WO2016049779A1

WO2016049779A1 - Efficient digital characterization of images

Info

Publication number: WO2016049779A1
Application number: PCT/CA2015/051001
Authority: WO
Inventors: David A. Kahn; George Andreescu
Original assignee: Annidis Corp
Current assignee: Annidis Corp
Priority date: 2014-10-02
Filing date: 2015-10-02
Publication date: 2016-04-07
Anticipated expiration: 2017-04-02

Abstract

A method and a device is provided for digitally representing an image of a known class using a combination of differential coding with a minimum resolution interval set by consideration of the image uncertainty level. A multitier arrangement is also provided for the encoding of each differential pixel count, such that the majority of differential pixel counts can be represented by small, e.g., two-bit words while the few remaining pixel counts or outliers are represented by larger bit words. For retinal images, this generally reduces the average number of bits per pixel to just over two. The method permits the size of the image data file to approach that minimum size characteristic of the fundamental information content without incurring excessive processing time or resources.

Description

EFFICIENT DIGITAL CHARACTERIZATION OF IMAGES

Field of Invention

[001] This application claims the benefit of U.S. Provisional

Application No. 62/058,912, filed October 2, 2014, the contents of which are hereby incorporated by reference herein.

Field of Invention

[002] The invention relates to the digital representation and

reconstruction of images, such as biomedical images, and in particular, images of a retina or a choroid.

Background

[003] The large size of the digital data files currently required for retinal images is undesirable both because of the costs of storage and the costs and duration of transmission through an external network such as the Internet. It is therefore highly desirable to reduce the image data file size while retaining all the information relevant to retinal health and ensuring with high confidence that no false or misleading information is added.

[004] The field of image compression has its roots in images used for consumer applications such as hobby photography, and more latterly into medical applications. However, the assessment of image content and quality has remained in the subjective domain. This has permitted the use of lossy image compression, where the reconstructed image is different from the original image but the differences are either too small to notice or small enough to substantially avoid the impression of significant degradation. The most well known method of lossy image compression conforms to the JPEG standard. For example, US Patent 5933194, "Method and circuit for determining quantization interval in image encoder" explicitly uses human visual criteria.

[005] Lossless image compression is conventionally achieved by first modeling the image to identify regions of identical pixel patterns and then coding using short identification words wherever the patterns occur in the image. The net effect is that the reconstructed image is identical in every way with the original image. While this is fully satisfactory from a functional perspective, the degree of compression attainable with images is usually modest. Typically images can be reduced from 8 bits per pixel down to 3 or 4 bits/pixel, depending on the characteristics of the image.

[006] For example, lossless compression schemes such as JPEG-LS rely heavily on the presence within the image of repeated patterns that need to be identified. They act without a priori knowledge of the image and are commonly computationally intensive in both the compression and reconstruction phases with processing times of the order of seconds. Typically, the compression achieved is highly dependent on the image content and the result can lie anywhere (Weinberger, M .J., Seroussi, G. and Sapiro G. "The LOCO-I Lossless Image Compression Algorithm : Principles and Standardization into JPEG-LS") between 0.9 (fax balls) and 5.7 (a finger) bits per pixel, with 3.8 bits/pixel being typical in medical imaging (JPEG-LS Transfer Syntaxes Status: DICOM Correction Item - Final Text CP- 174, 2000/09/25).

[007] The use of JPEG-LS with a limited loss could increase the compression even further; however, a risk of false artifacts is introduced.

[008] The development of ever more powerful computers made feasible by faster clock-rates, multiple processor cores, and inexpensive memory, has made it increasingly possible to carry out advanced image processing with the objective of either improving the presentation for subjective viewing by enhancing the features of primary interest, or of replacing the human assessment by an automated process for identifying the presence, location and quantity of features of pathological interest. In either case, the objective is not to create a more realistic or "subjectively true" image but to identify, extract from, and enhance the image information and features of specific interest.

[009] Such enhancement processes include but are not restricted to the use of Fourier spatial filtering, correlation detection, histogram enhancement of image contrast, changes in the hue and brightness of colour images, the use of false colours, and the addition of contour lines to better identify regional boundaries and shapes.

[0010] With the introduction of automated image enhancement and feature identification, the use of subjective standards of acceptability for image compression becomes inappropriate. Instead are required objective standards of image compression. Such a requirement suggests or mandates an approach to image coding and compression assessment based upon the principles of information theory.

Information Theory Applied to a Single Pixel

[0011] Information Theory was initially developed in the context of telecommunications for the most economic encoding and transmission of speech. However, the principles are entirely deployable in the context of encoding, storing or transmitting image data files. The invention to be described applies in particular to images in an electronic form such as those generated using an image sensor such as a CCD.

[0012] An optical image is made up of a quantity of pixels, each associated with a level of irradiance. This level is initially in the form of a quantity of irradiant energy represented by a photon count that is transformed by the image sensor into a photoelectron count. This in turn is transformed through a capacitance into a voltage (electric potential) that is then amplified and digitized by an analogue-to-digital converter (ADC).

[0013] Information theory is partly based on the understanding that the uncertainty introduced by random noise limits the resolution level or precision of any signal bearing information, and partly based on the probabilistic concept of information entropy. The presence of noise limits the number M of separable, identifiable states of a signal. The probability of the signal being in any one of these M states is denoted pi.

[0014] The total information entropy I of the signal, expressed in bits, is given by: I = -∑pilog₂pi bits Equ. 1 where the integral operates over all M states.

