Chapter 5: CS689 1

Computational Medical Imaging Analysis Chapter 5: Processing and Analysis

Jun Zhang

Laboratory for Computational Medical Imaging & Data AnalysisDepartment of Computer Science

University of KentuckyLexington, KY 40506

Chapter 5: CS689 2

5.1a: Challenges in Comprehending Information in Biomedical Images

Image enhancement and restorationAutomated and accurate segmentation of structures and features of interest Automated and accurate registration and fusion of multimodality or multispectral informationClassification of image content, namely tissue characterization and typingQuantitative measurement of image properties and features, including a discussion of the “meaning” of image measurement

Chapter 5: CS689 3

5.2a: Image Enhancement and Restoration

Image enhancement methods attempt to improve the quality of an image We can make certain features in the image more recognizable or prominent Examples are amplification of edges or reduction of noise to increase the contrast between regions of an imageIt is also possible to increase the visibility of features at a certain scale or with a certain spectral signature

Chapter 5: CS689 4

5.2b: Tradeoffs in Detail and Noise

There is an inherent tradeoff between amplifying detail and reducing noise when applying image enhancement techniquesProcedures that enhance visibility of detail also increase the noise; and conversely, procedures that applied to reduce noise also reduce detail. (Denosing usually makes edge blurred)Many techniques have been developed to achieve image enhancement using both linear and nonlinear techniques (such as PDE based denosingtechniques)

Chapter 5: CS689 5

5.2c: Histogram Operations

The histogram of an image is a function that relates the number of pixels in an image to the range of brightness values of those pixels Normally a 2D graph, with abscissa showing the number of pixels and ordinate showing the brightness values Any point on the graph indicates the number of pixels in the image that have the same brightness levelIt usually has one or more peaks and valleys that corresponds to the gray levels of the image that are most common and least common throughout the image

Chapter 5: CS689 6

5.2d: Histogram Illustration

Chapter 5: CS689 7

5.2e: Use of Histogram

The global statistical manipulation of image gray scale values is based on histogram matching Evaluation of histograms can reveal that some brightness (gray) levels may be “underutilized” as far as efficient display is concerned Histogram equalization is a response to such an evaluation and refers to “spreading out” or “stretching” the gray levels so that they are all used as evenly as possibleThis manipulation can take the full advantage of the display system, may alter the original data

Chapter 5: CS689 8

5.2f: Histogram of A Mosaic

Chapter 5: CS689 9

5.2g: Histogram of A Scene

Chapter 5: CS689 10

5.2h: Histogram Equalization

Histogram “flattening” or “equalization” uses some ideal “flat” histogram shape for histogram matching, which will maximize contrast in the image If the flattening step is used to preserve contrast while moving from a high-resolution gray scale to a lower resolution gray scale, this “wasted gray scale”will tend to cause loss of detail A slight modification of histogram flattening that effectively limits the maximum slope of the two cumulative functions can be used to transmit maximum information content in the low-resolution image

Chapter 5: CS689 11

5.2i: Illustration of Histogram Equalization

Originalimage

Originalhistogram

Equalizedimage

Histogramof equalizedimage

Chapter 5: CS689 12

5.3a: Spatial Filtering

Spatial filtering involves the replacement of image values at each voxel location with some function of that pixel and its neighbors A linear filter (convolution) uses a weighted sums and is reversible A simple filter is to replace each pixel by the computed mean or average of itself and its eight closest neighborsThe size of the neighborhood (kernel of the convolution) may vary for different effect

Chapter 5: CS689 13

5.3b: Spatial Filtering (II)

The most common goal of pixel averaging is to reduce noise in the image An accompanying result is smoothed or blurred edges in the image Blurring and computation time increase with increase in the size of the neighborhood (kernel)To highlight differences between pixels in an image, each pixel may be replaced by the differences between itself and the mean of its neighborhood. This is “unsharp masking” for edge enhancement

