GB2480065A

GB2480065A - Determining the porosity of dyed geological samples by analyzing colour images of the samples

Info

Publication number: GB2480065A
Application number: GB1007404A
Authority: GB
Inventors: Barrie Trevor Wells; Ricki Paterson Walker
Original assignee: CONWY VALLEY SYSTEMS Ltd
Current assignee: CONWY VALLEY SYSTEMS Ltd
Priority date: 2010-05-04
Filing date: 2010-05-04
Publication date: 2011-11-09
Anticipated expiration: 2030-05-04
Also published as: GB2480065B; GB201007404D0

Abstract

A method of analysis of an electronic image of a sample is disclosed. The method comprises: identifying manually a first set of elements within the image that have a colour value that indicates a corresponding area of an imaged object meets a required criterion and a second set of elements within the image that have a colour value that indicates a corresponding area of an imaged object does not meet the required criterion. Then, the colour space of the image is divided into two corresponding regions 10, 12. An automatic analysis of the image is then performed to determine which of its elements fall within the first region or second region of the colour space and thereby identify which areas of the sample meet the required criterion. The method has particular application to the petrographic analysis of the porosity of rock samples that have been dyed. The criterion is that sufficient dye has been absorbed by the sample to indicate that it has porosity.

Description

Analysis of geological samples This invention relates to the analysis of geological samples. It has particular, but not exclusive, application to the petrographic aialysis of the porosity of samples of rock to quantify their porosity.

As the worldrs freely-available reserves of hydrocarbons (particularly, oil and gas) and other deposits diminish, sparse reserves, which might hitherto have been considered too expensive or difficult to exploit, are now considered valuable. Therefore, there is an increasing demand for accurate assessment of samples taken during exploration for new sites from which oil can be extracted.

A technique commonly used is to take a thii section of rock, effectively a two-dimensionth slice through a sample of rock, and examine it using various techniques, mostly manual, to determine the sectionTs properties. The properties of the section are then considered to be representative of the properties of the rock in bulk.

One property of importance in many applications, including ground water and pollution monitoring, as well as in exploration of exploitable resources, is porosity of the rock. When a thin section is dyed, the dye is taken up by pore space within the section. It is then possible to analyse an image of the rock to estimate how much of the image has a colour that corresponds to that of the dye, which provides an initial estimate of the porosity of the rock. This process can be automated by using software on a computer to count pixels in the image that are a colour similar to that of the dye.

However, differential take-up of the dye, the presence of rocks of a colour similar to that of the dye, and partial take-up in microporosity, amongst other reasons, mean that a simple automated image analysis would provide a crude estimate of the porosity at best. Analysis of the image by a human expert can provide a significantly better result, but this is a very labour-intensive procedure, which is therefore slow and expensive.

An aim of this invention is to provide a method and system for performing an analysis of a rock sample to establish its porosity that achieves a more accurate result with a greater degree of automation than has been possible using conventional techniques.

To this end, from a first aspect, the invention provides a method of analysis of an electronic image of a sample, in which the image comprises a plurality of image elements each of which has a colour value within a colour space that corresponds to the colour of a respective area of the object, the method comprising: a. identifying manually a first set of elements within the image that have a colour value that indicates a corresponding area of an imaged object meets a required criterion; b. identifying manually a second set of elements within the image that have a colour value that indicates a corresponding area of an imaged object does not meet the required criterion; c. dividing the colour space into a first region that corresponds to colour values that indicate a corresponding area of an imaged object meets the required criterion and a second region that corresponds to colour values that indicate a corresponding area of an imaged object does not meet the required criterion; and d. performing an automatic analysis of the image to determine which of its elements fall within the first region of the colour space and which elements fall within the second region of the colour space and thereby identify which areas of the sample meet the required criterion.

Steps a. to c. have the effect of training the system what to look for in a sample, whereby an automatic analysis of the whole sample can be performed in step d. The invention allows the accuracy of an analysis performed by a human expert to be effectively extended to a far greater area of the sample than would otherwise be practical or economically justified.

In typical embodiments, the colour values are within a three-dimensional colour space, such as the RGB colour space. Preferably, between steps b. and c., the three-dimensional colour space is mapped into a two-dimensional space, which is subsequently partitioned in step c.