[0015] If all M states have the same probability, then p, = 1/ and the equation simplifies to:

I = log₂M bits Equ. 2

[0016] The quantity M can be expressed in terms of the signal-to-noise power ratio SNR:

M = 1 + SNR Equ. 3

[0017] The combination of Equs 2 and 3 yields the well-known Shannon-Hartley equation as applied to a single bit period.

I = log₂ (1 + SNR) Equ. 4

[0018] In this context of addressing an image as an aggregate of information, the pixel is analogous to the bit period and the signal energy is proportional to the square of the count "n" associated with each pixel. Where the image is characterized by pixels with photoelectron counts, unlike the situation normally addressed by the Shannon-Hartley equation, the quantity proportional to the uncertainty associated with each pixel is not constant but varies with the photoelectron count. This resolution limit or uncertainty is sometimes called the quantum noise. The total noise energy contribution N can be expressed as :

N = r² + n Equ. 5 where V is the readout noise of the image sensor expressed in

photoelectrons

and "n" is the quantum noise component which equals the square root of the proportional photoelectron count energy contribution n².

[0019] The pixel SNR therefore becomes:

SNR = n²/(r²+n) Equ. 6 [0020] Except in very weak images, the quantum noise greatly exceeds the readout noise and the equation for the SNR then simplifies to :

SNR = n Equ. 7

[0021] It can be shown that because of the quantum noise uncertainty, the number of discernable levels in a photoelectron count is not "n" but Vn. From this, the information entropy associated with a single pixel photoelectron count of "n" comes to:

I = log2( n) = (log₂n)/2 bits Equ. 8

For example, if the photoelectron count were 8300 (or 8.3 ke), the information content would be 6.5 bits. This assumes that all counts from 0 to 8.3 ke are equally probable. Thus the information content would be less than half of the required pixel word size of 14 bits. This illustrates that the file size of a quantum noise limited image can in principle be reduced in size by at least 50% with no loss of information.

Information Theory Applied to an Entire Image

[0022] If the information content of eac pixel were statistically independent of the information content of every other pixel, the total information content of the image would be the product of the pixel count and the mean information count per pixel. However, in most applications where images are captured from natural phenomena such as the retina, there is a substantial degree of statistical correlation between the counts in different pixels. This has the effect of substantially decreasing the information entropy of the image.

[0023] Where there is a global degree of pixel count correlation, the effect on the image is one of low contrast or apparent fading. This is common. Supplementing this is the correlation with pixels within the neighbourhood surrounding a pixel. The correlation within the neighbourhood arises partly from the limitations of the imaging system as for example defined by the Optical Transfer Function, and partly by the intrinsic properties of the region under observation, e.g., the retina. [0024] In principle, the information entropy of an image could be calculated based upon statistical knowledge of the image. This would generate the minimum number of bits to which an image could be compressed without loss of information. However, the calculation is potentially onerous and the encoding process to implement such compression would be computationally intensive.

The Impact of Uncertainty

[0025] Both the readout noise and the quantum noise from an image sensor are random and independent. Their impact on any pixel is uncorrelated to their impact on any other pixel. They uniformly limit the irradiance resolution across the image by imposing a resolution limit, a level of uncertainty. They do not introduce or change in a systematic manner any shapes, features or other image artefacts. The impact on the image quality of an increase in uncertainty can in principle be fully compensated by the simple expedient of increasing the irradiance of the image, as may be achieved by increasing the illumination level on the region under surveillance, or by using larger optics to gather more light.

[0026] The ADC is another source of resolution limit generally called the quantization noise or uncertainty, also random. Under the assumption that the signal amplitude probability is constant over the quantization interval it can be shown that the root mean square value of the quantization uncertainty is given by the quantization interval divided by the square root of 12. For example, if the quantization interval Δ were 64, the root mean square (RMS) value of the quantization uncertainty would have a value of 18.5.

[0027] The ADC sets a lower limit to the brightness resolution of the image. When an image is digitized, the brightness resolution is inevitably reduced and there is some consequent loss of information. If the quantization noise level is small in comparison to the uncertainty level of the pixel count, the loss of information will be negligibly small. However, whenever an ADC is used, the process is not in principle lossless from an information perspective; the issue is the degree or proportion of loss incurred.

[0028] In addressing the issue of information loss in a digital camera system, the loss incurred by the ADC is rarely considered and claims of lossless compression invariably address only what happens after the ADC. However, in principle, the performance of the camera in preserving the information integrity of the image should always factor in the ADC.

[0029] A measure of the quantization noise contribution to degradation is the quantization noise figure (NF). This is the decibel ratio of the uncertainty level with quantization to the uncertainty level without quantization. Where the signal comes from a photoelectric image sensor, where Δ is the quantization interval, the NF is given by:

NF = 10 log₁₀(l + Δ²/(12(η + r²))) dB Equ. 9

[0030] The noise figure is similar in value to the increment in signal power required to restore the SNR in the presence of quantization and so fully preserve the information content. Table 1 below shows on the top row the quantization noise figure, while the lower row shows the required increase in optical signal energy. (The photoelectron count "n" is assumed large enough to make the readout noise contribution of "r" negligible.)

Table 1 Signal increment required to compensate quantization noise figure.