Chapter 5: CS689 14

5.3c: Spatial Filtering (I)Original Kernel size 5x5

Chapter 5: CS689 15

5.3d: Spatial Filtering (II)Kernel size 9x9 Kernel size 15x15

Chapter 5: CS689 16

5.3e: Unsharp Masking

Chapter 5: CS689 17

5.3f: Unsharp Masking with Scales

Chapter 5: CS689 18

5.3g: Unsharp Masking Illustration

Originalblurred

Mean filterKernel 3x3

Edge enhancedimage

Chapter 5: CS689 19

5.4a: Frequency Filtering

Many advanced image enhancement techniques are developed in the Fourier domain Fourier’s theorem states that any waveform (including the 2D and 3D spatial waveforms that are images) can be expressed as the sum of sinusoidal basis functions at varying frequencies, amplitudes, and relative phases Reducing image noise, enhancing image contrast and edge definition, and other types of operations can be performed on the Fourier transform of an image

Chapter 5: CS689 20

5.4b: Advantages of Frequency Filtering

Operations in frequency space can often be faster than spatial convolution, especially if the convolution mask (region) is large (speed of filtering)Frequency filtering permits certain operations that are problematic in the spatial domain, such as enhancing or suppressing specific frequencies in the image High frequencies in an image can be suppressed using a low-pass frequency filter. This will suppress noise in the image, but also image detail

Chapter 5: CS689 21

5.4c: Low-pass Filter (I)

Original image Blurred image with Gaussian noise

Chapter 5: CS689 22

5.4d: Low-Pass Filter (II)

Low-pass filter withcut-off frequency 0.3

Low-pass filter withcut-off frequency 0.5

Chapter 5: CS689 23

5.4e: High-Pass Filtering

High-pass filter enhances the high frequencies in the image, and increases both detail and noiseFrequency domain filtering may selectively enhance or suppress periodic patterns in the image or judicious selection of frequency filter functions, which is called band-pass filtering

Chapter 5: CS689 24

5.4f: High Frequency Filtering

High frequency filter with cut-offat 0.5

Applied to a clone image

Image produced with Sobel operator

Chapter 5: CS689 25

5.5a: Image Restoration

Linear system theory is based on the supposition of linear relationships among all components of an imaging system, a reasonable assumption over the normal range of modern medical imaging systems Linear system can be completely characterized by their response to impulse functions, which are finite amount of electrical energy occurring over zero time The impulse response (point-spread function, or psf) can be used to predict the output of the system to any arbitrary input by the process of convolution, essentially replacing each of the points in an image with its appropriately scaled impulse response

Chapter 5: CS689 26

5.5b: Deconvolution

The highest frequencies or sharpest details of an image are generally degraded or lost It is possible to use the point-spread function to mathematically deblur or sharpen an image (deconvolution)The process of debluring an image is different from image enhancementEnhancement is to make certain things sharper or more prominent, deconvolution is to restore the image to more exactly represent its original object

Chapter 5: CS689 27

5.5c: Methods of Deconvolution

Knowing psf is the key for successful deconvolutionPsf can be measured empirically, theoretically estimated, or make reasonable estimates of it on the fly from the acquired data Wiener filter minimizes mean-squared-error between the true object and the restoration of the objectIterative nonlinear restoration techniques are usually betterBlind deconvolution is used when the measurement of the psf is difficult or tedious

Chapter 5: CS689 28

5.5d: Deconvolution (Example)

Turbulences on the surface of Jupiter: original and restored

Chapter 5: CS689 29

5.6a: Image Segmentation

Segmentation is spatial partitioning of an image into its constituent parts, or isolating specific objects in an image Segmentation is often confused with and used interchangeably with classification Image classification means identifying what an object in the image is, or what type of object each pixel belongs to Segmentation: manual, automatic, semiautomatic (assisted manual)

Chapter 5: CS689 30

5.6b: Manual Segmentation

Manual segmentation involves interactive delineation of the structure boundary in an image by a trained operator This is often the most accurate approach if an expert is doing the work and is not fatigued or hampered by limiting interface devicesThe drawbacks are time consuming, error prone, subjectively biased, and not reproducible. Multiple operators and images from different scanners increase the variability of the defined borders

