Repeated polygonal shapes or repeated colours are sources of visual patterns. Another important source of patterns are the presence of convex sets and convex hulls in digital images, especially in naturally camouflaged or in artificially camouflaged objects . A set A is convex provided the line segment connecting any points A is contained in A. A convex hull is the smallest convex set containing a set of points (see the attached image). Also, see the many convex sets in the natural camouflage of the dragon in the attached image and in
http://www.google.ca/url?sa=t&rct=j&q=&esrc=s&source=web&cd=14&ved=0CCQQFjADOAo&url=http%3A%2F%2Fdl.mycommerce.com%2Fwgt%2F9f3a1646c2829ec59a8eb14e75c5ff39%2F1b8198605693ddfd3bcf98d46a2be20f%2Frn_v43325%2F0521199115_0521152577_Animal.pdf&ei=1qLdU6blI8KzyAS02ICYDg&usg=AFQjCNF92EF4zkYvByBaskyvTu8m46m6Lg&bvm=bv.72197243,d.aWw
Convex sets have many applications in the study of digital images. For example, convex sets are used in solving image recovery problems:
https://www.ljll.math.upmc.fr/~plc/ip2.pdf
and in image restoration:
https://www.google.ca/search?as_q=math+digital+images&as_epq=convex+sets&as_oq=&as_eq=&as_nlo=&as_nhi=&lr=&cr=&as_qdr=all&as_sitesearch=&as_occt=any&safe=images&tbs=&as_filetype=&as_rights=&gws_rd=ssl
Convexity recognition is useful in object shape analysis in digital images:
http://www.ee.oulu.fi/mvg/files/pdf/pdf_513.pdf?origin=publication_detail
Another important application of convexity is rooftop and building detection in aerial images:
http://www3.stat.sinica.edu.tw/statistica/oldpdf/A19n45.pdf
As with salience I do not see much future in characterising patterns by pre-selected features; there are always unseen patterns that don't fit any training that has taken place.
To discover salient patterns in pictures, you may want to consider the semantic distance between patterns as a means salient patterns. The notion of semantic distance comes from a 1962 article by Alt (I will dig out the reference or send you a copy of Alt's article, if you are interested). In terms of feature selection, a lot depends on what we are looking for. For many pattern-based picture classification problems, shape features work well at the pixel gradient orientation level.
Best,
Jim
Yes I would be very interested in the Alt reference. Features are OK if you know what you are looking for. Idesa run out after a while I find.
Dear Professor Stentiford,
Good morning from Winnipeg at sunrise time.
I just now sent you a copy of Alt's 1962 article. The BibTeX for article is in a sticky
note at the top of page 1.
Best,
Jim
Jim, Thanks for the paper
It is interesting that the problems in 1962 are still with us! One of the problems in feature spaces is that they restrict solutions. A may be similar to B and B similar to C. The metric in a feature space often forces A to be similar to C but this may not actually be the case.
Regards
Fred
Fred, many thanks for your observation.
One way round the problem you mention is to consider the problem of selecting salient features, restricting the selection to features that help us avoid set pattern generation instability. That is, we need to select features that inhibit the generation of patterns that drift or wander away from a set pattern motif (every set in a stable pattern will be sufficiently near a set called the pattern motif).
I agree with you that feature spaces do restrict solutions. Perhaps restricted solutions are desirable. The transitivity problem that you mention will not go away,
however. In general, similarity is defined by a tolerance relation rather than a more desirable equivalence relation.
Best,
Jim
I have read that salient image region detectors are promising with small set of data with low resolution of images. Therefore, if we need to apply these detectors on high resolution images, it is highly required to downscale images for better processing and detecting.
Hasan:
Salient image regions in both low and high resolution images can be detected in a satisfactory manner, provided we define saliency in terms of "sufficient nearness".
To do this, we need to consider the original suggestion by Alt in 1962 and define a similarity distance between sets of picture points (identified with picture regions). A region that is close enough to a region-of-interest would be considered salient. This approach to saliency should work, independent of image resolution.
Prof. James Peters:
Thank you for the clarification. Allow me please to quote your answer for another question by different researcher about the Salient detectors for large data with high resolution images.
Hasan:
Yes, of course, you can quote my answer. Sometimes things are easier said than done (wise folk saying). Ultimately, detecting largescale salient patterns in pictures stems from a comparison of picture point (pixel) feature values. A satisfactory saliency detection method for largescale pictures usually requires parallel programing (see, e.g., the SIP 2013 paper coauthored by Chris Henry and several others).
@Hasan Hadi Khaleel: it is highly required to downscale images for better processing and detecting.
Downscaling digital images can be accomplished in a number of ways. One of those ways is to detect and analyse the presence of convex shapes such as parallelograms in digital images. This process is described on page 1454 in
X. Huoo, X. Ni, Detectability of convex-shaped objects in digital images, its fundamental limit and multi scale analysis, Statistica Sinica 19, 2009, 1439-1462:
http://www3.stat.sinica.edu.tw/statistica/oldpdf/A19n45.pdf
Dear James Peters,
Yes, there are many applications of convexity, or convex sets, which sounds very similar to Christopher Alexander's positive space, one of the 15 structural properties he developed in The Nature of Order: http://en.wikipedia.org/wiki/The_Nature_of_Order
People tend to perceive things from this perspective of convexity in order to see identifiable pieces of a whole. This perspective (focusing on individuals) however is somehow contradictory to the holistic (or fractal) perspective. For example, drop a wine glass on the ground, and it is very likely broken into many pieces. These many pieces are actually mixed up with convex and concave ones. This mixed up is the same for natural cities we identified or detected using massive geographic information; see related paper: http://arxiv.org/ftp/arxiv/papers/1501/1501.03046.pdf
Having said so, may I draw a tentative conclusion as such? The perspective of convexity is Euclidean, focusing on individual, relying on human perception, whereas the fractal or holistic perspective is not necessary to be convex only, but mixed up with convex and concave ones. For example, the math snowflake is concave in essence, and is made of many convex triangles of course.
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