[0031] In general, to minimize the image file size, the quantization interval should be chosen to be as large as possible consistent with achieving the required image quality. For example, if the quantization noise were set to be about a quarter of the pixel value uncertainty, giving a quantization noise figure of 1.0 dB, the required increase in illumination level would be 0.8 dB. Discounting readout noise, this example would imply a quantization interval Δ of 1.77V(n), where the factor 1.77 sets the level of information reduction. A small interval of illumination is generally not an onerous requirement on the overall imaging system design. The quantization granularity results in a reduction of the information content that is directly related to the quantization noise figure. The reduction R is given by NF*logio2 or 0.30 NF bits. If the NF has a value of 1.0 dB, the reduction in information per pixel would be 0.30 bits. Where a typical retinal pixel carries 6.3 bits of information, the information reduction associated with a quantization interval noise figure of ldB would be less than 5%.

[0032] Therefore, there exists a need to find an efficient coding method that significantly reduces the number of bits required for the image file while being practically manageable (simple) and not damaging to the file integrity by significantly adding or subtracting information.

Summary of the Invention

[0033] The invention is fundamentally a method of digitally

representing an image using a combination of differential coding with a minimum resolution interval set by consideration of the uncertainty level associated with each differential count. The invention also includes a multitier arrangement for the encoding of each differential pixel count, such that the majority of differential pixel counts can be represented by small, e.g., two-bit words while the few remaining pixel counts or outliers are represented by larger bit words. For retinal images, this generally reduces the average number of bits per pixel to just over two, the excess depending upon the statistics of the differential pixel counts.

[0034] The overall impact of such encoding is such that all

contributions to the limits in precision are random, do not systematically generate or remove any image artefacts, and can be fully compensated by a small increase in illumination level. In this sense, the encoding can be considered to be a form of lossless compression. [0035] In an embodiment, there is provided a method of digitally representing an image belonging to a class of images, the image comprising a plurality of pixels, each pixel having a count value with a level of

uncertainty, the count values and uncertainty levels having known statistical characteristics of the class of images to which the image belongs and neighbouring count values being substantially correlated, the method comprising : converting the pixel count values of the image into a digital form wherein the uncertainty introduced by quantization is substantially less than the prior uncertainty level ; determining a differential count value for each of the plurality of pixels, wherein the differential count value for each pixel is a difference between the count value of the each pixel and a count value of an adjacent preceding pixel and the differential count value for each pixel comprises both a sign and a magnitude component, and wherein a pixel without a preceding pixel keeps the count value of the pixel, and wherein each differential count value is associated with an initial differential count digital word; discarding from each initial differential count digital word a first number of most significant bits and a second number "d" of least significant bits, wherein the first number of most significant bits have the value of "0", and wherein the value of the first number is set equal to the number of zero value bits following the largest non-zero bit of the maximum differential count value magnitude from the class of image, and wherein, the second number "d" of least significant bits is set as a number of bits having a value less than a digital interval taking a value less than a product of an information reduction factor and a minimum differential uncertainty count value magnitude from the class of images. [0036] In a further embodiment, the method further comprises: selecting a threshold of differential count magnitude based on the known statistical characteristics of the class of images to which the image belongs, wherein a substantial majority of the differential counts have magnitudes less than the threshold magnitude; and representing each of the substantial majority of differential count values with a second bit word representing both the sign and the magnitude of the value.

[0037] In a further embodiment, the method further comprises: representing each of the differential count values having magnitudes equal to or exceeding the threshold with a third bit word representing both the sign and the magnitude of the value, wherein initial bits of the third bit word are set to a unique second bit word.

Brief Description of the Drawings

[0038] Figure 1 is a histogram of differential photoelectron counts for pixels in an example of a retinal image.

[0039] Figure 2 is a flow chart according to a method of the present invention to digitally represent an image.

[0040] Figure 3 is a schematic view of binary words used to encode pixels of an image according to an example of the present invention.

[0041] Figure 4 is a schematic view of an encoded row word map in accordance with an example of the present invention.

[0042] Figure 5 is a schematic view of an encoded frame word map in accordance with an example of the present invention.

[0043] Figure 6 is a flow chart according to a method of the present invention to reconstruct a digitally represented image. Detailed Description of Embodiments

[0044] Particular embodiments of the present invention will now be described with reference to the drawings. It will be understood by the skilled reader, however, that various modifications to the embodiments described herein are possible. Such modifications are intended to fall within the scope of the present invention, which is described by the claims.

[0045] The use of differential coding for efficient encoding is well known. It applies particularly to information from natural phenomena such as sound or images. The basic process is to have the image file hold the differences between the count values of adjacent samples (pixels) rather than the count values themselves. In order to quantify the applicability of differential coding to retinal images, differential histograms were created from a series of typical images.

[0046] Different biomedical images will have different characteristic statistics pertaining to the contrast and the spatial frequency content. Thus a retinal image using a photoelectron image sensor will differ from a cardiac image based on an acoustic probe or an MRI image of a kidney. Moreover the uncertainty values of pixel counts derived from an acoustic or MRI image sensor will be independent of the pixel count, unlike the uncertainty values derived from photoelectronic image sensors.

[0047] It is typical of biomedical and similar natural images that the contrast level is low. This is because there is substantial correlation between the count value of any pixel and other pixels in its proximate neighbourhood. This is the interrelationship between the count values that enables differential encoding to substantially reduce the size of the data words representing the image.

[0048] In the special case of images that are collected through the generation of photoelectrons, there is also an interrelationship between the pixel photoelectron count and the minimum value of the associated uncertainty in the count. Specifically, if the photoelectron count is "n", the uncertainty or standard deviation of the count cannot be less than the square root of n. This relationship also applies to images formed from X rays and ionizing radiation.