Chapter 5: CS689 31

5.6c: Manual Segmentation (Example)

Chapter 5: CS689 32

5.6d: Draw Contour

Chapter 5: CS689 33

5.7a: Thresholding (Semiautomatic Segmentation)

A gray scale range is chosen that represents the object of interest. Voxels that are within the gray scale are set to one, all other voxelsare set to zeroThe technique is successful if the specified gray scale is unique to and encompasses the entire object of interestThe threshold range can be determined interactively with a side-by-side display of the gray scale and thresholded images

Chapter 5: CS689 34

5.7b: Color Image Thresholding

Chapter 5: CS689 35

5.7c: Thresholding using Histogram

Histogram can be used to select threshold values A value at the minimum between the two peaks of a bimodal histogram is often used as a threshold value It is advisable to blur (smooth) the image before histogram thresholdingVisually selecting the threshold values is

usually the best, but not reproducible

Chapter 5: CS689 36

5.7d: Example of Histogram Thresholding

Chapter 5: CS689 37

5.8a: Region Growing

An image or volume can be divided into regions based on associated regional characteristics, such as homogeneity of gray scale The most basic form of region growing is based solely on thresholdingConnectivity criteria can be combined with thresholding to produce more powerful region growing performance A pixel is connected if it satisfies the thresholdingcondition and is connected to the seed pixel at a specified number of sides and/or corners

Chapter 5: CS689 38

5.8b: Seeded Region Growing

Chapter 5: CS689 39

5.8c: Region Growing in a Diffusion Weighted Image

Chapter 5: CS689 40

5.9a: Mathematical Morphology

Mathematical morphology involves a convolution-like process using various shaped kernels, called structuring elements The structuring elements are mostly symmetric: squares, rectangles, and circles Most popular morphological operations are erode, dilate, open, and closeThe operations can be applied iteratively in selected order to effect a powerful process

Chapter 5: CS689 41

5.9b: Erode Functions

Erode function is a reducing operation. It removes noise and other small objects, breaks thin connections between objects, removes an outside layer from larger objects, and increases the size of holes within an objectFor binary images, any pixel that is set (1) and has a neighbor that is not set (0), is set to 0 The minimum function is the equivalence of an erosion The neighbors considered are defined by the structuring element

Chapter 5: CS689 42

5.9c: Illustration of Erosion Function

Erosion with a 3x3 square structuring element

Chapter 5: CS689 43

5.9c: Example of Erode Function

Input image Eroded image

Chapter 5: CS689 44

5.9d: Erosion Example

Input image Eroded image

Chapter 5: CS689 45

5.10a: Dilation Function

The dilate function can be thought of as an enlarging function, the reverse of erode For any binary data, any 0 pixel that has a 1 neighbor, where the neighborhood is defined by the structuring element is set to 1 For gray scale data, the dilate is a maximum functionThe dilation fills small holes and cracks and adds layers to objects in a binary image

Chapter 5: CS689 46

5.10b: Example of Dilation

Input image Dilated image

Chapter 5: CS689 47

5.10c: Dilated Image

Input image Dilated image

Chapter 5: CS689 48

5.11a: Erosion – Dilation Functions

Erode and dilate are essentially inverse operations, they are often applied successively to an image volume An erosion followed by a dilation is called an open A morphological open will delete small objects and break thin connections without loss of surface layers A dilation followed by an erosion is called closeThe close operation fills small holes and cracks in an object and tends to smooth the border of an object

Chapter 5: CS689 49

5.11b: Example of Open Operation

Input image Opened image

Chapter 5: CS689 50

5.11c: Example of Open Operation

Input image Opened image

Chapter 5: CS689 51

5.11d: Example of Close Operation

Input image Closed image

Chapter 5: CS689 52

5.11e: Example of Close Operation

Input image Closed image

Chapter 5: CS689 53

5.11f: An Automated Segmentation

(a)original image, (b) thresholding, (c) erosion, (d) dilation,(e) closing, (f) mask rendering, (g) volume rendering

