The left ventricle (LV) is one of the four chambers (two atria and two ventricles) in the human heart. At the same time, its effectiveness largely depends on the degree of homogeneity and resolution of the objects present in the image.
Cardiac Magnetic Resonance Imaging
Need of Left Ventricle Segmentation
Congenital heart defect (CHD) - a defect in the structure of the heart and large vessels of a newborn;. Image noise originates from the patient (thermal noise) and is added during signal processing in the receiver chain [10].
Concept of Segmentation
Scope of Image Segmentation
Dimensionality
In the last decade, segmentation techniques have gained importance in the quantitative analysis of medical images and in image-guided interventional procedures. The hypothesis of this research work is whether the appropriate use of an immersive environment can improve (in terms of accuracy, speed and user experience) classical 2D and 3D (i.e. 2D+time) slice-based image segmentation techniques.
Selected Literature Survey
Level set methods [22-24] that have been widely used in medical image segmentation overcome some of the limitations. The k-nearest neighbor (kNN) classifier [33] is a generalization of this approach, where the pixel is classified according to the majority vote of the k nearest training data.
Advantages of Random Walk for CMR Image Segmentation
ADVANTAGES OF RANDOM WALK FOR CMR IMAGE SEGMENTATION 16described below. MOTIVATION AND ORGANIZATION OF THE THESIS 17and 4) Intuitive segmentations.
Motivation and Organization of the Thesis
Motivation
The difficulty that arose in distinguishing two adjacent objects is shown in Figure 1.4(b), where the intensity values in each region differ little from each other. The histogram (Figure 1.4(c)) clearly indicates the presence of more than one intensity region in the object (right ventricle is cleaner compared to LV) itself.
Thesis Contributions
The chance of moving from a vertex to its adjacent neighbor through an edge depends on the weight of the edge. The equivalent 4-connected grid topology and undirected weighted graph of the image (Figure 2.1(c)) are shown in Figure 2.2(b) and Figure 2.2(c), respectively.
Methodological Analysis
We use pixel to refer to the basic image element and node for graph-theoretic discussions and exchange in this on-demand thesis. To obtain the probability (potential) of each node, the linear system is selected once per label with the seed nodes of the other based labels (i.e. the potentials of the other seed nodes are fixed to zero).
Proposed Modification for Seeds Placement
Suppose the user accidentally places the initial seed point in the area highlighted in pink (left end inside the LV) in the blood pool, as shown in Figure 2.6(b). The main reason for the formation of such an unwanted contour is the presence of many small marks in the blood pool area.
Proposed Method for Seeds Selection
Heat Conduction Through the Rod
To introduce homogeneous boundary conditions to the general boundary value problem, it is assumed that as time → ∞, the temperature in the rod does not depend on . The frequency ω depends on the position amplitudes in the rod and the diffusion coefficient c is assumed to be unity. Now the next immediate step is to find the place where a significant change in conductivity occurs in the rod.
Adaptive Threshold Technique
The dynamic statistical parameters, described in the next subsection, set a low threshold value for the high intensity region and a high threshold value for the low intensity region. New particles encountered in the vector update the statistical parameters automatically showing the change in regions. In the next subsection, the effect of the number of seeds in the calculation is discussed.
Effect of Larger Number of Seeds on Computation
To compensate for this, we use a simple discarding scheme to select a minimal but sufficient number of seeds from the set of initial seeds obtained in Section 2.3. There are many papers reporting this method in the literature, but we limit ourselves to the one reported in [67] which is known to give an optimal solution. In addition to seed selection and placement, the approach weighting function plays a key role in the segmentation process.
Weighting Function in Random Walk Approach
Dependency of Random Walk Approach Performance on β
A random walk is determined by the transition probabilities P (c, q) = prob(xi+1 =q|xi =c), which are independent of i[76]. The random walk should be ergodic, and it is when the unique stationary distribution π(q) is satisfied. W(c, z) is the (weighted) degree of c. The two conditions for ergodicity are equivalent to the condition that the graph is 1) connected and 2) non-bipartite, which is true.
Method for Selecting β
- Region of Constant Amplitude
- Background Region
- Selection of β
- Theoretical Verification
The first step is to put all the points in order of increasing x-coordinates (if two points have the same x-coordinate, their order is determined by their y-coordinates). For a polygon (such as a triangle), the surface normal is the vector cross product of two non-parallel edges of the polygon. Therefore, in each case, the vector cross product depends on the magnitudes of the individual vectors, as do the surface normals, which directly depend on the values of the elements.
Experimental Analysis
Conclusions
The combination of the above strategies successfully segments the blood group region of the LV (endocardial wall) consisting of many sub-labels. To obtain important information about the LV, the outer wall of the myocardial muscle (epicardium) is as important as the blood group. Instead, we intend to use the boundary of the blood pool to obtain the epicardial wall, as described in the next chapter.
Selected Literature Survey
Motivation
As a result, the human operator is needed to provide global information and the human operator is very well known to cause variability in performance. If Random Walk is implemented at all, it is clear that the output will be counterproductive. Because the intensity difference between the heart muscle and the surrounding muscles is very small, the final contour must also include the unwanted surrounding muscles.
Active Contour Model
- General Edge Detector
- Active Contours
- Geometric Active Contour Model
- Geodesic Active Contour Model
The internal energy is the part that depends on the intrinsic properties of the snake, such as its length. This internal energy is so called because it characterizes the shape of the contour, independent of the gray levels in the image. By reducing this energy function (i.e. making it more negative) the snake will move towards brighter parts of the image.