[0049] Figure 1 shows a typical differential histogram from a retinal image. It shows a close similarity to a normal distribution that can be characterized by a standard deviation and a mean that in this particular case of differential coding equals zero. The vertical scale shown is arbitrary.

[0050] The results from five such histograms are summarized in Table 2. The top row shows the mean photoelectron count per pixel for the entire image. The next row shows the mean quantum noise uncertainty per pixel. The next row shows the mean quantum noise uncertainty per differential pixel; this is a factor of V2 higher than the row above. The next row shows the standard deviation of the differential counts. The next five rows show the respective values below which 90%, 99%, 99.9%, 99.99% and 100% of the differential counts occur.

Table 2 Retinal image statistics

[0051] The ratios of the differential standard deviation (DSD) to the mean count per pixel of the images are all similar at about 2%. The mean differential quantum noise is typically 94% of the differential standard deviation. The largest differential counts (bottom row) are typically a factor of about nine greater than the standard deviation. [0052] The mean and minimum values of the differential uncertainty within the images can be obtained from a large body of data collected from the specific class of image. As biomedical photoelectronic images are characteristically of low contrast, the distribution of count values is clustered around the mean level and the minimum value of the differential uncertainty is not much less than the mean value of the differential uncertainty, where the value of the differential uncertainty is substantially equal to the square root of the sum of the two counts from adjacent pixels.

Digitally Encoding Images

[0053] Using the information outlining the statistics of the image, it is possible to design in detail an encoding arrangement that combines the discarding of least significant bits with the technique of differential encoding to achieve a substantial reduction in the bit count required to accurately represent the image.

ADC Quantization Interval and pre-ADC Gain

[0054] The ADC quantization interval and pre-ADC gain are usually set by the image sensor manufacturer and are beyond the control of the overall system designer. For the quantization not to significantly impact the information content, the associated quantization noise must be much less than the quantum noise inherent in the signal. This is generally the case. For example, Column 2 of Table 2 shows the minimum quantum noise as having a value of 69, whereas a typical scientific image sensor such as the PCO2000 has a quantization interval of 2.1 photoelectrons. From Equ. 8, this combination would then have a noise figure of only 0.003 dB, essentially zero. The pre-ADC gain should ideally be such that the quantization interval corresponds to a multiple of two photoelectrons, but this is not a critical requirement.

Post-ADC Minimum Interval

[0055] After the ADC, each pixel count is represented by a digital word that may be 16 bits in size. Similarly, after the differential process where the counts of adjacent pixels are subtracted, each differential counts is initially represented by a digital word of 16 bits.

[0056] The bit length can be greatly reduced at both ends of the word by discarding from the digital word a first number of most significant bits and a second number of least significant bits. The statistical values derived from each type of image and imaging equipment can be used to determine the number of bits to be discarded at either end of the differential word. In all cases, however, the maximum value of the differential pixel count from the class of images is used to determine the first number of most significant bits to be discarded and the minimum count value of the differential uncertainty from the class of images is used to determine the second number of least significant bits to be discarded.

[0057] Based on the large body of data collected from the specific class of image, the statistical distribution of the differential count values can be obtained, including a maximum value. Where this maximum value is represented by a bit word, the most significant non-zero bit can be identified. For this class of images, all most significant bits of the digital word representing powers of two greater than the aforementioned non-zero bit can be discarded.

[0058] For example, column 4 of Table 2 shows that the largest differential count has a value of 1378 corresponding to 2^Λ10.43. The most significant non-zero bit therefore represents a value of 2^Λ 10 or 1024. Therefore bits of value 2048 (2^Λ11) and above can be discarded for images within this class.

[0059] Moreover, a number of least significant bits may be determined to be discarded, in effect increasing the quantization interval. Column 2 of

Table 2 also shown that the minimum differential uncertainty count has a value of 98 that corresponds with 7 of the least significant bits, resulting in a worst case requirement for only 5 bits to represent a differential count being made up of a sign bit and 4 magnitude bits. For example, consideration of

Tables 1 and 2 shows the weakest image to occur with sample 2. This has a mean count of 4803 per pixel associated with a quantum noise level of 69. After the adjacent pixel count subtraction procedure, the associated quantum noise uncertainty level increases to 98. The ldB Noise Figure (NF) objective, corresponding to a linear noise factor of (NF/IO^IO or 1.26, would be achieved if the increased quantization uncertainty level were less than or equal to 50, satisfying the inequality 1 + (50/98) 2 < 1.26. Assuming a uniform probability of differential count value across the increased quantization interval, the quantization uncertainty can be shown and is well known to take a value of 1/V12 or 0.29 of the quantization interval. The differential count uncertainty is defined by the standard deviation of the said differential count from its mean value if the measurement were to be repeated many times. To achieve a quantization noise figure of less than ldB, the inequality 1 + (C/Q)^A2 < 1.26 must be satisfied where C is the quantization uncertainty value and Q the differential count uncertainty value. Moreover C = 0.29 I where I is the quantization interval . Combining these two requirements leads to the requirement that K 1.77 Q, where the factor 1.77 sets the level of information reduction. In the above example, this would indicate a requirement for the quantization interval to be less than 1.77 x 98 or 173 or 2^Λ7.44. The most significant bit is then 2^Λ7 (128) . Therefore the increased quantization interval is set to 128; in this case, the six least significant bits of the digital word can be discarded, and this results in a worst case NF of 0.6 dB.