Chapter 5: CS689 54

5.12a: Active Contours (Snakes)

Segmenting an object in an image with active contours involves minimizing a cost function based on certain properties of the desired object boundary and contrast in the image Smoothness of the boundary curve and local gradients in the image are usually considered Snake algorithms search the region about the current point and iteratively adjust the points of the boundary until an optimal, low cost boundary is found It may get caught in a local minimum (initial guess)

Chapter 5: CS689 55

5.12b: Example of A Snake Algorithm

Initial contour in green, yellowis intermediate contour

Final contour convergedin 25 iterations

Chapter 5: CS689 56

5.12c: Active Contour with Level-Set Method

Chapter 5: CS689 57

5.13a: Image Registration

Registration in biomedical image sciences means brining into spatial alignment separately acquired images of the same object When accurately registered, each separate image will have the same coordinate system and a given voxel in one image will represent the same physical volume as the corresponding voxel in another image Interpolation is usually involved in the resamplingand/or reformatting process

Chapter 5: CS689 58

5.13b: Registration and Fusion

Registration is required for multispectralanalysis or classification of image features from different images recorded over time and/or fused from different modalities Image fusion means the actual combining into a single image of information from registered multiple imagesFused displays can be accomplished using various combinations of color, gray scales, transparency, etc

Chapter 5: CS689 59

5.13b*: Example of Registration

MRI

SPECT

MRI +SPECT

Chapter 5: CS689 60

3.13b*: Co-Registration

CoregisteredSPECT-MRIimage. The SPECTimage was pasted inopaque mode on the top of black-and-whiteMRI image, whichprovides ananatomical template

Chapter 5: CS689 61

5.13c: Steps in Image Registration

Feature extractionPairing of corresponding featuresCalculation of transformation parametersPerforming the transformationCalculation of transformation parameters is the most challenging part of the processIt may involve optimization of a prescribed cost function achieved by iterating the solution Both rigid body and elastic types of transformation are possible

Chapter 5: CS689 62

5.13d: Transformations

In rigid body transformation, all the points and objects in an image are assumed to move as a whole and do not move relative to each other Translation and rotation are the only motionsAffine transformation maps straight lines to straight lines and preserve parallel lines, but angles between these lines can change Projective transformations involve registering different dimensional spaces, e.g., registering 3D images to 2D images

Chapter 5: CS689 63

5.13e: Rigid Body Registration

Rigid body registration between two individuals

Chapter 5: CS689 64

5.14a: Unimodal Registration

The reconstruction of 3D structures from microscope images of serial sections requires precise realignment of each sections to its neighborsUnimodal registration is within the same imaging modality Volumetric unimodality registration is required to use medical images quantitatively to study disease progression, monitor patient response to treatment, and evaluate surgical performance for quality control Patient motion artifacts may occur for serial sections

Chapter 5: CS689 65

5.14b: Composite Images Un-registered

20 MRI scans of thesame slice of an MSpatient. Note that thelocation and orientation differences

Chapter 5: CS689 66

5.14c: Composite Images Registered

The same images registered.Each of the scans is aligned,and the changes in lesions can easily be tracked over time

Chapter 5: CS689 67

5.14d: Intra-Patient Registration

Chapter 5: CS689 68

5.15a: Multimodal Registration

By combining information contained in multiple images of complementary modalities, synergism is achieved as voxel-by-voxel tissue characteristics can be determined with greater subtlety and precisionThe relation of structure to function can be revealed by combining structural and functional images Color analysis is a commonly encountered example of multiple band data in which the bands are inherently coregistered

Chapter 5: CS689 69

5.15b: Fusion of CT and MRI (Liver)

