Blob Detection: Unveiling Patterns in Visual Data

By Fouad Sabry

What is Blob Detection

In the field of computer vision, blob detection algorithms are designed to identify areas within a digital image that are distinct from the regions that surround them in terms of characteristics such as brightness or color characteristics. In a more casual sense, a blob is a region of a picture in which certain qualities remain constant or almost constant. All of the points that make up a blob might be considered to be comparable to one another in some way. The use of convolution is the method that is utilized the most frequently for blob detection.

How you will benefit

(I) Insights, and validations about the following topics:

Chapter 1: Blob detection

Chapter 2: Edge detection

Chapter 3: Canny edge detector

Chapter 4: Scale-invariant feature transform

Chapter 5: Scale space

Chapter 6: Feature (computer vision)

Chapter 7: Difference of Gaussians

Chapter 8: Corner detection

Chapter 9: Ridge detection

Chapter 10: Scale-invariant feature operator

(II) Answering the public top questions about blob detection.

(III) Real world examples for the usage of blob detection in many fields.

Who this book is for

Professionals, undergraduate and graduate students, enthusiasts, hobbyists, and those who want to go beyond basic knowledge or information for any kind of Blob Detection.

• Language: English
• Publisher: One Billion Knowledgeable
• Release date: May 1, 2024

Book preview

Chapter 1: Blob detection

The goal of blob detection techniques in computer vision is to identify areas of a digital image that have significantly different characteristics from their surroundings. All the points inside a blob can be considered to be somewhat similar to each other, hence the term blob is used to describe an area of a picture where certain qualities are constant or essentially constant. Convolution is the most often used technique for blob detection.

The two primary types of blob detectors are I differential approaches, which are based on derivatives of the function with respect to position, and (ii) local extrema methods, which are focused on detecting the local maxima and minima of the function. These detectors are also known as interest point operators or interest region operators according to the most up-to-date nomenclature in the field (see also interest point detection and corner detection).

There are several reasons to investigate and refine blob detectors. The primary motivation is to supplement the data provided from edge and corner detectors by providing more information about regions. In the earliest studies in the field, blob detection was utilized to isolate relevant sections. These spots on the image could serve as indicators of objects or object portions for the purposes of object recognition and/or tracking. Histogram analysis is just one area where blob descriptors can be put to use for peak identification in the context of segmentation. Blob descriptors are also frequently used as the fundamental building blocks in the fields of texture analysis and texture recognition. Recently, blob descriptors have been widely used to indicate the presence of informative picture features for appearance-based object detection based on local image statistics, and as interest points for wide baseline stereo matching. In a similar vein, ridge detection can be used to indicate the existence of linear items.

The Laplacian of the Gaussian distribution was the basis for one of the earliest and most widely used blob detectors (LoG).

Given an input image f(x,y) , A Gaussian kernel is used to convolve this image.

{\displaystyle g(x,y,t)={\frac {1}{2\pi t}}e^{-{\frac {x^{2}+y^{2}}{2t}}}}

at a certain scale t to give a scale space representation

L(x,y;t)\ =g(x,y,t)*f(x,y)

.

Then, the output of a Laplacian operation

\nabla ^{2}L=L_{xx}+L_{yy}

is computed, which usually results in strong positive responses for dark blobs of radius {\textstyle r^{2}=2t} (for a two-dimensional image, {\textstyle r^{2}=dt} for a {\textstyle d} -dimensional image) and strong negative responses for bright blobs of similar size.

When using this operator at a single scale, the fundamental issue is, however, is that the operator's reaction is highly dependant on the correlation between the blob structures' sizes in the image domain and the pre-smoothing kernel's Gaussian size.

In the picture domain, capturing blobs of varying (unknown) sizes automatically, Therefore, it's important to consider multiple levels at once.

Taking into account the scale-normalized Laplacian operator is a simple technique to construct a multi-scale blob detector with automatic scale selection.

{\displaystyle \nabla _{\mathrm {norm} }^{2}L=t\,(L_{xx}+L_{yy})}

also, to identify scale-space extrema, that are points that are simultaneously local maxima/minima of {\displaystyle \nabla _{\mathrm {norm} }^{2}L} with respect to both space and scale (Lindeberg 1994, 1998).

Thus, given a discrete two-dimensional input image f(x,y) a three-dimensional discrete scale-space 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 ({\hat {x}},{\hat {y}}) and scales {\hat {t}} is performed according to

{\displaystyle ({\hat {x}},{\hat {y}};{\hat {t}})=\operatorname {argmaxminlocal} _{(x,y;t)}((\nabla _{\mathrm {norm} }^{2}L)(x,y;t))}

.

Keep in mind that this blob concept defines the term in a simple and mathematically precise operational manner, leading to a blob identification technique that is both effective and reliable.

Blobs defined from scale-space maxima of the normalized Laplacian operator have several fundamental qualities, such as responses that are translationally invariant, transformations of images by means of rotation and resizing.

