Research pepars

Assessing Cardiac Dynamics based on X-Ray

Coronary Angiograms

Cardiac cycles is of importance for diagnosing coronary artery diseases and exploring pathogenesis of related circulation deficits and myocardial anomalies.

Specialists diagnose end systolic contour with end-diastolic contour of the left

Ventricle (LV) and measuring the ventricular volume. But various errors occurred in this performance, so we cannot be ensured this method.

When doing cardiac researchers it is rather difficult to quantitatively estimate the

deformation, such as expansion, contraction, and twisting, due to representations with spherical harmonic functions and they neglected variations of global location and orientation of the heart.so, bifurcation points extracted from in vivo angiograms is rather limited and they are sparsely distributed over the myocardia surface. Therefore, motion estimation results

from such limited data are not accurate enough.

Method

For this research used Parameters of each component are separately estimated based on non-rigid motion theory. And they followed following steps

1. Reconstructing 3-D Vessel Skeletons from Angiograms

The main advantage of this method is that matching between the

Angiogram pair in point-by-point manner is avoided.

2. Estimating Global Rigid Motion

In this quantitatively estimate global rigid motion.

3. Estimating Global Deformation

They first compensate the global rigid motion according to estimated parameters before analysing global deformation.

Human heart as a whole is believed to be an elastic body and its shape changes periodically over cardiac cycles. Therefore, we build a global shape model according to 3-D coronary vessel skeletons to estimate cardiac global deformations. In recent years, the

Deformable surface model has been widely used in the field of computer vision and image processing resulting in a globally smooth and coherent surface [8]. Especially,

Super quadrics (SQ) surface [9] has received more and more attentions because of its advantages of compact representation and robust recovery of 3-D objects.

A Tutorial on Motion Estimation

Parameters of three-dimensional motion (rotation, translation) play an important role in image motion modeling. If these parameters are known precisely, the object motion can be accurately predicted. The 3D relative movement of objects and camera induces 2D motion on the image plane via a suitable projection system called as apparent motion or optical flow. Motion is perceived when a change in the image intensity on the screen is seen.

Motion estimation methods

• feature/region matching methods

• pel-recursive methods

• deterministic model based methods

• stochastic model based methods

• optical flow based methods

1. feature/region matching methods

Estimate motion by correlating/matching features or particular regions of the sequence from one frame to another.

Matching process –

Assumed that pixels belonging to the block are displaced with the same amount, which means a requirement of smoothness and decreasing side information on motion vectors.

The metrics used to perform motion estimation by block matching can be either maximizing the cross-correlation function or minimizing an error criterion.

There are two type of search strategies

1.      full-search (exhaustive)

The former is an exhaustive search within a predetermined maximum displacement range.

2.      suboptimal (non-exhaustive)

The latter is a non-exhaustive search procedure specified to decrease the search time, developed in several algorithms.

a.      2D logarithmic search

·         Stepwise implementation

·         evaluating the matching criterion for five points (the center of the search window and the four midpoints between the center and the four borders)

·         winner-one showing minimum dissimilarity among them

·         other four points around the winner with unchanged distance are taken, unless the current central point or a boundary point give a minimum matching criterion value. In this case, the distance among the five points has to be reduced. The minimum is reached when the last set of points is on a 3 × 3 2D grid.

b.      Conjugate direction search

·         two step approach,

·         matching criterion is evaluated separately by rows and then by columns, or vice versa

·         The row coordinate is fixed at an initial position, and the minimum of the chosen criterion is found along the horizontal direction. Then, the same kind of evaluation is done for the vertical direction starting from the column coordinate obtained by the previous step.

c.       Multiresolution block matching

There are pyramid with set of images, taken at different resolutions

lowest level is the original image itself,

at each step, the upper level is obtained low-pass filtering the lower one using particular weights, and then subsampling by 2×2

search algorithm finds the initial motion vectors estimation starting from the top,

and then refine them on, making them propagate to the next level. Each level gives an

improvement in the evaluation of the vectors.

d.      Hierarchical block matching

Method first applied to the two frames at their lowest resolution level. (From low to high)

the result of each level is passed onto the next higher resolution level and used as initial estimates of the displacement vector field. These initial values are then updated by the values

lower resolution levels purpose -  estimate the major part of the displacement;

higher resolution levels purpose -  fine-tune the estimates obtained at lower resolution levels.

e.       Overlapped block matching

·         to reduce or totally eliminate blocking artefacts.