This mapping may be performed using a chromaticity mapping, such as the CIE 1931 XYZ colour space. In some embodiments, the mapping may be done in a simpler space of lower dimension.

Each element of the image may include a single image pixel, or it may include a plurality of pixels. In the latter case, the colour value may correspond to a function of the colour values of each of the pixels in the image element.

In step c., the colour space may be divided into respective regions each of which corresponds to a superset of the colour values of each of the first and second sets of elements identified in steps a. and b. For example, each region may be bounded by a convex hull that surrounds a respective one of the first and second set of elements identified in steps a. and b.

If the regions identified in step c. are found to overlap, then an adjustment step is performed to remove the overlap. For example, this may be done by manual correction of one or more of the sample elements identified in steps a. or b. Step c. is then repeated on the corrected sample elements.

This invention has particular application to analysis of an image of a sample of rock that has been dyed. The required criterion is that sufficient dye has been absorbed by the sample to indicate that it has porosity, this typically being indicated by the depth of colour in the sample that is produced by absorption of the dye.

From a second aspect, this invention provides a computer software application operative, when executed on a computer, to perform a method embodying the first aspect of the invention.

From a third aspect, the invention provides a computer system comprising computer hardware and software embodying the second aspect of the invention.

An embodiment of the invention will now be described in detail, by way of example, and with reference to the accompanying drawings in which: Figure 1 is a representation of a stained sample of rock to be analysed; and Figure 2 is a monochromatic representation of a chromaticity diagram showing points collected during a sampling process and resulting partitioning of the colour space represented in the diagram in an embodiment of the invention.

To perform an analysis using an embodiment of the invention, a sample of rock to be analysed is stained in a manner that is conventionally used in petrography. This stains porous parts of the sample blue. A digital image of the sample is then captured that is encoded in an RGB colour space, and processed by software.

An example of such an image is shown in Figure 1. Areas indicated at "B" are strongly coloured blue, and are identified by a petrographer to have absorbed sufficient dye to be identified as sufftciently "blue" to be considered as being pore space.

An overview of an analysis process using an embodiment of the invention is as follows.

a. software causes an image such as that shown in Figure 1 to be displayed to a petrographer on a visual display unit; b. the software then allows the petrographer to identify a sample of points within the image as being "porous" or "not porous"; c. from the sample of points identifted by the petrographer, the software analyses colour values of a set of pixels within the image that correspond to points in a set P that have been identified as porous and colour values of a set of pixels within the image that correspond to points in a set N that have been identified as not porous; d. regions are identified within a colour space containing the pixels of the image that contain, respectively, pixels corresponding to porous and not-porous points; and e. other pixels in the image are analysed to determine to which region of the colour space they belong and, by implication, to determine whether the corresponding point in the image represents a porous or non-porous region of the sample.

Therefore, the method expands the manual analysis of an expert petrographer of a small number of points to an automatic analysis of a larger number of points.

The analysis tool used to apply this technique is a "chromaticity diagram". These diagrams represent a mathematically defined colour space, created by the International Commission on Illumination (CIE) in 1931, called the CIE 1931 XYZ colour space. This colour space is used to map points in a 3-dimensional (R-G-B) space to a 2-D (x-y) space.

Operation of this embodiment uses a number of techniques to partition this 2-D space into two regions -one of which indicates sufficient colouration to indicate "porosity", and the other indicates that there is insufficient dye, thereby indicating "non-porosity". The image of the sample can then be analysed to determine what proportion of it would be determined as being porous.

The input to the algorithm can be derived from the set of points obtained from a petrographic point-counting process performed by an expert analysing a sample using conventional techniques. Alternatively, it can be derived from a petrographer performing a similar analysis of an image, but with the sole intention of generating an input set for further processing in the invention. In either case, each of these points has been classified by the petrographer, and as such can be described as being a "porosity" point or a "non-porosity" point. Also, each point has associated with it an image pixel, namely the pixel under the crosshair displayed on the visual display unit for which the classification was made. The Red (R), Green (G) and Blue (B) colour values that uniquely define the colour of this pixel are coordinates of the pixel in a 3-dimensional (RGB) colour space.

