Udacity. Edge detection. Motivations[edit] The purpose of detecting sharp changes in image brightness is to capture important events and changes in properties of the world.

It can be shown that under rather general assumptions for an image formation model, discontinuities in image brightness are likely to correspond to:[2][3] discontinuities in depth,discontinuities in surface orientation,changes in material properties andvariations in scene illumination. In the ideal case, the result of applying an edge detector to an image may lead to a set of connected curves that indicate the boundaries of objects, the boundaries of surface markings as well as curves that correspond to discontinuities in surface orientation. Thus, applying an edge detection algorithm to an image may significantly reduce the amount of data to be processed and may therefore filter out information that may be regarded as less relevant, while preserving the important structural properties of an image.

Sobel operator. A color picture of a steam engine The Sobel operator applied to that image Formulation[edit] where Since the Sobel kernels can be decomposed as the products of an averaging and a differentiation kernel, they compute the gradient with smoothing.

For example, Deriche edge detector. Deriche edge detector is an edge detection operator developed by Rachid Deriche in 1987.

It's a multistep algorithm used to obtain an optimal result of edge detection in a discrete two-dimensional image. This algorithm is based on John F. Canny's work related to the edge detection (Canny's edge detector) and his criteria for optimal edge detection: Detection quality – all existing edges should be marked and no false detection should occur.Accuracy - the marked edges should be as close to the edges in the real image as possible.Unambiguity - a given edge in the image should only be marked once. No multiple responses to one edge in the real image should occur. For this reason, this algorithm is often referred to as Canny-Deriche detector. Differences between Canny and Deriche edge detector[edit] Deriche edge detector, like Canny edge detector, consists of the following 4 steps: Corner detection. Output of a typical corner detection algorithm Formalization[edit]

Corner detection. Corner detection. Corner detection. Corner detection. Corner detection. Corner detection. Output of a typical corner detection algorithm Formalization[edit] A corner can be defined as the intersection of two edges.

A corner can also be defined as a point for which there are two dominant and different edge directions in a local neighbourhood of the point. An interest point is a point in an image which has a well-defined position and can be robustly detected. This means that an interest point can be a corner but it can also be, for example, an isolated point of local intensity maximum or minimum, line endings, or a point on a curve where the curvature is locally maximal.

In practice, most so-called corner detection methods detect interest points in general, and in fact, the term "corner" and "interest point" are used more or less interchangeably through the literature.[1] As a consequence, if only corners are to be detected it is necessary to do a local analysis of detected interest points to determine which of these are real corners. Principal curvature-based region detector. Local region detectors can typically be classified into two categories: intensity-based detectors and structure-based detectors.

Intensity-based detectors depend on analyzing local differential geometry or intensity patterns to find points or regions that satisfy some uniqueness and stability criteria. These detectors include SIFT, Hessian-affine, Harris-Affine and MSER etc.Structure-based detectors depend on structural image features such as lines, edges, curves, etc. to define interest points or regions. These detectors include edge-based region (EBR) and scale-invariant shape features (SISF) From the detection invariance point of view, feature detectors can be divided into fixed scale detectors such as normal Harris corner detector, scale invariant detectors such as SIFT and affine invariant detectors such as Hessian-affine. The PCBR detector is a structure-based affine-invariant detector. Radon transform. Radon transform.

Maps f on the (x, y)-domain into f on the (α, s)-domain. Radon transform of the indicator function of two squares shown in the image below. Lighter regions indicate larger function values. Black indicates zero. Original function is equal to one on the white region and zero on the dark region. In mathematics, the Radon transform is the integral transform which takes a function f defined on the plane to a function Rf defined on the (two-dimensional) space of lines in the plane, whose value at a particular line is equal to the line integral of the function over that line.

Radon transform. Maximally stable extremal regions. In computer vision, maximally stable extremal regions (MSER) are used as a method of blob detection in images.

This technique was proposed by Matas et al.[1] to find correspondences between image elements from two images with different viewpoints. This method of extracting a comprehensive number of corresponding image elements contributes to the wide-baseline matching, and it has led to better stereo matching and object recognition algorithms. Terms and Definitions[edit] Maximally stable extremal regions. Blob detection. In computer vision, blob detection methods are aimed at detecting regions in a digital image that differ in properties, such as brightness or color, compared to surrounding regions.

Informally, a blob is a region of an image in which some properties are constant or approximately constant; all the points in a blob can be considered in some sense to be similar to each other. The most common method for blob detection is convolution. Given some property of interest expressed as a function of position on the image, there are two main classes of blob detectors: (i) differential methods, which are based on derivatives of the function with respect to position, and (ii) methods based on local extrema, which are based on finding the local maxima and minima of the function. With the more recent terminology used in the field, these detectors can also be referred to as interest point operators, or alternatively interest region operators (see also interest point detection and corner detection). . And. Difference of Gaussians. Mathematics of difference of Gaussians[edit] Given a m-channels, n-dimensional image.

Blob detection. In computer vision, blob detection methods are aimed at detecting regions in a digital image that differ in properties, such as brightness or color, compared to surrounding regions. Informally, a blob is a region of an image in which some properties are constant or approximately constant; all the points in a blob can be considered in some sense to be similar to each other. The most common method for blob detection is convolution. Given some property of interest expressed as a function of position on the image, there are two main classes of blob detectors: (i) differential methods, which are based on derivatives of the function with respect to position, and (ii) methods based on local extrema, which are based on finding the local maxima and minima of the function.

With the more recent terminology used in the field, these detectors can also be referred to as interest point operators, or alternatively interest region operators (see also interest point detection and corner detection). . And. Histogram of oriented gradients. The histogram of oriented gradients (HOG) is a feature descriptor used in computer vision and image processing for the purpose of object detection. The technique counts occurrences of gradient orientation in localized portions of an image. This method is similar to that of edge orientation histograms, scale-invariant feature transform descriptors, and shape contexts, but differs in that it is computed on a dense grid of uniformly spaced cells and uses overlapping local contrast normalization for improved accuracy.

Robert K. Theory[edit] The essential thought behind the histogram of oriented gradients descriptor is that local object appearance and shape within an image can be described by the distribution of intensity gradients or edge directions. GLOH. Speeded up robust features. To detect interest points, SURF uses an integer approximation of the determinant of Hessian blob detector, which can be computed with 3 integer operations using a precomputed integral image. Its feature descriptor is based on the sum of the Haar wavelet response around the point of interest.

These can also be computed with the aid of the integral image. SURF descriptors have been used to locate and recognize objects, people or faces, to reconstruct 3D scenes, to track objects and to extract points of interest. SURF was first presented by Herbert Bay, et al., at the 2006 European Conference on Computer Vision. An application of the algorithm is patented in the United States.[1] An "upright" version of SURF (called U-SURF) is not invariant to image rotation and therefore faster to compute and better suited for application where the camera remains more or less horizontal.

Algorithm and features[edit] Ridge detection. Ridge detection is the attempt, via software, to locate ridges (or edges) in an image. Kernel (image processing) Depending on the element values, a kernel can cause a wide range of effects. The above are just a few examples of effects achievable by convolving kernels and images. The origin is the position of the kernel which is above (conceptually) the current output pixel.

Kirsch operator. The Kirsch operator or Kirsch compass kernel is a non-linear edge detector that finds the maximum edge strength in a few predetermined directions. It is named after the computer scientist Russell A. Kirsch. Mathematical description[edit] The operator takes a single kernel mask and rotates it in 45 degree increments through all 8 compass directions: N, NW, W, SW, S, SE, E, and NE. Kirsch operator.