[0060] While a lesser value of increased quantization interval may be chosen, further reducing the noise figure, the resulting word representing a pixel would be longer and the increase in image quality would be insubstantial.

[0061] The post ADC minimum interval should be maximized subject to maintaining an acceptable signal-to-noise ratio without needing to significantly raise the signal energy. A suitable target would be to have a NF of ldB associated with this minimum interval; this would require the optical signal level to be increased by 20% (0.8dB) to maintain the signal-to-noise ratio that would have been obtained without the minimum interval. [0062] If weaker images are encountered, e.g. from autofluorescence images, or if the incremental energy required to maintain the information content is to be made less than 20%, the minimum interval must be decreased. This would result in a small increase in the file size. Conversely, if more power is available, the file size could be slightly decreased.

Differential Pixel Word Size

[0063] Consideration of Table 2 shows that somewhere between 90% and 99% of the differential pixel counts could be defined by a 2-bit word with an interval of 128. In the proposed code, the two bits would represent the values of zero (00), + 128 (01) and -128 (10) where the "11" word would indicate a differential magnitude of 192 (1.5 intervals) or more.

[0064] Consideration of the table shows an approximately linear relationship between the logarithm of the complement of the various percentages, and the differential counts. From this relationship, the percentage corresponding to a differential count of less than 192 can be calculated. For the five data sets, this value ranges between 94.5% and 97.4% for a mean of 95.9%. This shows that a 2-bit word can define the differential pixel count for typically 95.9% of the image.

Accommodating the Outliers

[0065] To accommodate the 4.1% of pixels that cannot be represented with a 2-bit word (i.e., "outliers"), a word is added whenever an outlier occurs. Although the introduction of additional bits is counter-productive to efficient coding, the overall increase is small because this occurs only with a small proportion of the image. The presence of an outlier is identified by the 2-bit word being 11 indicating that the differential magnitude is equal to or in excess of 192.

[0066] As the largest differential magnitude indicated in the table has a value of 1378, if the LSB is 128, a word of at least five bits is required to accommodate all the outliers. For example, one bit could be assigned to the sign and the remaining four bits can address count values from 192 to 1920. [0067] Therefore, as preferred words have lengths in multiples of two, the preferred additional word would include one pad bit to bring it to 6 bits that when combined with the initial 2-bit word of "11" would result in an 8- bit word. Where 95.9% of the pixels required 2 bits and 4.1% required an additional 6 bits, the average number of bits required per pixel would only rise from 2.0 to 2.25, a small increase.

[0068] It is proposed to reserve the all-ones 4-bit word 1111 as a row marker. Therefore, the second bit of the additional outlier word is assigned as the pad bit and set to zero to avoid confusion with the row marker. The first bit of the additional word is the sign bit. The final four bits of value 128, 256, 512 and 1024 define the magnitude. Again, to prevent confusion with the row marker, the all-ones data sequence is disallowed, restricting the range to 1792. This still retains a good margin over the maximum differential count.

[0069] In summary, the code will assign 2-bit words to about 95.9% of the differential pixels and 8-bit words to the balance of outliers. The 8-bit word will consist of: 1,1, sign, 0, x, y, z, w where the latter four letters represent digits with the values of either zero or 128, 256, 512 or 1024.

[0070] Figure 2 illustrates a method of digitally representing an image belonging to a class of images. The image comprises a plurality of pixels, and each pixel has a count value with a level of uncertainty. The count values and uncertainty levels have statistical characteristics of the class of images to which the image belongs and neighbouring count values being substantially correlated. The statistical characteristics of the class of images is known from prior investigations. The class of the image belonging to comprises both the nature of the image and the equipment used to capture the image. In 202, the pixel count values of the image are converted into a digital form, for example, by an A/D converter, and quantization interval is substantially less than the uncertainty level. In 204, a differential process is applied to the count values by determining a differential count value for each of the plurality of pixels, wherein the differential count value for each pixel is a difference between the count value of the each pixel and a count value of an adjacent preceding pixel and the differential count value for each pixel comprises both a sign and a magnitude component, and wherein a pixel without a preceding pixel keeps the count value of the pixel, and wherein each differential count value is associated with an initial differential count digital word. For example, the initial differential count digital word may be 16 bits. In 206, the initial differential count digital word is compressed by discarding from each differential count digital word a first number of most significant bits and a second number "d" of least significant bits, these two numbers being determined and fixed for each class of image and not changing between images within the same class. In particular, the first number of most significant bits have the value of "0", and the first number of the most significant bits is determined from the value of the maximum differential count from the class of images that is represented by a bit word, such that the most significant bit has a non-zero value, and all bits representing powers of two greater than the said most significant non-zero bit are discarded; and a second number "d" of least significant bits represent a value substantially less than the minimum level of uncertainty known from the characteristics of the class of images to which the image belongs. For example, the first number of most significant bits may be 5 bits and the second number ^ed" of least significant bits may be 6 bits.

