Digital holography is an inherently three-dimensional (3D) technique for the capture of real-world objects. Many existing 3D imaging and processing techniques are based on the explicit combination of several 2D perspectives (or light stripes, etc.) through digital image processing. The advantage of recording a hologram is that multiple 2D perspectives can be optically combined in parallel, and in a constant number of steps independent of the hologram size. Although holography and its capabilities have been known for many decades, it is only very recently that digital holography has been practically investigated due to the recent development of megapixel digital sensors with sufficient spatial resolution and dynamic range. The applications of digital holography could include 3D television, virtual reality, and medical imaging. If these applications are realized, compression standards will have to be defined. We outline the techniques that have been proposed to date for the compression of digital hologram data and show that they are comparable to the performance of what in communication theory is known as optimal signal quantization. We adapt the optimal signal quantization technique to complex-valued 2D signals. The technique relies on knowledge of the histograms of real and imaginary values in the digital holograms. Our digital holograms of 3D objects are captured using phase-shift interferometry. We complete the compression procedure by applying lossless techniques to the quantized holographic pixels.
Digital holography can be used to capture the whole Fresnel field from a reflective or transmissive object. Applications
include imaging and display of three-dimensional (3D) objects, and encryption and pattern recognition
of two-dimensional (2D) and 3D objects. Often, these optical systems employ discrete spatial light modulators
(SLMs) such as liquid-crystal displays. In the 2D case, SLMs can encode the inputs and keys during encryption
and decryption. For 3D processing, the SLM can be used as part of an optical reconstruction technique for 3D
objects, and can also represent the key during encryption and decryption. However, discrete SLMs can represent
only discrete levels of data necessitating a quantisation of continuous valued analog information. To date, many
such optical systems have been proposed in the literature, yet there has been relatively little experimental evaluation
of the practical performance of discrete SLMs in these systems. In this paper, we characterise conventional
phase-modulating liquid-crystal devices and examine their limitations (in terms of phase quantisation, alignment
tolerances, and nonlinear response) for the encryption of 2D and 3D data. Finally, we highlight the practical
importance of a highly controlled discretisation (optimal quantisation) for compression of digital holograms.
Compression is essential for efficient storage and transmission of three-dimensional (3D) digital holograms.
The inherent speckle content in holographic data causes lossless compression techniques, such as Huffman and
Burrows-Wheeler (BW), to perform poorly. Therefore, the combination of lossy quantisation followed by lossless
compression is essential for effective compression of digital holograms. Our complex-valued digital holograms of
3D real-world objects were captured using phase-shift interferometry (PSI). Quantisation reduces the number of
different real and imaginary values required to describe each hologram. Traditional data compression techniques
can then be applied to the hologram to actually reduce its size. Since our data has a nonuniform distribution,
the uniform quantisation technique does not perform optimally. We require nonuniform quantisation, since in
a histogram representation our data is denser around the origin (low amplitudes), thus requiring more cluster
centres, and sparser away from the origin (high amplitudes). By nonuniformly positioning the cluster centres
to match the fact that there is a higher probability that the pixel will have a low amplitude value, the cluster
centres can be used more efficiently. Nonuniform quantisation results in cluster centres that are adapted to the
exact statistics of the input data. We analyse a number of iterative (k-means clustering, Kohonen competitive
neural network, SOM, and annealed Hopfield neural network), and non-iterative (companding, histogram, and
optimal) nonuniform quantisation techniques. We discuss the strengths and weaknesses of each technique and
highlight important factors that must be considered when choosing between iterative and non-iterative nonuniform
quantisation. We measure the degradation due to lossy quantisation in the reconstruction domain, using
the normalised rms (NRMS) metric.
We report on recent advances made in the area of holographic image processing of three-dimensional (3D) objects. In particular, we look at developments made in the areas of encryption, compression, noise removal, and 3D shape extraction. Results are provided using simulated objects and real-world 3D objects captured using phase- shift digital holography.
Wavelets are used extensively in image processing due to the localized frequency information that can be conveyed by the wavelet transform. This and other characteristics of wavelet transforms can be exploited very effectively for the compression of images. We apply the wavelet transform to digital holograms of three-dimensional objects. Our digital holograms are complex-valued signals captured using phase-shift interferometry. Speckle gives them a white noise-like appearance with little correlation between neighboring pixels. In our analyses we concentrate on the discrete wavelet transform and Haar dyadic bases. We achieve compression through quantization of the wavelet transform coefficients. We quantize the discrete wavelet coefficients in each of the subbands depending on the dynamic range of the coefficients in that subband. Finally, we losslessly encode these subbands to quantify the high compression ratios achieved. We outline the three issues that need to be dealt with in order to improve the compression ratio of wavelet based techniques for particular applications as (i) determining a good criterion for ascertaining the coefficients that have to be retained, (ii) determining a quantization strategy and quantization error appropriate to one's particular application, and (iii) compression of the bookkeeping data.
