 Blob detection

Feature detection Output of a typical corner detection algorithmEdge detection Canny · CannyDeriche · Differential · Sobel · Prewitt · Roberts Cross Interest point detection Corner detection Harris operator · Shi and Tomasi · Level curve curvature · SUSAN · FAST Blob detection Laplacian of Gaussian (LoG) · Difference of Gaussians (DoG) · Determinant of Hessian (DoH) · Maximally stable extremal regions · PCBR Ridge detection Hough transform Structure tensor Affine invariant feature detection Affine shape adaptation · Harris affine · Hessian affine Feature description SIFT · SURF · GLOH · HOG · LESH Scalespace Scalespace axioms · Implementation details · Pyramids In the area of computer vision, blob detection refers to visual modules that are aimed at detecting points and/or regions in the image that differ in properties like brightness or color compared to the surrounding. There are two main classes of blob detectors (i) differential methods based on derivative expressions and (ii) methods based on local extrema in the intensity landscape. With the more recent terminology used in the field, these operators can also be referred to as interest point operators, or alternatively interest region operators (see also interest point detection and corner detection).
There are several motivations for studying and developing blob detectors. One main reason is to provide complementary information about regions, which is not obtained from edge detectors or corner detectors. In early work in the area, blob detection was used to obtain regions of interest for further processing. These regions could signal the presence of objects or parts of objects in the image domain with application to object recognition and/or object tracking. In other domains, such as histogram analysis, blob descriptors can also be used for peak detection with application to segmentation. Another common use of blob descriptors is as main primitives for texture analysis and texture recognition. In more recent work, blob descriptors have found increasingly popular use as interest points for wide baseline stereo matching and to signal the presence of informative image features for appearancebased object recognition based on local image statistics. There is also the related notion of ridge detection to signal the presence of elongated objects.
The Laplacian of Gaussian
One of the first and also most common blob detectors is based on the Laplacian of the Gaussian (LoG). Given an input image f(x,y), this image is convolved by a Gaussian kernel
at a certain scale t to give a scalespace representation . Then, the Laplacian operator
is computed, which usually results in strong positive responses for dark blobs of extent and strong negative responses for bright blobs of similar size. A main problem when applying this operator at a single scale, however, is that the operator response is strongly dependent on the relationship between the size of the blob structures in the image domain and the size of the Gaussian kernel used for presmoothing. In order to automatically capture blobs of different (unknown) size in the image domain, a multiscale approach is therefore necessary.
A straightforward way to obtain a multiscale blob detector with automatic scale selection is to consider the scalenormalized Laplacian operator
and to detect scalespace maxima/minima, that are points that are simultaneously local maxima/minima of with respect to both space and scale (Lindeberg 1994, 1998). Thus, given a discrete twodimensional input image f(x,y) a threedimensional discrete scalespace volume L(x,y,t) is computed and a point is regarded as a bright (dark) blob if the value at this point is greater (smaller) than the value in all its 26 neighbours. Thus, simultaneous selection of interest points and scales is performed according to
 .
Note that this notion of blob provides a concise and mathematically precise operational definition of the notion of "blob", which directly leads to an efficient and robust algorithm for blob detection. Some basic properties of blobs defined from scalespace maxima of the normalized Laplacian operator are that the responses are covariant with translations, rotations and rescalings in the image domain. Thus, if a scalespace maximum is assumed at a point (x_{0},y_{0};t_{0}) then under a rescaling of the image by a scale factor s, there will be a scalespace maximum at (sx_{0},sy_{0};s^{2}t_{0}) in the rescaled image (Lindeberg 1998). This in practice highly useful property implies that besides the specific topic of Laplacian blob detection, local maxima/minima of the scalenormalized Laplacian are also used for scale selection in other contexts, such as in corner detection, scaleadaptive feature tracking (Bretzner and Lindeberg 1998), in the scaleinvariant feature transform (Lowe 2004) as well as other image descriptors for image matching and object recognition.