Red: fused MRI and CT. Top-right: MRI, Lower-right: CT

The red part is fromthe CT image, thegreen part is fromthe MRI image

Chapter 5: CS689 70

5.15c: Fused Image from CT and PET

Left: CT image. Middle: PET image. Right: fused image

CT is used asbackground, andPET image as the blue color

Chapter 5: CS689 71

Registration Quality and Error Metric

Corresponding points: The most straightforward registration error metric is the mean Euclidean distance between corresponding points in both images.It exhibits a global minimum at the point of perfect registration, and to increase monotonically with increased rigid misregistrationThe corresponding points may be determined by attaching extrinsic fiducial markers rigidly patient bony structures, or by expert identification of intrinsic anatomic landmarks

Chapter 5: CS689 72

Landmarks for Registration

Four points used for registration. The center of the trachea cross-section on slice A and the centers of the cross-sectionsof sternum, trachea, and vertebra in slice B

Chapter 5: CS689 73

Corresponding Surfaces

Corresponding image surfaces are used for intra- and intermodality registrationThey can be simple isosurfaces or carefully chosen hand-segmented contoursThe selected surfaces must correspond, and rigid structures are preferable to soft tissues as surface featuresSurface-based metrics have greater number of coordinate points involved and are complete lack of correspondence information

Chapter 5: CS689 74

Example of Surface RegistrationOriginal right lung

Initialsurfaceregistration

After 25iterations

Surface is in red

Chapter 5: CS689 75

Corresponding Image Features

For intramodality registration, the mean squared error between corresponding image voxels has the required minimum at the point of proper registrationWe can minimize the normalized standard deviation of the gray values of voxels in one image that correspond to voxels of a single gray value in the otherThe joint entry among images can be minimized, or, the mutual information among the images can be maximized

Chapter 5: CS689 76

Corresponding Feature Registration

PET image shows tumor, CT image shows location

Chapter 5: CS689 77

Search Strategy

An optimization method is used to optimize the cost function, once a registration feature (surface, point, voxel) is determinedThe dimensionality of search space is high (6 DOF for 3D rigid registration, with higher DOF for increasing severity of elasticity)Effective optima search strategies include gradient descent, Powell’s method, simplexThey involve iterative testing of trial orientations to detect local extrema of the evaluative function

Chapter 5: CS689 78

Optima Search Methods

Gradient descent methods require the calculation of complex local gradient of error function for search direction and step sizePowell’s method conducts a bounded golden interval search in one DOF, and iterates to other DOF until convergenceSimplex method is a set of (N+1) trial orientations for rapid estimation of the direction of the greatest gradient, without computational burden of gradient computation

Chapter 5: CS689 79

Registration of Ultrasound and SPECT

Registered image of heart fromultrasound and SPECT images

Chapter 5: CS689 80

Confounding Factors

Gray scale inhomogeneity can cause the segmented shape of an object surface used for registration to not coincide exactlyThe drift in voxel size over time may be an important confounding factor for longitudinal MRI studiesAccurate intermodality scale factors are often difficult to calculateScale space searches must be carefully bounded, and their results may be suspect, particularly if volumetric difference measures are made from the registered images

Chapter 5: CS689 81

Registration Error

Source Target Registered

Error beforeregistration

Error afterregistration

Chapter 5: CS689 82

Evaluating and Validating Image Registration

Translating and rotating a copy of an image volume by known amounts and then registering that copy to the originalThe best-case accuracy of the algorithm can be assessed as the correct solution is knownAdditive noise can be added to simulate real-world conditions, gray scale remapping can be applied to simulate intermodal applicationsParts of the copy can be erased to simulate partially overlapping scans

Chapter 5: CS689 83

Evaluating and Validating Image Registration (Clinical Setting)

An expert can grade registration for qualityThis relates algorithm’s performance directly to the currently used “gold standard”Multiple experts can improve repeatability, but residual error below visual detection may existPhantom (suitable materials and geometric features) experiments can be used to isolate sources of errorPatient images with attached markers provide the most complete validation of rigid registration algorithms applied to real data

Chapter 5: CS689 84

6.1a: Multispectral Classification

A number of separate measurements are collected for each sample in a multispectraldata setEach sample is “vector values”, such as RGB images, a CT image and an MR image of the same part of a patient’s bodyIndividual channels (or bands) may allow different distinctions to be made about each pixel in the image

