Question

Explain in brief all the below questions .

1. Affine image transform. Geometric image degradations.

2 Biomedical image classification: discriminate analysis

3 Biomedical image classification: k-nearest-neighbour (k-NN) classifier, k-means clustering

4. Biomedical image classification: hierarchical clustering, structural/syntactic classification

Answer 1

1, In biomedical imaging systems, the analysis of the interior of an organ is critical to detect eventual diseases or for surgical operations. So, to get a better view of the organs in 3D coordinate system, the affine transform (AT) has to be applied on the acquired volumetric image. The AT is also applied for biomedical CT image registration. The AT consists of four basic operations viz. rotation, shearing, scaling and translation.

Affine transformation is a linear mapping method that preserves points, straight lines, and planes. Sets of parallel lines remain parallel after an affine transformation.

The affine transformation technique is typically used to correct for geometric distortions or deformations that occur with non-ideal camera angles. An affine transformation is any transformation that preserves collinearity (i.e., all points lying on a line initially still lie on a line after transformation) and ratios of distances (e.g., the midpoint of a line segment remains the midpoint after transformation). In general, an affine transformation is a composition of rotations, translations, magnifications, and shears.

u = c11x + c12y + c13

v = c21x + c22y + c23 c13 and c23 affect translations, c11 and c22 affect magnifications, and the combination affects rotations and shears.

A shear in the x direction is produced by u = x + 0.2y v = y

This produces as both a shear and a rotation. u = x + 0.2y v = −0.3x + y

A rotation is produced by θ is produced by u = x cos θ + y sin θ v = −x sin θ + y cos θ

The main reason for the image degradation is geometric distortion and blurring caused by turbulence. Here a method to eliminate geometric distortion and blur and to recover a single high-quality image from the degraded sequence images. First, use optical flow technology to register the sequence images, thereby suppressing the geometric deformation of each frame. Next, sequence images are summed by a temporal filter to obtain a single blurred image. Then, the graph Laplacian matrix is used as the cost function to construct the regularization term. The final clear image and point spread function are obtained by iteratively solving the problem. Experiments show that the method can effectively eliminate the distortion and blur, restore the image details, and significantly improve the image quality.

2,Discriminant analysis is statistical technique used to classify observations into non-overlapping groups, based on scores on one or more quantitative predictor variables. For example, a doctor could perform a discriminant analysis to identify patients at high or low risk for stroke.Linear discriminant analysis (LDA), normal discriminant analysis (NDA), or discriminant function analysis is a generalization of Fisher's linear discriminant, a method used in statistics, pattern recognition, and machine learning to find a linear combination of features that characterizes or separates two or more classes of objects or events. The resulting combination may be used as a linear classifier, or, more commonly, for dimensionality reduction before later classification.

3,

The two most commonly used algorithms in machine learning are K-means clustering and k-nearest neighbors algorithm.

Often those two are confused with each other due to the presence of the k letter, but in reality, those algorithms are slightly different from each other.

KNN represents a supervised classification algorithm that will give new data points accordingly to the k number or the closest data points, while k-means clustering is an unsupervised clustering algorithm that gathers and groups data into k number of clusters.

K-nearest neighbors

Being a supervised classification algorithm, K-nearest neighbors needs labelled data to train on.

With the given data, KNN can classify new, unlabelled data by analysis of the k number of the nearest data points. Thus, the variable k is considered to be a parameter that will be established by the machine learning engineer.

K-means clustering is able to gradually learn how to cluster the unlabelled points into groups by analysis of the mean distance of said points. In this case, the variable k depicts the number of clusters or different groups in which the data will be gathered. The algorithm functions by moving the data in such manner that error function is minimized.

4 Hierarchical clustering, also known as hierarchical cluster analysis, is an algorithm that groups similar objects into groups called clusters. The endpoint is a set of clusters, where each cluster is distinct from each other cluster, and the objects within each cluster are broadly similar to each other.  

There are two types of hierarchical clustering, Divisive and Agglomerative.

In divisive or top-down clustering method we assign all of the observations to a single cluster and then partition the cluster to two least similar clusters.

In agglomerative or bottom-up clustering method we assign each observation to its own cluster. Then, compute the similarity (e.g., distance) between each of the clusters and join the two most similar clusters. Finally, repeat steps 2 and 3 until there is only a single cluster left.

Syntactic pattern recognition or structural pattern recognition is a form of pattern recognition, in which each object can be represented by a variable-cardinality set of symbolic, nominal features. This allows for representing pattern structures, taking into account more complex interrelationships between attributes than is possible in the case of flat, numerical feature vectors of fixed dimensionality, that are used in statistical classification.

Syntactic pattern recognition can be used instead of statistical pattern recognition if there is clear structure in the patterns. One way to present such structure is by means of a strings of symbols from a formal language. In this case the differences in the structures of the classes are encoded as different grammars.

An example of this would be diagnosis of the heart with ECG measurements. ECG waveforms can be approximated with diagonal and vertical line segments. If normal and unhealthy waveforms can be described as formal grammars, measured ECG signal can be classified as healthy or unhealthy by first describing it in term of the basic line segments and then trying to parse the descriptions according to the grammars. Another example is tessellation of tiling patterns.

A second way to represent relations are graphs, where nodes are connected if corresponding subpatterns are related. An item can be labeled as belonging to a class if its graph representation is isomorphic with prototype graphs of the class.

Typically, patterns are constructed from simpler sub patterns in a hierarchical fashion. This helps in dividing the recognition task into easier subtask of first identifying sub patterns and only then the actual patterns.