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A real-time implementation of gradient domain high dynamic range compression using a local Poisson solver

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Abstract

This paper presents a real-time hardware implementation of a gradient domain dynamic range compression algorithm for high dynamic range (HDR) images. This technique works by calculating the gradients of the HDR image, manipulating those gradients, and reconstructing an output low dynamic range image that corresponds to the manipulated gradients. Reconstruction involves solving the Poisson equation. We propose a Poisson solver that utilizes only local information around each pixel along with special boundary conditions, and requires a small and fixed amount of hardware for any image size, with no need to buffer the entire image. The hardware implementation is described in VHDL and synthesized for a field programmable gate array (FPGA) device. The maximum operating frequency achieved is fast enough to process high dynamic range videos with one megapixel per frame at a rate of about 100 frames per second. The hardware is tested on standard HDR images from the Debevec library. The output images produced have good visual quality.

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Abbreviations

HDR:

High dynamic range

VHDL:

VHSIC hardware description language

VHSIC:

Very high scale integrated circuit

FPGA:

Field programmable gate array

TMO:

Tone mapping operator

FFT:

Fast Fourier transform

PSNR:

Peak signal-to-noise ratio

i, j :

Indices used for pixels in full-size images; i = 0, 1, 2,…,N–1 and j = 0, 1, 2,…,N–1

I k :

The input image and its scale versions (for k = 0, 1, 2, 3, 4), each full-size. I 0 is the log-luminance high dynamic range input image, and the scale versions are each produced by applying a 2D approximate Gaussian filter to the input image

I out :

The full-size output image, a low dynamic range version of the input

u, v :

Indices used for pixels in local windows and gradient matrices. A local window is cut out around a particular pixel (i, j) in the full-size inputs

\( \mathcal{I}^{k} \) :

Local (6 × 6) windows extracted from the full-size input and scale images (for k = 0, 1, 2, 3, 4). Indices are u = −1, 0, 1, 2, 3, 4 and v = −1, 0, 1, 2, 3, 4

\( \mathcal{I}^{out} \) :

The (6 × 6) local output window produced in one step of the local method. Indices are u = −1, 0, 1, 2, 3, 4 and v = −1, 0, 1, 2, 3, 4. Given that the windows are extracted around pixel (i, j) in the full-size input and scale images, pixel (2, 2) from this output image is pixel (i, j) in the full-size output image I out

\( \mathcal{G}^{H} \), \( \mathcal{G}^{V} \) :

4 × 4 matrices, horizontal and vertical gradients for each of the 16 pixels in the middle of a local window, computed using forward differences. Indices are u = 0, 1, 2, 3 and v = 0, 1, 2, 3

\( \mathcal{H}^{k} \), \( \mathcal{V}^{k} \) :

4 × 4 matrices, the horizontal and vertical gradients for each of the 16 pixels in the middle of a local window at each scale (for k = 0, 1, 2, 3, 4), computed based on central differences. Indices are u = 0, 1, 2, 3 and v = 0, 1, 2, 3

\( \mathcal{C}^{k} \) :

A 4 × 4 matrix, the one-norm of the horizontal and vertical gradients based on central differences for each of the 16 pixels in the middle of a local window. Indices are u = 0, 1, 2, 3 and v = 0, 1, 2, 3

Ψ:

A 4 × 4 matrix, an attenuation factor for the horizontal and vertical gradients for each of the 16 pixels in the middle of a local window. Indices are u = 0, 1, 2, 3 and v = 0, 1, 2, 3

\( \hat{\mathcal{G}}^{H},\hat{\mathcal{G}}^{V} \) :

4 × 4 matrices, the horizontal and vertical gradients for each of the 16 pixels in the middle of a local window after manipulation. Indices are u = 0, 1, 2, 3 and v = 0, 1, 2, 3

\( {\text{div}}\hat{\mathcal{G}} \) :

A 3 × 3 matrix, the divergence of the manipulated gradients, computed using backward differences. Indices are u = 1, 2, 3 and v = 1, 2, 3

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Authors and Affiliations

  1. Department of Electrical and Computer Engineering, University of Akron, Akron, OH, USA

    Lavanya Vytla & Joan E. Carletta

  2. Electrical and Computer Engineering and Computer Science Department, Ohio Northern University, Ada, OH, USA

    Firas Hassan

Authors
  1. Lavanya Vytla
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  2. Firas Hassan
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  3. Joan E. Carletta
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Correspondence to Joan E. Carletta.

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Vytla, L., Hassan, F. & Carletta, J.E. A real-time implementation of gradient domain high dynamic range compression using a local Poisson solver. J Real-Time Image Proc 8, 153–167 (2013). https://doi.org/10.1007/s11554-011-0198-5

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  • DOI: https://doi.org/10.1007/s11554-011-0198-5

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