The difference of Gaussians approach
From the fact that the scalespace representation L(x,y,t) satisfies the diffusion equation
it follows that the Laplacian of the Gaussian operator can also be computed as the limit case of the difference between two Gaussian smoothed images (scalespace representations)
 .
In the computer vision literature, this approach is referred to as the Difference of Gaussians (DoG) approach. Besides minor technicalities, however, this operator is in essence similar to the Laplacian and can be seen as an approximation of the Laplacian operator. In a similar fashion as for the Laplacian blob detector, blobs can be detected from scalespace extrema of differences of Gaussians.
The determinant of the Hessian
By considering the scalenormalized determinant of the Hessian, also referred to as the Monge–Ampère operator,
where HL denotes the Hessian matrix of L and then detecting scalespace maxima of this operator one obtains another straightforward differential blob detector with automatic scale selection which also responds to saddles (Lindeberg 1994, 1998)
 .
The blob points and scales are also defined from an operational differential geometric definitions that leads to blob descriptors that are covariant with translations, rotations and rescalings in the image domain. In terms of scale selection, blobs defined from scalespace extrema of the determinant of the Hessian (DoH) also have slightly better scale selection properties under nonEuclidean affine transformations than the more commonly used Laplacian operator (Lindeberg 1994, 1998). In simplified form, the scalenormalized determinant of the Hessian computed from Haar wavelets is used as the basic interest point operator in the SURF descriptor (Bay et al. 2006) for image matching and object recognition.
The hybrid Laplacian and determinant of the Hessian operator (HessianLaplace)
A hybrid operator between the Laplacian and the determinant of the Hessian blob detectors has also been proposed, where spatial selection is done by the determinant of the Hessian and scale selection is performed with the scalenormalized Laplacian (Mikolajczyk and Schmid 2004):
This operator has been used for image matching, object recognition as well as texture analysis.
Affineadapted differential blob detectors
The blob descriptors obtained from these blob detectors with automatic scale selection are invariant to translations, rotations and uniform rescalings in the spatial domain. The images that constitute the input to a computer vision system are, however, also subject to perspective distortions. To obtain blob descriptors that are more robust to perspective transformations, a natural approach is to devise a blob detector that is invariant to affine transformations. In practice, affine invariant interest points can be obtained by applying affine shape adaptation to a blob descriptor, where the shape of the smoothing kernel is iteratively warped to match the local image structure around the blob, or equivalently a local image patch is iteratively warped while the shape of the smoothing kernel remains rotationally symmetric (Lindeberg and Garding 1997; Baumberg 2000; Mikolajczyk and Schmid 2004, Lindeberg 2008/2009). In this way, we can define affineadapted versions of the Laplacian/Difference of Gaussian operator, the determinant of the Hessian and the HessianLaplace operator (see also HarrisAffine and HessianAffine).
Greylevel blobs, greylevel blob trees and scalespace blobs
A natural approach to detect blobs is to associate a bright (dark) blob with each local maximum (minimum) in the intensity landscape. A main problem with such an approach, however, is that local extrema are very sensitive to noise. To address this problem, Lindeberg (1993, 1994) studied the problem of detecting local maxima with extent at multiple scales in scalespace. A region with spatial extent defined from a watershed analogy was associated with each local maximum, as well a local contrast defined from a socalled delimiting saddle point. A local extremum with extent defined in this way was referred to as a greylevel blob. Moreover, by proceeding with the watershed analogy beyond the delimiting saddle point, a greylevel blob tree was defined to capture the nested topological structure of level sets in the intensity landscape, in a way that is invariant to affine deformations in the image domain and monotone intensity transformations. By studying how these structures evolve with increasing scales, the notion of scalespace blobs was introduced. Beyond local contrast and extent, these scalespace blobs also measured how stable image structures are in scalespace, by measuring their scalespace lifetime.