Modified Active Contour Without Edges (MACWE)
MODIFIED ACTIVE CONTOUR WITHOUT EDGES (MACWE) 58-length smooth curve that takes into account the desired image properties. The fitting energy (Equation 3.3.1) must be minimized when the curve exactly lies on the object boundary (as shown in Figure 3.3, the fourth option). In connection with our goal, since two different intensity regions must be accommodated in the object, i.e. blood pool and myocardium, the first option (in Figure 3.3) must be fulfilled.
Presentation of Results
Conclusions
Weighting Function in the Approach
The vertices are the graph's representation of the image pixels, and the edges are the representation of each pixel's relationship to its surrounding neighbors (edge weights). INFLUENCE OF WEIGHING FUNCTION IN RANDOM-WALK-INPUT 68 In equation 4.1.2, β is the parameter to be determined by the operator. An attempt has been made (as discussed in Chapter 2) previously to obtain its value from the background region present in the CMR image.
Nature of Gaussian Weighting Function
INFLUENCE OF WEIGHT FUNCTION IN RANDOM WALK APPROACH 69 where the normalized intensitypi is defined by. The performance of Gaussian weight function [88] is perfect on clean images where the objects are homogeneous and well separated. DIFFERENCE FROM GAUSSIAN WEIGHTING FUNCTION 71 know the outcome of Gaussian weighting function and then one can realize the essence of any.
Difference of Gaussian Weighting Function
Presentation of Results
A combined segmentation algorithm (inner and outer contour) is implemented using Gaussian and DoG weighting functions. It can also be observed that the segmentation improvement is little possible even after applying DoG, if the object is almost homogeneous (for example in Figure 4.4(a) and 4.5(a)). The ground-truth equivalents of the CMR test images are given at the same time (shown here in Figure 4.6), and other proposed features are also described at the same time.
Difference of Laplacian of Gaussian Weighting Function
Presentation of Results
In addition, some other images from the dataset (ground truth equivalents) are shown in Figure 4.11.
Laplacian of Derivative of Gaussian Weighting Function
Presentation of Results
Figure 4.16 shows some CMR images from the dataset (ground truth equivalents) to indicate the intensity distribution in LV. The results are shown in Figures 4.14 and 4.15, and it is quite clear that the performance due to LoDroG is much better than that of the Gaussian weighting function. It is also observable that the papillary muscles are well segmented, indicating the efficiency of LoDroG, in contrast to Gaussian and DoG (and to some extent DoLoG) weighting function.
Conclusions
Pratt’s Figure of Merit
Pratt's Figure of Merit is used to compare the result of an edge detection algorithm to the known ground truth. It returns a number between 0 and 1 based on the quality of edge detection, with 1 being the best. F is defined as a closed line that exists within the area E in areas where the contours are not equal to B.
Hausdorff’s Distance
Let A and B (shown in Figure 5.2(c)) be two similar closed lines corresponding to the contour of an object: contourA = setpoints, contourB = setpoints. Let areasC, DandE be defined as: C = area enclosed by contourA,D = area enclosed by contourB andE = C XOR D. The intercept of each of these lines with contours A and B defines some corresponding points on both contours.
Unsupervised Evaluation Criteria
Intra-Region Uniformity Criteria
In practice, they calculate the amount of business for a thresholded image using the gray-level convergence matrix of the image. That is, those entries of the co-occurrence matrix that represent the percentage of object-background adjacencies are summed. The larger the value of the intra-region index, the more the homogeneity of the specific object in the image.
Inter-Regions Contrast
The lower the load, the smoother the threshold images and the better the segmentation result. Consequently, the better the segmentation result, the higher the performance of the applied algorithm. METHOD OF MINIMUM DISTANCES (MMD) 96 where NR, wi, mi, li, andlij indicate the number of regions, the weight associated with each region.
Maximum of Minimum Distances (MMD) Method
MAXIMUM OF MINIMUM DISTANCE (MMD) METHOD 97 Table 5.1: Evaluation of segmentation by Random Walk approach with Gaussian and DoG as weighting function. MAXIMUM OF MINIMUM DISTANCE (MMD) METHOD 98 Table 5.2: Evaluation of segmentation by Random Walk approach using Gaussian and DoLoG as weighting function. MAXIMUM OF MINIMUM DISTANCE (MMD) METHOD 99 Table 5.3: Evaluation of segmentation by Random Walk approach with Gaussian and LoDroG as weighting function.
Presentation of Results
Conclusions
In this work we dealt with ischemic CMR images, where the objects in the image are unclear and non-homogeneous. A user interactively labels a small number of pixels with known labels (called seeds), for example "object" and "background" in the image. Intensity inhomogeneity is often observed in the left ventricle and this causes significant problems when applying this segmentation algorithm to such CMR images.
Tracks for Future Work
TRACKS FOR FUTURE WORK 106difference between Laplacian or Gaussian (DoLoG) and Laplacian or Derivative of Gaussian (LoDroG). Positron emission tomography (PET) and single photon emission computed tomography (SPECT) belong to the former group. This section describes the direct relationship between the image variance and the candidate variable.
Wave Propagation in a Cantilever Beam Subjecting the Impact Moment
Heat Conduction Through a Slab
To introduce the homogeneous boundary conditions to the problem, it is assumed that ast→ ∞, the temperature in the rod does not depend on. Using the method of separation of variables and implementation of the boundary conditions, we solve for the homogeneous part as. 7.3.21).
Wave propagation in a beam subjecting torque
Derivative of Gaussian (DroG) weighting function
Bernhard, "NMR imaging of materials," Measurement Science and Technology, vol. http://www.cis.rit.edu/htbooks/mri. Malik, “Normalized slices and image segmentation,” IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. Canny, “A computational approach to edge detection,” IEEE Transactions on Pattern Analysis and Machine Intelligence, vol.