Chapter 5: CS689 85

6.1b: Multispectral Imaging Technique

Infrared image Visible Image Multispectral image

Chapter 5: CS689 86

6.1c: Multispectral MRI Classification

48 hour old stroke in a two year old. a) T2-W MRI, b) manually classified from T2-weighted MRI, c) Automatically classified MR multispectral image

Chapter 5: CS689 87

6.2a: Methods

The goal of multispectral classification is to accurately and quickly identify scene objects with a minimum of operator intervention by taking advantage of the additional information available in multispectral imagesEntire images are analyzed in multispectral space and their pixels labeled as belonging to spectral and information classes in feature spacePixels in the classified image are assigned class numbers and typically color coded to visualize the classification results in the form of a thematic map

Chapter 5: CS689 88

6.2b: Multispectral Brain Image

Normal MRI of teenage female with sickle cell disease. a) T2-weighted MRI. b) manually classified from T2-weightedMRI. c) automatically classified MR multispectral image

Chapter 5: CS689 89

6.2c: Image Space and Preprocessing

Bands should be selected to enhance the contrast and segmentability of the features of interestPrincipal component analysis can be used to transform the multispectral data into a new spectral coordinate system that enhances feature contrastsPixel data is remapped into a new spectral space such that the most variance is in band 1, next most in band 2, etc.Data from each band must be spatially registered3D data may require denoise to ensure consistency

Chapter 5: CS689 90

6.2d: Unsupervised Classification

Unsupervised classifiers require no prior knowledge of feature characteristics but attempt to identify features in multispectral spacePixels associated with the clusters are assigned to classes in feature spaceUnsupervised classification allows the automatic identification of spectral clusters, may illustrate spectral classes to be used or to be segmented in supervised classifiersThe spectral classes can be used to generate multispectral signatures of classes in feature space

Chapter 5: CS689 91

6.2e: Supervised Classification

Supervised classifiers require training samples taken to be representative pixels of features to be identified in the feature spaceIt depends on expert-defined training samples known to belong to specified feature space classesPixels are classified and assigned values in feature space on the basis of some criteria for how similar they are to previously identified pixels in the training samplesExamples like k-means algorithm

Chapter 5: CS689 92

6.2f: Multispectral Space

Histogram values of certain range may be taken as belonging to a class in feature spaceA bimodal histogram may be suggestive of two classes in feature space A scattergram can be used to visualize clusters in multispectral space for two spectral bandsThe scattergram is not good for visualizing more than two spectral bands

Chapter 5: CS689 93

6.2g: Multispectral Visualization

Chapter 5: CS689 94

6.3f: Histogram Inference

Chapter 5: CS689 95

6.3a: Unsupervised Algorithms

Unsupervised classifiers have the potential to be more reproducible as no expert is needed to identify pixelsSome parameters may be required, e.g., the number of output classes, criteria for starting a new class, number of iterations, uncertainty of class boundaries, or other stopping criteriaMany data mining algorithms can be applied for supervised and unsupervised classifications, may be tailored for medical image classificationsThe question is how to prepare medical image data for the data mining algorithms

Chapter 5: CS689 96

6.3b: The Chain Method

It is a basic squared-error type of classifier using the Euclidean distance in feature space as the metricIt can be used as an initial classifier to find out class centroids for more advanced methods The first pixel is set to be in a class by itself and becomes the centroid for that classSubsequent pixels are assigned to an existing class if close enough, otherwise a new class is startedClass centriods are updated every time a new pixel is added to a classA centroid is a mean value of the pixels in that class

Chapter 5: CS689 97

6.3c: The Isodata Method

Isodata method is initialized with a set of starting class centroids. Updates are performed as in the Chain methodIsodata with merge adds the additional refinement of providing a threshold of change for classes to merge when close enough, or split as they growSmall clusters are either discarded or merged with the closest larger clusters

Chapter 5: CS689 98

6.4a: Supervised Algorithms

Supervised classifiers require the expert guidance of a set of known classes and their characteristicsTraining samples may be a set of selected pixels from the input data being classified or a predetermined set of standard spectral signatures for the classes to be identifiedSupervised classifiers are more popular than unsupervised classifiers