Compression and encryption/decryption are necessary for secure and
effcient storage and transmission of image data. We present an
optical encryption technique that takes advantage of both the
massive parallelism inherent in optical systems and the flexibility
offered by digital electronics. The encryption is performed using a
phase mask and Fresnel propagation. We nonuniformly quantize the
complex-valued encrypted hologram pixels using an artificial neural
network. The in-line digital holograms of three-dimensional objects
were created using phase-shift interferometry. With our lossy data
compression technique we achieved good quality decryption and
reconstruction from objects with a compression ratio of 32.
Digital holograms of real-world three-dimensional objects have been captured using phase-shift digital holography. These holograms have complex-valued pixels and a white noise appearance. Uniform and nonuniform scalar quantisation compression have already been applied to the hologram data with some success. Although each complex-valued pixel can itself be treated as a vector of length two, we extend the analysis using a multidimensional vector quantisation technique based on k-means clustering. This involves an a-by-b blockwise decomposition of the data and mapping it to an ab-dimensional space. Degradation due to lossy compression is measured in the reconstruction domain.
Digital holography is an inherently three-dimensional (3D) technique for the capture of real-world objects. Many existing 3D imaging and processing techniques are based on the explicit combination of several 2D perspectives (or light stripes, etc.) through digital image processing. The advantage of recording a hologram is that multiple 2D perspectives can be optically combined in parallel, and in a constant number of steps independent of the hologram size. Although holography and its capabilities have been known for many decades, it is only very recently that digital holography has been practically investigated due to the recent development of megapixel digital sensors with sufficient spatial resolution and dynamic range. The applications of digital holography could include 3D television, virtual reality, and medical imaging. If these applications are realised, compression standards will have to be defined. We outline the techniques that have been proposed to date for the compression of digital hologram data and show that they are comparable to the performance of what in communication theory is known as optimal signal quantisation. We adapt the optimal signal quantisation technique to complex-valued 2D signals. The technique relies on knowledge of the histograms of real and imaginary values in the digital holograms. Our digital holograms of 3D objects are captured using phase-shift interferometry.
Digital holography is a successful technique for recording and reconstructing three-dimensional (3D) objects. The recent development of megapixel digital sensors with high spatial resolution and high dynamic range has benefited this area. We capture digital holograms (whole Fresnel fields) using phase-shift interferometry and compress then to enhance transmission and storage effciency. Lossy quantization techniques are applied to our complex-valued holograms as the initial stage in the compression procedure. Quantization reduces the number of different real and imaginary values required to describe each hologram. We outline the nonuniform quantization techniques that we have had some success with thus far, and present our latest results with two techniques based on companding and histogram approaches. Companding quantization attempts to combine the effciency of uniform quantization with the improved performance of nonuniform quantization. Our results show that companding techniques can be comparable with k-means and neural network clustering algorithms, while only requiring a single-pass processing step. In addition, we report on a novel lossy compression technique that utilizes histogram data to quantize digital holograms. Here, we use the results of a histogram analysis to inform our decision about the best choice for quantization values.
We report on the results of a study into the characteristics of the blockwise discrete Fourier transform (DFT) coefficients of digital hologram data, with the aim of efficiently compressing the data. We captured digital holograms (whole Fresnel fields) of three-dimensional (3D) objects using phase-shift interferometry. The complex-valued fields were decomposed into nonoverlapping blocks of 8x8 pixels and transformed with the DFT. The inter-block distributions of the 64 Fourier coefficients were analyzed to determine the relative importance of each coefficient. Through techniques of selectively removing coefficients, or groups of coefficients, we were able to trace the relative importance of coefficients throughout a hologram, and over multiple holograms. We used rms error in the reconstructed image to quantify importance in the DFT domain. We have found that the positions of the most important coefficients are common throughout four of the five digital holograms in our test suite. These results will aid us in our aim of creating a general-purpose DFT quantization table that could be universally applied to digital hologram data of 3D objects as part of a JPEG-style compressor.
Digital holograms are capable of encoding three-dimensional (3D) information of a scene or object. Uniform quantization has been used in the past to compress digital holograms with some success. We have developed nonuniform quantization techniques that operate on the complex-valued hologram data for increased performance. Our digital holograms of 3D objects are captured using phase-shift digital interferometry. The quantized holographic pixels are coded using lossless techniques to achieve compression rates in excess of 40.
We propose two lossy data compression techniques for complex-valued digital holograms of three-dimensional objects. The techniques employ unsupervised artificial neural networks to nonuniformly quantize the real and imaginary values of digital holograms. The digital holograms of real-world three-dimensional objects were captured using phase-shift interferometry. Our techniques are compared experimentally with the uniform quantization approach, and with an alternative nonuniform quantization technique based on the k-means clustering