[0071] In 208, a threshold of differential count value is selected based on the known statistical characteristics of the class of images to which the image belongs, and the magnitudes of a substantial majority of differential count values less than the magnitude of the threshold value. For example, the first threshold may be selected to be higher than 90% of the differential count values. In 210, each of the substantial majority of differential count values is represented with a second bit word and a digital interval value. The digital interval value is less than or equal to 2^Λ (d + 1). In the case that the second number "d" of least significant bits is 6 bit, the digital interval value is 128. In 212, each of the differential count values having magnitudes equal to or exceeding the threshold is represented with a third bit word representing both the sign and the magnitude of the value, where initial bits of the third bit word are set to a unique second bit word. [0072] Figure 3 illustrates examples of the 2-bit words that can be used to represent the majority of differential counts of pixels, and the 8-bit words that can be used to represent the outliers. Word 301 is the word 'ΟΟ', which is used to represent a rounded differential pixel value of zero. Word 302 is the word ^ι0 , which is used to represent a rounded differential pixel value of +128. Word 303 is the word 'ΙΟ', which is used to represent a rounded differential pixel value of -128. Word 204 is the two-bit word '11', which indicates that the differential count of a pixel cannot be adequately represented by words 301, 302 or 303. Word 304 would be read in conjunction with the following six bits to form the 8-bit word 305, which represents the outlier pixel. Word 305 consists of: 1,1, sign, 0, LSB, B2, B3, MSB, where the latter four letters represent digits with the values of either zero or 128, 256, 512 or 1024.

Constructing the Words

[0073] The word containing the differential count is initially constructed by subtraction of the two 16-bit words holding the values of the adjacent pixels. The resulting word has no more than 10 bits, typically being less than 6 bits. Of these bits, those of value 64 and less will eventually be discarded leaving a 2-bit word containing the information of the sign, the magnitude plus or minus 128, or an outlier indication. However, the issue arises as to when to round up and when to round down. If this is not handled properly, a systematic error will build up during the subsequent image reconstruction phase.

[0074] The systematic error described above can be avoided by using a carry over process. The differential value should first be rounded to the nearest multiple of 128, the Least Significant Bit (LSB). If it is equidistant, it should be rounded to the direction opposite to that of the previous rounding. If there is no previous rounding, i.e., between the first two pixels of the row, and the differential value is equidistant it should be rounded down; this is an arbitrary choice.

[0075] The difference between the rounded value and the non-rounded value is then carried over to the next differential pixel count calculation. Clearly there is nothing carried over for use in the case of the first two pixels of a row, but there is a carryover value to be used in calculating the differential pixel count value between the 2^nd and 3^rd pixels and all subsequent pixel pair counts of the row.

[0076] This process is now described in a more formal manner. Let the pixel values be labeled Pi, P₂, P3 etc. where the subscript number indicates the pixel position in the row. These values are in a 16-bit format.

[0077] The first differential pixel value before rounding is given by:

This is still in a 16-bit format. However, one of the pad bits that would normally be zero should be assigned to be a sign bit. This could be the first or last bit of the 16-bit word. This is then rounded to the nearest multiple of 128 as described earlier. This will generate a 2-bit number. Let this number be labelled δι₂ :

δΐ2 = Round[A₁₂] Equ. 11

[0078] The carryover number C₁₂ is now calculated by subtracting thus:

The carryover value will lie anywhere between -64 and +64. It will consist of a sign bit and six other bits, padded with one bit to create an 8-bit word.

[0079] The next differential pixel value is given by:

Δ₂₃ = P₂ - P₃ Equ. 13

[0080] From this, the next 2-bit differential pixel value δ₂₃ is calculated thus : δ₂₃ = Round[A₂₃ + C12] Equ. 14 [0081] Then the next carryover term C₂₃ is given by:

C₂₃ = Δ₂₃ - δ₂₃ + Ci2 Equ. 15

[0082] Generalizing, for i = 1 to Col (the number of pixel columns) and

Διπ+ιι - Pi - P (i + l) Equ. 16

(i-_l)i — Δ(ί-ΐ)ί - δ(|-ΐ)ΐ + C(i-2)(i-_l) Equ. 17 δ_ί(ί+_ΐ) = Round[A_i(i+1) + C_(l-i)i] Equ. 18

[0083] The carryover at the end of the row is not used.

[0084] While the above arrangement is sound, there may be ways of achieving the same result more efficiently with respect to computing resources.

[0085] Figure 4 shows a schematic view of an example of an encoded row of pixels. The row consists of a row marker 401 which, in the present embodiment, is the 4-bit word ΊΙΙ . Next the 16-bit word 402 appears, which corresponds to the pixel value (non-differential) of the first pixel of the row. Next, words 403 each comprise binary words representing the differential pixel value of each subsequent pixel in the row. Words 403 can a 2-bit word 301, 302 or 303, and/or a 4-bit word, and/or a 8-bit word 305, depending on the value of the differential pixel count value within a selected confidence intervals, and the minimal interval value.

The Frame Structure

[0086] It is proposed that the image be constructed on a row-by-row basis starting at the top left. However, it will be understood that this selection is arbitrary, and that images may be constructed on a column-by- column basis as well.

[0087] The first word can be a row marker of four consecutive l's. Next, the first pixel value can be transmitted in full in a 16-bit word. The subsequent words can consist of the differences between adjacent pixel values as defined above. The process is repeated for each row.

[0088] At the end of the final row, two consecutive row markers are sent to indicate the end of the frame (not shown in Figure 4).

[0089] An example of the entire frame word map is shown in Figure 5. The frame begins with a frame marker 501, which in the described embodiments comprises the 8-bit word Next, a row or column marker word 401 is included to indicate the beginning of a row or column of pixels. Then, a 16-bit word 402 is included to indicate the pixel value (non- differential) of the first pixel in the row or column. Then, a series of words 403 are included to indicate the differential pixel value of each subsequent pixel in the row or the column. Once all pixels in the row or column have been described, a row or column marker 401 is inserted to indicate the beginning of the next row or column. The pattern continues until each row of the frame has been fully described. Once the final pixel of the final row or column has been described, two consecutive row/column markers are included, which indicates the end of the frame.