Mathematical transformations are applied to convert these R-G-B coordinates first into an X-Y-Z triplet and then a 2-D (x-y) pair. There are many different mathematical models that can be used to transform R-G-B coordinates into X-Y-Z triplets. This embodiment uses a linear matrix transformation model of the form R A11 42 43 X G = A21 A22 A23 Y B A31 42 A33 Z and the related inverse transformation. The values of the coefficients in the linear transformation matrix are determined by the chromaticity coordinates and the luminance component of the primaries in the colour system. Luminance values are determined from a set of base colours together with a simplifying assumption. The final step is then to define the relationship between X-Y-Z and R-G-B coordinates, as a matrix relationship between R (the R-G-B matrix), C (a conversion matrix) and T (the tn-stimulus matrix), of the form R=C*T The coefficients of the conversion matrix C can then be derived analytically from a given set of initial conditions. Experiments are used to derive different sets of conversion matrix coefficients that should be used for different types of rock sample images to achieve the best results in terms of porosity determination for each sample.

The set of 2-D (x-y) points, one for each of the points as classified by the petrographer, are plotted within the 2-D space of the chromaticity diagram. As shown in Figure 2, the points classified as "porous" are grouped at 12 and those that are classified "not porous" are grouped at 10.

The next stage of the process is to partition this 2-D space into a "porosity" space and a "not-porosity" space. This can be achieved in a number of different ways in different embodiments of the invention.

In a first embodiment, the process forms a convex hull -indicated at 20 in Figure 2 -of P (of the set of "porosity" points) and a convex hull -indicated at 22 in Figure 2 -of N (of the set of "non-porosity" points) and to use these sets as a starting point for forming the partition. If the convex hulls overlap, then the attention of the user is drawn by the software to those points that lie within the region of overlap, and the user is given the opportunity to re-classify some or all of these points as being porous or non-porous. (For instance, one or more of the points may have been incorrectly classified by the petrographer, and this erroneous classification could be the cause of the overlapping convex hulls.) Once any overlap is resolved, it is then possible to classify every single image element as indicating "porosity" or "non-porosity". The convex hulls can be used to classify a pixel in more than one way. One option is that if an image pixel lies within the convex hull of P, then it is classified as "porosity", and similarly for N and "non-porosity". There are likely to be some pixels that do not lie in either of the convex hulls. In this instance, for each of these points, a petrographer is presented with the option of classifying the point as representing "porosity" or "non-porosity", and this information is used to expand the convex hulls accordingly. Alternatively, each pixel can be classified according to which of the two convex hulls it lies nearest to in the 2-D chromaticity diagram. This alternative method leaves no pixels unclassified. In both cases, every image pixel is classified as representing "porosity" or "non-porosity", and as a result the entire image is classified. The same classification can be applied to images of further samples. Provided that the further samples are sufficiently similar to that from which the training set was derived, then the existing partitioned colour space can be reused, so avoiding the need for further manual input.

In alternative embodiments, the 2-D chromaticity diagram can be partitioned using a Delaunay triangulation based approach. The union of the sets P and N (as defined above) is triangulated using a standard Delaunay triangulation algorithm. An algorithm as described in the paper "Output-Sensitive Algorithms for Computing Nearest-Neighbour Decision Boundaries" (by Bremner et a!.) is applied in order to compute a boundary line that partitions the space. The triangles forming the Delaunay triangulation of the union of the sets P and N are classed as being bichromatic if they contain a bichromatic Delaunay edge, i.e., an edge of the triangle has one vertex from the set P and the other from the set N. The set of bichromatic Delaunay edges is obtained from the complete Delaunay transformation, and then an image element is classified using a nearest-neighbour decision rule with relation to this boundary line.