Thus, if a scale-space 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 scale-space maximum at {\displaystyle \left(sx_{0},sy_{0};s^{2}t_{0}\right)} in the rescaled image (Lindeberg 1998).

Because of its extremely practical quality, the topic of Laplacian blob detection can be extended to include, local extremes in the scale-normalized distribution Other applications of Laplacian include scale selection, for instance, when detecting corners, scale-aware monitoring of features (Bretzner and Lindeberg 1998), in image matching and object recognition using scale-invariant feature transform (Lowe, 2004) and other image descriptors.

Both the Laplacian operator and other similar scale-space interest point detectors have their scale selection features studied in (Lindeberg 2013a). Other scale-space interest point detectors, such as the determinant of the Hessian operator, are demonstrated to outperform the Laplacian operator and its difference-of-Gaussians approximation in (Lindeberg 2013b, 2015) when it comes to picture-based matching using local SIFT-like image descriptors.

From the fact that the scale space representation L(x,y,t) satisfies the diffusion equation

\partial _{t}L={\frac {1}{2}}\nabla ^{2}L

it follows that the Laplacian of the Gaussian operator \nabla ^{2}L(x,y,t) can also be computed as the limit case of the difference between two Gaussian smoothed images (scale space representations)

{\displaystyle \nabla _{\mathrm {norm} }^{2}L(x,y;t)\approx {\frac {t}{\Delta t}}\left(L(x,y;t+\Delta t)-L(x,y;t)\right)}

.

This method is often referred to as the difference of Gaussians (DoG) method in the computer vision field. Although there are some subtle differences, this operator can be thought of as an approximation of the Laplacian operator and shares many of its properties. See (Lindeberg 2012, 2015) for an explicit relation between the difference-of-Gaussian operator and the scale-normalized Laplacian blob detector. Blobs can also be identified from the extrema of differences of Gaussians in scale space. The SIFT algorithm (Scale-Invariant Feature Transform) is one implementation of this strategy; for more, see Lowe (2004).

By taking into account the Hessian determinant after scaling it, we may, also referred to as the Monge–Ampère operator,

{\displaystyle \det H_{\mathrm {norm} }L=t^{2}\left(L_{xx}L_{yy}-L_{xy}^{2}\right)}

where HL denotes the Hessian matrix of the scale-space representation L and then detecting scale-space maxima of this operator one obtains another straightforward differential blob detector with automatic scale selection which also responds to saddles (Lindeberg 1994, 1998)

{\displaystyle ({\hat {x}},{\hat {y}};{\hat {t}})=\operatorname {argmaxlocal} _{(x,y;t)}((\det H_{\mathrm {norm} }L)(x,y;t))}

.

The blob points ({\hat {x}},{\hat {y}}) and scales {\hat {t}} are also defined from an operational differential geometric definitions that leads to blob descriptors that are covariant with translations, transformations of images by means of rotation and resizing.

With regards to the picking of scales, Scale selection qualities for non-Euclidean affine transformations are marginally improved for blobs constructed from scale-space extrema of the determinant of the Hessian (DoH) (Lindeberg 1994), 1998, 2015).

Condensed version, The SURF descriptor (Bay et al.) uses the scale-normalized determinant of the Hessian calculated from Haar wavelets as its fundamental interest point operator.

) in 2006 for use in pattern recognition and picture matching.

The determinant of the Hessian operator has superior scale selection capabilities under affine image transformations than the Laplacian operator, as shown in a full analysis of their respective selection properties published in (Lindeberg 2013a). For image-based matching with local SIFT-like or SURF-like image descriptors, it has been shown in (Lindeberg 2013b, 2015) that the determinant of the Hessian operator performs significantly better than the Laplacian operator or its difference-of-Gaussians approximation, as well as better than the Harris or Harris-Laplace operators, leading to higher efficiency values and lower 1-precision scores.

For blob detection, a hybrid operator between the Laplacian and the determinant of the Hessian has been developed, where the determinant of the Hessian is used for spatial selection and the scale-normalized Laplacian is used for scale selection. (Mikolajczyk and Schmid 2004):

{\displaystyle ({\hat {x}},{\hat {y}})=\operatorname {argmaxlocal} _{(x,y)}((\det HL)(x,y;t))}{\displaystyle {\hat {t}}=\operatorname {argmaxminlocal} _{t}((\nabla _{\mathrm {norm} }^{2}L)({\hat {x}},{\hat {y}};t))}

This operator has found application in texture analysis, object recognition, and picture matching.

These blob detectors with automatic scale selection produce blob descriptors that are robust against spatial transformations like translations, rotations, and uniform rescalings. However, perspective distortions are also present in the images that make up the input to a computer vision system. Creating a blob detector that is invariant to affine transformations is a logical way to obtain blob descriptors that are more resistant to perspective transformations. By iteratively warping the shape of the smoothing kernel to match the local image structure around the blob, or, equivalently, by warping a local image patch while