Chapter 5: CS689 99

6.4b: Statistical Classifiers

The maximum likelihood or Gaussian classifier algorithm calculates the class centers in feature space for the training samplesThe directions of the principal components of the feature values and the standard deviations along each spectral components are computedA pixel is classified by computing its probability of belonging to each class, and is assigned to the most likely classAccuracy of classification depends on a good estimate of mean vector and covariance matrix for each class in the feature space

Chapter 5: CS689 100

6.4c: Neural Network

Neural Network classifier builds a standard feed-forward neural network and trains it on the class samplesThe number of input nodes is the number of bandsThe number of output nodes is the number of defined classes in the training samplesThe number of hidden nodes is set heuristicallyNeural network classifies all of feature space by drawing nonlinear boundaries between the classes and train and run quickly with a limited number of classes

Chapter 5: CS689 101

6.4d: Parzen Windows Classifier

Also known as probabilistic neural networkIt builds up sophisticated estimates of the underlying probability distribution of each class from the individual training samplesIt draws near-optimal boundaries that approach Bayes optimalIt is more computation intensive, but is often the best for complex distributions of sample points

Chapter 5: CS689 102

6.4e: Euclidean Distance Classifiers

When training data is limited, it is difficult to get a good estimate of the mean vectorDistance information-based classifiers may be betterMinimum distance or nearest neighbor classifiers assign unknown pixels to the class of sample that is closest in feature spaceThink about the k-means algorithm or the k–nearest neighbor algorithm

Chapter 5: CS689 103

6.4f: Drawbacks of Distance Classifiers

Covariance data is not used in minimum distance algorithms, spectral clustering is assumed to spread evenly in the spectral domainElongated and asymmetric classes having more variation in a particular band are not well modeled with minimum distance methodsInput bands should be scaled to the same dynamic range

Chapter 5: CS689 104

6.5a: Spatial and Feature Context

Spatial context and contextual clues can be used to produce more accurate classificationA pixel is more likely to be neighbor to pixels of its own class than to be isolatedA single pixel of healthy tissue is unlikely surrounded by malignant tissuesContextual information can be incorporated into a classification algorithm, or applied as a filter after classification

Chapter 5: CS689 105

6.5b: Iterative Refinements

An estimate of the likelihood for each class is calculated for each class in statistically based classifiersThis information can be used during iterative relaxation where initial or previous classification of pixels with low classification confidence is reconsideredRelaxation can be iterated until no more pixels are classified or the number of changed pixels is below a specified threshold

Chapter 5: CS689 106

6.6a: Verification of Feature Maps

Thematic map verification involves verifying that pixels are correctly labeledEmpirical verification involves comparing sample pixels from the thematic map to the reference dataAn error matrix can be calculated as a simple ratio for each class of the number of pixels correctly and incorrectly classifiedMultispectral volumetric analysis of brain MRI can show significant deviation from normal values Each clinical problem with multispectral analysis will require its own protocol to select parameters to enhance segmentation of structures of interest

Chapter 5: CS689 107

6.7a: Feature Space Applied

Classification results are presented in two main waysA thematic map in which pixels are color coded to identify components of the sceneA numeric report based on pixel counts for each classMultispectral classification can be a valuable tool for object segmentation, particularly for objects consisting of many small disconnected components

Chapter 5: CS689 108

6.7b Classification Applications

Segmented objects can be used for object-oriented volume renderingObject volume is easily calculated from pixel countsThis can be used to detect and measure tumor size and brain volumeTime series studies have measured response of tumor volume to therapy, as well as changes due to aging

Chapter 5: CS689 109

6.7c Clinical Applications

Detection of malignancies in biospy specimensMeasuring tumor response to radiotherapyDetection of multiple sclerosisWe need to develop computer based automatic procedures that have high level confidence of accuracy, before they can be applied in clinical situations They have to be tested with many clinical studies and with large population groups before they can be approved for clinical use