Image Reconstruction

[0090] The image reconstruction process is relatively simple. After the first row marker is identified, the first pixel value is given by the next 16-bit word. The second pixel value is given by adding to the first pixel value the decoded 2-bit word that comes next. This process is repeated until the end of the row. If the 2-bit word is the outlier marker 11, this and the following 6-bit word are used to calculate the interval value to determine the next pixel value.

[0091] Figure 6 describes a method for reconstructing an image comprised of pixel count values and pixel locations from a bit sequence comprising a frame marker, column or row marker, and bit words representing the pixels of the image as described above. In 602, the method identifies a frame marker and a row or column marker from the bit sequence. In 604, immediately after a row or column marker a first pixel is identified. In 606, from the associated bit word identified form the bit sequence, a differential count value for the first pixel is decoded and calculated. In 608, the method determines whether a subsequent pixel count value is represented by a bit word with a different number of bits from that of a preceding bit word by determining whether the unique bit word is present to determine whether the subsequent bit word is a longer bit word. In 610, the differential count value for the subsequent pixel from the associated subsequent bit word is decoded and calculated. In 612, the associated differential count value for the subsequent pixel is added to the preceding pixel count value to reconstruct the count value of the subsequent pixel.

Handling Low-level Images

[0092] The coding arrangements described above will work well with retinal reflection images having pixel count values of over 4000. However, they may be unsuitable for use with images where the mean pixel counts may have values as low as 100. Moreover, as the light level decreases, the resolution limit is increasingly set by the readout noise of the sensor. Readout noise may typically be 9 photoelectrons. This will be the largest noise source for pixel photoelectron counts of less than 81 photoelectrons.

[0093] In addressing this, we first estimate the magnitude of the pixel count below which the coding scheme described above would not be satisfactory. For this, a criterion of an increase of noise level of ldB over the quantum limit is suggested, this increase being a result of the quantization noise level of 128/V12 = 37. The quantum noise level resulting in such an increase would take a value of 51.3. This in turn would imply a pixel count value of 2632. Therefore, an adaptation of the coding plan is needed to handle images with mean pixel photoelectron counts of less than 2632.

[0094] It is proposed that the low level images should be substantially handled with the 2-bit word as before, but the minimum interval should be reduced from 128. Consider first the capabilities and limitations of using an interval of 32. The 2-bit words would then handle differential values between

-48 and +48, while the 8-bit outlier word would handle differential magnitudes up to 448. The resulting interval quantization uncertainty would be 32/V12 = 9.2. The combination of readout noise and quantum noise consistent with a quantization noise figure of less than ldB would then equal 18. Assuming the readout noise level of 9e, the pixel photoelectron count would need to be at least 244.

[0095] Assuming similar statistics to those in Table 2, the use of an interval of 32 can handle images with mean pixel photoelectron counts of up to 2000. If weak images with counts above 2000 but below 2768 need to be handled, an interval of 64 would be appropriate. Similarly, if very weak images with counts less than 96 need to be handled, an interval of 16 would be appropriate.

[0096] The first pixel of each row should be represented by a 16-bit word as before.

[0097] It is important to identify when the lower level process is required for efficient encoding and if it is present when image reconstruction is required. One option is to define a priori that certain images are at low levels and carry out the encoding and reconstruction routines accordingly. Another option is for the encoding algorithm to initially calculate the mean count value per pixel and assign the lower level process if this value is below 2000. In this case, the a priori knowledge would only be needed at the reconstruction stage. A third option would be to assign a bit within the image envelope information indicating whether the high or low level encoding scheme is used. This assignation could either be dependent on the mean pixel count value or set a priori.

Error Handling

[0098] If an error is made in reading a word, the effect of the error will propagate along the remainder of the row. However, the renewal of the differential coding at the start of each row contains the error spread, preventing further propagation. The existence of an error within a row could be detected by means of the addition of a parity check word or a Cyclic Redundancy Check (CRC) overhead. This could be used to request a re-read of the row. The simpler parity check will fail if there is an even number of errors.

[0099] The encoding and reconstruction arrangements described are simple in computing terms and will not require much processing time. If the computing hardware is sufficiently fast, they would be compatible with realtime video applications. Moreover they are lossless in the sense of neither adding nor subtracting information that cannot be fully compensated for by a small increase in signal energy. Typically, the impact on the image is equivalent to uniformly reducing the image energy by 20%.

[00100] Unlike lossless data compression schemes, the scheme described in the present invention dispenses entirely with modeling and is essentially a coding process. The reduction to 2.25 bits/pixel represents a better performance than is typically achieved using lossless JPEG-LS.

[00101] The encoding principles used are well matched to exploit the characteristics of retinal images captured by a digital camera. These principles allow even greater efficiencies to be achieved but at the cost of more complexity. For example, instead of breaking the data into two groups one of 2-bit words and one of 8-bit words, they may be split into three groups, 2-bit, 4-bit and 8-bit words. They may be applied to other types of image wherever a significant amount of correlation is present between adjacent pixel values and where the image pixel values have uncertainties.

[00102] While the ldB noise criterion has been used extensively in the description, the invention may also work with a wide range of quantization noise figure and minimum interval noise figure values.

[00103] While the invention is directed towards the efficient encoding of retinal images, it may also be applied to any type image where the recorded pixel count levels include a random noise component. This could for example apply to acoustic, X ray and MRI images.