Claims

Claims 1. A method of analysis of an electronic image of an object, in which the image comprises a plurality of image elements each of which has a colour value within a colour space that corresponds to the colour of a respective area of the object, the method comprising: a. identifying manually a first set of elements within the image that have a colour value that indicates a corresponding area of an imaged object meets a required criterion; b. identifying manually a second set of elements within the image that have a colour value that indicates a corresponding area of an imaged object does not meet the required criterion; c. dividing the colour space into a first region that corresponds to colour values that indicate a corresponding area of an imaged object meets the required criterion and a second region that corresponds to colour values that indicate a corresponding area of an imaged object meets the required criterion; and d. performing an automatic analysis of the image to determine which of its elements fall within the first region of the colour space and which elements fall within the second region of the colour space and thereby identify which areas of the sample meet the required criterion.
2. A method according to claim 1 in which the colour values of the image are within a three-dimensional colour space, such as the RGB colour space.
3. A method according to claim 1 or claim 2 in which, between steps b. and c., the three-dimensional colour space is mapped into a two-dimensional space, which is subsequently partitioned in step c.
4. A method according to claim 3 in which the mapping may be performed using a chromaticity mapping, such as the CIE 1931 XYZ colour space.
5. A method according to any preceding claim in which each element of the image includes a single image pixel.
6. A method according to any one of claims 1 to in which each element includes a plurality of pixels.
7. A method according to any preceding claim in which, in step c., the colour space is divided into respective regions each of which corresponds to a superset of the colour values of each of the first and second set of elements identified in steps a. and b.
8. A method according to claim 7 in which each region is bounded by a convex hull that surrounds a respective one of the first and second set of elements identified in steps a. andb.
9. A method according to any preceding claim in which, if the regions identified in step c. are found to overlap, then an adjustment step is performed to remove the overlap.
10. A method according to claim 9 in which the adjustment step includes manual correction of one or more of the sample elements identified in steps a. or b.
11. A method of analysis of an electronic image of a sample substantially as herein described with reference to the drawings.
12. A method of analysis of an electronic image of a sample of rock that has been dyed.
13. A method of analysis of an electronic image of a sample of rock according to claim 12 in which the required criterion is that sufficient dye has been absorbed by the sample to indicate that it has porosity, this being indicated by the depth of colour in the sample that is produced by absorption of the dye.
14. A computer software application operative, when executed on a computer, to perform a method according to any preceding claim.
15. A computer system comprising computer hardware and software according to claim 14.AMENDMENTS TO CLAIMS HAVE BEEN FILED AS FOLLOWS1. A method of analysis of a sample of rock by making an electronic image of the sample, the image comprising a plurality of image elements each of which has a colour value within the RGB colour space that corresponds to the colour of a respective area of the sample, the method comprising: a. identifying manually a first set of elements within the image that have a colour value that indicates a corresponding area of the sample meets a required criterion; b. identifying manually a second set of elements within the image that have a colour value that indicates a corresponding area of the sample does not meet the required criterion; c. mapping the colour space into a two-dimensional colour space; d. dividing the two-dimensional colour space into a first region that corresponds to colour values that indicate a corresponding area of the sample of rock meets the required criterion and a second region that corresponds to colour values that indicate a corresponding area of the sample of rock does not meet the required criterion; and e. performing an automatic analysis of the image to determine which of its elements fall within the first region of the two-dimensional colour space and which elements fall within the second region of the colour space and thereby identify which areas of the sample meet the required criterion.2. A method according to claim 1 in which the mapping is performed using a chromaticity mapping.3. A method according to claim 2 in which the two-dimensional colour space is the CTE 1931 XYZ colour space.4. A method according to any preceding claim in which each element of the image includes a single image pixel.5. A method according to any one of claims 1 to 3 in which each element includes a plurality of pixels.6. A method according to any preceding claim in which, in step d., the colour space is divided into respective regions each of which corresponds to a superset of the colour values of each of the first and second set of elements identified in steps a. and b.7. A method according to claim 6 in which each region is bounded by a convex hull that surrounds a respective one of the first and second set of elements identified in steps a. and b.8. A method according to any preceding claim in which, if the regions identified in step d. are found to overlap, then an adjustment step is performed to remove the overlap.9. A method according to claim 8 in which the adjustment step includes manual correction of one or more of the sample elements identified in steps a. or b.10. A method of according to claim 9 in which the required criterion is that sufficient dye has been absorbed by the sample to indicate that it has porosity, this being indicated by the depth of colour in the sample that is produced by absorption of the dye.11. A method of analysis of a sample of rock substantially as described herein with reference to the accompanying drawings.12. A computer software application operative, when executed on a computer, to perform a method according to any preceding claim.13. A computer system comprising computer hardware and software according to claim 12. (\J (\J (\J