It was proposed that regions of interest and scale descriptors obtained in this way, with associated scale levels defined from the scales at which normalized measures of blob strength assumed their maxima over scales could be used for guiding other early visual processing. An early prototype of simplified vision systems was developed where such regions of interest and scale descriptors were used for directing the focusofattention of an active vision system. While the specific technique that was used in these prototypes can be substantially improved with the current knowledge in computer vision, the overall general approach is still valid, for example in the way that that local extrema over scales of the scalenormalized Laplacian operator are nowadays used for providing scale information to other visual processes.
Lindeberg's watershedbased greylevel blob detection algorithm
For the purpose of detecting greylevel blobs (local extrema with extent) from a watershed analogy, Lindeberg developed an algorithm based on presorting the pixels, alternatively connected regions having the same intensity, in decreasing order of the intensity values. Then, comparisons were made between nearest neighbours of either pixels or connected regions.
For simplicity, let us consider the case of detecting bright greylevel blobs and let the notation "higher neighbour" stand for "neighbour pixel having a higher greylevel value". Then, at any stage in the algorithm (carried out in decreasing order of intensity values) is based on the following classification rules:
 If a region has no higher neighbour, then it is a local maximum and will be the seed of a blob.
 Else, if it has at least one higher neighbour, which is background, then it cannot be part of any blob and must be background.
 Else, if it has more than one higher neighbour and if those higher neighbours are parts of different blobs, then it cannot be a part of any blob, and must be background.
 Else, it has one or more higher neighbours, which are all parts of the same blob. Then, it must also be a part of that blob.
Compared to other watershed methods, the flooding in this algorithm stops once the intensity level falls below the intensity value of the socalled delimiting saddle point associated with the local maximum. However, it is rather straightforward to extend this approach the other types of watershed constructions. For example, by proceeding beyond the first delimiting saddle point a "greylevel blob tree" can be constructed. Moreover, the greylevel blob detection method was embedded in a scalespace representation and performed at all levels of scale, resulting in a representation called the scalespace primal sketch.
This algorithm with its applications in computer vision is described in more detail in Lindeberg's thesis ^{[1]} as well as the monograph on scalespace theory ^{[2]} partially based on that work. Earlier presentations of this algorithm can also be found in.^{[3]}^{[4]} More detailed treatments of applications of greylevel blob detection and the scalespace primal sketch to computer vision and medical image analysis are given in.^{[5]}^{[6]}^{[7]}
Maximally stable extremum regions (MSER)
Main article: Maximally stable extremal regionsMatas et al. (2002) were interested in defining image descriptors that are robust under perspective transformations. They studied level sets in the intensity landscape and measured how stable these were along the intensity dimension. Based on this idea, they defined a notion of maximally stable extremum regions and showed how these image descriptors can be used as image features for stereo matching.
There are close relations between this notion and the above mentioned notion of greylevel blob tree. The maximally stable extremum regions can be seen as making a specific subset of the greylevel blob tree explicit for further processing.
See also
 Blob extraction
 Corner detection
 Affine shape adaptation
 Scalespace
 Ridge detection
 Interest point detection
 Feature detection (computer vision)
 HarrisAffine
 HessianAffine
 PCBR
References
 Christopher Evans. Notes on the OpenSURF library. http://www.chrisevansdev.com/opensurf.html.
 H. Bay, T. Tuytelaars and L. van Gool (2006). "SURF: Speeded Up Robust Features". Proceedings of the 9th European Conference on Computer Vision, Springer LNCS volume 3951, part 1. pp. 404–417. http://www.vision.ee.ethz.ch/~surf/papers.html.
 L. Bretzner and T. Lindeberg (1998). "Feature Tracking with Automatic Selection of Spatial Scales" (abstract page). Computer Vision and Image Understanding 71 (3): pp 385–392. doi:10.1006/cviu.1998.0650. http://www.nada.kth.se/cvap/abstracts/cvap201.html.
 T. Lindeberg (1993). "Detecting Salient BlobLike Image Structures and Their Scales with a ScaleSpace Primal Sketch: A Method for FocusofAttention" (abstract page). International Journal of Computer Vision 11 (3): pp 283–318. doi:10.1007/BF01469346. http://www.nada.kth.se/~tony/abstracts/Lin92IJCV.html.