Claims

1. A method of digitally representing an image belonging to a class of images, the image comprising a plurality of pixels, each pixel having a count value with a level of uncertainty, the count values and uncertainty levels having known-statistical characteristics of the class of images to which the image belongs and neighbouring count values being substantially correlated, the method comprising: converting the pixel count values of the image into a digital form wherein the uncertainty level introduced by quantization is substantially less than the count uncertainty level; determining a differential count value for each of the plurality of pixels, wherein the differential count value for each pixel is a difference between the count value of the each pixel and a count value of an adjacent preceding pixel and the differential count value for each pixel comprises both a sign and a magnitude, and wherein a pixel without a preceding pixel keeps the count value of the pixel, and wherein each differential count value is associated with an initial differential count digital word; discarding from each initial differential count digital word a first number of most significant bits and a second number "d" of least significant bits, wherein the first number of most significant bits has a value of "0", and wherein the value of the first number is set equal to the number of zero value bits following the largest non-zero bit of the maximum differential count value magnitude from the class of image, and wherein, the second number "d" of least significant bits is set as a number of bits having a value less than a digital interval taking a value less than a product of an information reduction factor and a minimum differential uncertainty count value magnitude from the class of images.

2. The method of claim 1, representing each differential count value further comprising: selecting a threshold of differential count magnitude based on the known statistical characteristics of the class of images to which the image belongs, wherein a substantial majority of the differential counts have magnitudes less than the threshold magnitude; and representing each of the substantial majority of differential count values with a second bit word representing both the sign and the magnitude of the value.

3. The method of claim 2, further comprising: representing each of the differential count values having magnitudes equal to or exceeding the threshold with a third bit word representing both the sign and the magnitude of the value, wherein initial bits of the third bit word are set to a unique second bit word.

4. The method of claim 2 or 3, wherein the digital interval value is less or equal to 2^Λ (d +1) where d is the number of discarded least significant bits.

5. The method of claim 1, wherein the initial differential count word has 16 bits of which the most significant 5 bits and the least significant 6 bits are discarded, and wherein the first bit word comprises 5 bits representing a differential count value comprising 1 sign bit and 4 magnitude bits.

6. The method of claim 1, wherein the initial differential count word has 16 bits of which the most significant 7 bits and the least significant 4 bits are discarded, and wherein the bit word m comprises 5 bits representing a differential count value comprising 1 sign bit and 4 magnitude bits.

7. The method of claim 2 or 4, wherein the second bit word comprises two bits representing a sign and a magnitude with a digital interval of 128.

8. The method of claim 2 or 4, wherein the second bit word comprises two bits representing a sign and a magnitude with a digital interval of 32.

9. The method of claim 3, wherein the third bit word is further augmented by at least a padding bit to distinguish the differential count word from a row marker word.

10. The method of claims 2 to 9, wherein the first two bits of the first bit word comprise a sequence 00 representing a difference of 0, a sequence 01 representing a difference of plus one digital interval, a sequence 10 representing a difference of minus the one digital interval, and a sequence 11 being a unique word identifying the start of the longer bit word.

11. The method of claim 9, wherein the third bit word comprises 5 bits, and wherein the third bit word is prefixed by 2 unique bits and further augmented by 1 padding bit to extend it to 8 bits.

12. The method of claim 11, wherein the two bits are "11", and the padding bit is "0".

13. The method of claim 1, wherein the method is carried out row by row.

14. The method of claim 1, wherein the method is carried out column by column.

15. The method of any one of claims 1 to 14, wherein serial aggregation of differential count values are added frame markers and row or column markers and wherein each row or column marker is immediately followed by a full length pixel count value.

16. The method of any one of claims 1 to 15, wherein the rounding error associated with creating a differential count value word is carried forward such that in the determination of the value to be attached to the next pixel, the cumulative contribution of rounding errors is substantially zero.

17. The method of claim 1, wherein the image is created using an image sensor and wherein a quantity of photoelectrons is generated at each pixel location, this quantity being the count value of the pixel.

18. The method of claim 1, wherein the image comprises a biomedical image.

19. The method of claim 1, wherein the image comprises a retinal image.

20. The method of claim 1, wherein the class of the image belonging to comprises both the nature of the image and the equipment used to capture the image.

21. The method of claim 1, wherein within the class of image, the digital interval is maximized subject to taking a value less than the minimum standard deviation uncertainty value multiplied by an information reduction factor of 1.77, and the first number of least significant bits equals the number of bits of value less than the said digital interval.

22. The method of claim 3 or 9, wherein each bit of the unique second bit word comprises "1".

23. A method for reconstructing an image comprised of pixel count values and pixel locations from a bit sequence comprising a frame marker, column or row marker, and bit words according to claims 1 to 21, comprising: identifying a frame marker and a row or column marker; identifying a first pixel immediately after a row or column marker; decoding and calculating a differential count value for the first pixel from the associated bit word; determining whether the subsequent pixel count value is represented by a bit word with a different number of bits; decoding and calculating a differential count value for a subsequent pixel from the associated bit word; and adding the associated differential count value for the subsequent pixel to the preceding pixel count value.

24. The method of claim 23, further comprising detecting a parity check word.

25. The method of claim 23, further comprising detecting a Cyclic Redundancy Check overhead.

26. An encoding apparatus, comprising: a memory; and a processor, wherein the processor is configured to perform the method of any one of claims 1 to 22.

27. A decoding apparatus, comprising: a memory; and a processor, wherein the processor is configured to perform the method of any one of claims 23 to 25.