At this point, each crack-network (connected curve) is assumed to represent a meaningful object-of-interest as far as content-based analysis is concerned and this representation is
called a sub-object. A question at this point is whether the sub-object is sufficient to describe a meaningful pattern. Using perceptual means, one crack-network is not sufficient. The reasons for this are two-fold. Firstly, the crack detection process is an inherently unreliable process which results in segmentation errors such as line fragmentation. Secondly, crack patterns should be thought of as a combination of connected curves rather than just single connected curves. Furthermore, the regions covered by a sub-object are too small to offer meaningful features for the purpose of crack classification, information query and result representation.
Line grouping is a crucial stage in the intermediate level of computer vision, to close the gap between what is produced by state-of-the-art low-level algorithms and what is desired as input to high level algorithms. Processes such as edge detection for instance, produce imperfect contours and fragmentation. A line grouping algorithm is an approach that is meant to compensate for this weakness. Robbles Kelly et al. [123] produced groupings of straight line segments using eigenclustering. They were interested in locating groups of straight line segments that exhibit strong geometric affinity to one another. Guy and Medioni [124] demonstrated the use of a threshold-free and non-iterative technique which in a way resembles the Hough Transform [49,125,126] in terms of its voting approach. The paper also summarised significant work on line grouping, namely that of Lowe [127], Ahuja & Tuceryan [128], Dolan & Weiss [129], Mohan & Nevatia [130], Sha’ashua & Ullman [131], Parent & Zucker [132] and Heitger & von der Heydt [133].
While almost all work on line grouping has concentrated on grouping line segments and/or curves, this research is interested in grouping patterns which in most cases consist of com- binations of line segments, as the end result of the crack network structuring stage as described in Chapter 4. A representation of a crack-network, may evolve from a straight line, a curve, a combination of connected straight lines, a combination of curves and even a mixture of straight lines and curves. Grouping these crack-networks is a different kind of problem compared to the line grouping problem described in almost all the line grouping literature. The dependability of the solution on human perception is a fact that cannot be denied. The research on perceptual grouping [134] and perceptual organization [135] gains attention for its importance in computer vision. However, the subject is not straightfor- ward. Taking a quote from Sarkar and Boyer [136], it is clear how grouping crack networks on the basis of perception is a highly challenging task:
“Perception is not a mere passive recording of information impressed upon my sensory organs by the environment. Rather, it consists of an active construc- tion by means of which sensory data are selected, analyzed, and integrated with
properties not directly noticeable but only hypothesized, deduced, or antici- pated, according to available information and intellectual capacities”.
Perceptual organization, going back through history, is research that looks for underly- ing principles which would unify the various grouping abilities of human perception [135]. In the early twenties, Wertheimer [113], Koffka and K¨ohler founded the Gestalt School of Psychology, and demonstrated the importance of perceptual organization to human vi- sual perception. The first categorisation of perceptual organization rules, made by Max Wertheimer, is known asWertheimer’s Laws of Grouping. Some of the rules are as denoted below [134,135,137].
• Proximity - elements that are close.
• Similarity - elements which have similar shape, colour, orientation, size, etc.
• Continuation - elements that lie on a line or a smooth curve.
• Closure - elements, like lines or curves, that form a closed shape.
• Symmetry - elements which are placed in symmetric order.
• Familiarity - elements which are used to be seen together.
In most literature, these rules are usually denoted asgrouping cues or justcues. TheGestalt
psychologists [113] were among the first to address the issue of pre-attentive perception [124]. Many “laws of grouping” were formulated, but none in any algorithmic language. The choice of cues varies heavily with the anticipated outcome of the grouping process. For instance, to group fragments of line edges from an edge detection process, proximity
andcontinuation are the most appropriate criteria. On the other hand, in texture analysis,
cues such as similarity and familiarity are the most likely to succeed, if used to group or segment regular texture patterns. According to Sonka et al. [49], there are mutually related elements, which, in the literature on texture analysis, are known as primitives ortexels.
The current problem is viewed in a similar way. As discussed in Chapter 4, crack patterns originated from the most primitive form, a pixel, then combine with other primitives to form a line segment, eventually forming a crack-network which is a group of connected line- segments. This hierarchical structure is formed through a grouping process which is based on connectivity. Grouping processes vary tremendously in terms of level of difficulty from quick tasks of proximity and co-linearity based groupings to the difficult knowledge-based approach.
In the problem in hand, and looking from a general perspective, thecuesthat are appropri- ate in grouping crack-networks areproximity and similarity. The crack-network grouping
scheme implemented considers a crack-network as the primitive. Bearing in mind the diverse structural form of a crack-network, a typical cue used for line-segments such as
continuation cannot successfully group crack-networks.
In order to “measure” proximity and similarity, a two-stage technique is implemented us- ing conservative shape approximations characterised by the minimum bounding rectangle (MBR) and the rotated minimum bounding rectangle (RMBR) which were discussed in Section4.6.
The concerns in the analysis are time consumption and simplicity. Working on a very large image requires a large amount of computational load and the complex mathematical calculations will significantly slow down the process. Thus, simple approximations are chosen for a crack-network such as the MBR and the RMBR. They require a small number of parameters for object approximation as opposed to the convex hull [49], which needs a variable number of parameters. With a huge amount of crack-network in an image, the task of representing each of them by a simple approximation is highly desirable.