 T. Lindeberg (1994). ScaleSpace Theory in Computer Vision. Springer. ISBN 0792394186. http://www.nada.kth.se/~tony/book.html.
 T. Lindeberg (1998). "Feature detection with automatic scale selection" (abstract page). International Journal of Computer Vision 30 (2): pp 77–116. http://www.nada.kth.se/cvap/abstracts/cvap198.html.
 T. Lindeberg and J. Garding (1997). "Shapeadapted smoothing in estimation of 3{D} depth cues from affine distortions of local 2{D} structure". International Journal of Computer Vision 15: pp 415–434. http://www.nada.kth.se/~tony/abstracts/LG94ECCV.html.
 T. Lindeberg (2008/2009). ScaleSpace. "Scalespace". Encyclopedia of Computer Science and Engineering (Benjamin Wah, ed), John Wiley and Sons IV: 2495–2504. doi:10.1002/9780470050118.ecse609. ISBN 047005011X. http://www.nada.kth.se/~tony/abstracts/Lin08EncCompSci.html.
 D. G. Lowe (2004). "Distinctive Image Features from ScaleInvariant Keypoints". International Journal of Computer Vision 60 (2): pp 91–110. doi:10.1023/B:VISI.0000029664.99615.94. http://citeseer.ist.psu.edu/lowe04distinctive.html.
 J. Matas, O. Chum, M. Urban and T. Pajdla (2002). "Robust wide baseline stereo from maximally stable extremum regions". British Machine Vision Conference. pp. 384–393. http://cmp.felk.cvut.cz/~matas/papers/matasbmvc02.pdf.
 K. Mikolajczyk, K. and C. Schmid (2004). "Scale and affine invariant interest point detectors". International Journal of Computer Vision 60 (1): pp 63–86. doi:10.1023/B:VISI.0000027790.02288.f2. http://www.robots.ox.ac.uk/~vgg/research/affine/det_eval_files/mikolajczyk_ijcv2004.pdf.
 ^ Lindeberg, T. (1991) Discrete ScaleSpace Theory and the ScaleSpace Primal Sketch, PhD thesis, Department of Numerical Analysis and Computing Science, Royal Institute of Technology, S100 44 Stockholm, Sweden, May 1991. (ISSN 11012250. ISRN KTH NA/P91/8SE) (The greylevel blob detection algorithm is described in section 7.1)
 ^ Lindeberg, Tony, ScaleSpace Theory in Computer Vision, Kluwer Academic Publishers, 1994, ISBN 0792394186
 ^ T. Lindeberg and J.O. Eklundh, "Scale detection and region extraction from a scalespace primal sketch", in Proc. 3rd International Conference on Computer Vision, (Osaka, Japan), pp. 416426, Dec. 1990. (See Appendix A.1 for the basic definitions for the watershedbased greylevel blob detection algorithm.)
 ^ T. Lindeberg and J.O. Eklundh, "On the computation of a scalespace primal sketch", Journal of Visual Communication and Image Representation, vol. 2, pp. 5578, Mar. 1991.
 ^ Lindeberg, T.: Detecting salient bloblike image structures and their scales with a scalespace primal sketch: A method for focusofattention, International Journal of Computer Vision, 11(3), 283318, 1993.
 ^ Lindeberg, T, Lidberg, Par and Roland, P. E..: "Analysis of Brain Activation Patterns Using a 3D ScaleSpace Primal Sketch", Human Brain Mapping, vol 7, no 3, pp 166194, 1999.
 ^ JeanFrancois Mangin, Denis Rivière, Olivier Coulon, Cyril Poupon, Arnaud Cachia, Yann Cointepas, JeanBaptiste Poline, Denis Le Bihan, Jean Régis, Dimitri PapadopoulosOrfanos: "Coordinatebased versus structural approaches to brain image analysis". Artificial Intelligence in Medicine 30(2): 177197 (2004)
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