021 Macbook Pro M1. Note that the image used was a random 2048x2048x64 array that was a uint8 for average pooling and a uint64 for mode pooling to represent real use cases more fairly. In the table, read it as 2D or 3D downsamples, generating a single or multiple mip levels, with sparse mode enabled or disabled. The speed values are in megavoxels per a second and are the mean of ten runs.

dwnsmpl mips sparse AVG (MVx/sec) MODE (MVx/sec)
2x2 1 N 3856.07 1057.87
2x2 2 N 2685.80 1062.69
2x2 1 Y N/A 129.64
2x2 2 Y N/A 81.62
2x2x2 1 N 4468.55 336.85
2x2x2 2 N 2867.80 298.45
2x2x2 1 Y 1389.47 337.87
2x2x2 2 Y 1259.58 293.84

As the downsampling code's performance is data dependent due to branching, I also used connectomics.npy (5123 uint32 extended to uint64) to see how that affected performance. This data comes from mouse visual cortex and has many equal adjacent voxels. In this volume, the 2x2x2 non-sparse mode is much faster as the "instant" majority detection can skip examining half the voxels in many cases.

dwnsmpl mips sparse MODE (MVx/sec)
2x2 1 N 1078.09
2x2 2 N 1030.90
2x2 1 Y 146.15
2x2 2 Y 69.25
2x2x2 1 N 1966.74
2x2x2 2 N 1790.60
2x2x2 1 Y 2041.96
2x2x2 2 Y 1758.42

Considerations: downsample_segmentation

The downsample_segmentation function performs mode pooling operations provided the downsample factor is a power of two, including in three dimensions. If the factor is a non-power of two, striding is used. The mode pooling, which is usually what you want, is computed recursively. Mode pooling is superior to striding, but the recursive calculation can introduce defects at mip levels higher than 1. This may be improved in the future.

The way the calculation is actually done uses an ensemble of several different methods. For (2,2,1,1) and (2,2,2,1) downsamples, a Cython fast, low memory path is selected. (2,2,1,1) implements countless if. (2,2,2,1) uses a combination of counting and "instant" majority detection. For (4,4,1) or other 2D powers of two, the countless 2d algorithm is used. For (4,4,4), (8,8,8) etc, the dynamic countless 3d algorithm is used. For 2D powers of two, stippled countless 2d is used if the sparse flag is enabled. For all other configurations, striding is used.

Countless 2d paths are also fast, but use slightly more memory and time. Countless 3D is okay for (2,2,2) and (4,4,4) but will use time and memory exponential in the product of dimensions. This state of affairs could be improved by implementing a counting based algorithm in Cython/C++ for arbitrary factors that doesn't compute recursively. The countless algorithms were developed before I knew how to write Cython and package libraries. However, C++ implementations of countless are much faster than counting for computing the first 2x2x1 mip level. In particular, an AVX2 SIMD implementation can saturate memory bandwidth.

Documentation for the countless algorithm family is located here:

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