·         applying a windowing function to the error and then evaluated the “windowed MAD” to find the best match and consequently the displacement vector.

·         This method leads to both a good trade-off between higher computational cost and also less prediction error.

2.Pel-recursive methods

Aims to estimate the displacement vectors for each pixel of a frame in a recursive manner. This is done using a recursive method (called descent method) that moves pixel by pixel both spatially (horizontally and vertically) and temporally (same position in two consecutive frames).

Several algorithms have been developed in this field, which mainly differ on the

kind of approach they implement.

·         Netravali-Robbins

It is based on the steepest descent algorithm and it aims to estimate the motion

vectors minimizing the squared DFD (Displacement Frame Difference). The estimated displacement is defined in a recursive

way

·         Bergmann

He proposed a modified version of the Netravalli-Robbins by using the Newton-

Raphson’s algorithm instead of the steepest descent one. The advantage is that the proposed

method converges to the minimum faster than using the steepest descent one

3.Optical flow based methods

Several techniques have been developed to approach the computation of optical flow

• ·         Gradient-based approach

The first method being proposed is the Horn and Schunck one. The method initially makes the assumption of moving object and moving sensor. The second method is the Lucas and Kanade one. The iteration is not done in a strict pixel by pixel way, but considering a small neighborhood of the pixel.

• ·         Correlation-based approach

The frame is here divided into fixed-size non overlapping blocks and a matching by a searching window defined by some a priori rule is performed through the image. The displacement to the block that shows the highest likelihood or the lowest dissimilarity is taken as measure of the translation a motion vector to our reference block.

• ·         Spatio-temporal energy based approach

Gabor filter is able to select some frequency components from the signal it is filtering. The main idea is to detect motion in the frequency domain, usingparticular spatiotemporal filters, Gabor energy filters

Block Matching Algorithms For Motion Estimation

Block Matching Algorithms For Motion Estimation

Motion estimation is that the patterns corresponding to objects and background in a frame of video sequence move within the frame to form corresponding objects on the subsequent frame.

Block matching is to divide the current frame into a matrix of ‘macro blocks’ that are then compared with corresponding block and its adjacent neighbors in the previous frame to create a vector that stipulates the movement of a macro block from one location to another in the previous frame.

Block matching algorithms used for motion estimation in video compression. It implements and compares 7 different types.

Exhaustive Search (ES)

This algorithm calculates the cost function at each possible location in the search window. This leads to the best possible match of the macro-block in the reference frame with a block in another frame. The resulting motion compensated image has highest peak signal-to-noise ratio as compared to any other block matching algorithm. However this is the most computationally extensive block matching algorithm among all. A larger search window requires greater number of computations.

Three Step Search (TSS)

This is one of the earliest attempts at fast block matching algorithms. It runs as follows

1.      Start with search location at center

2.      Set step size ‘S’ = 4 and search parameter ‘p’ = 7

3.      Search 8 locations +/- S pixels around location (0,0) and the location (0,0)

4.      Pick among the 9 locations searched, the one with minimum cost function

5.      Set the new search origin to the above picked location

6.      Set the new step size as S = S/2

7.      Repeat the search procedure until S = 1

The resulting location for S=1 is the one with minimum cost function and the macro block at this location is the best match.

There is a reduction in computation by a factor of 9 in this algorithm. For p=7, while ES evaluates cost for 225 macro-blocks, TSS evaluates only for 25 macro blocks.

New Three Step Search (NTSS)

TSS uses a uniformly allocated checking pattern and is prone to miss small motions. NTSS is an improvement over TSS as it provides a center biased search scheme and has provisions to stop half way to reduce the computational cost. It was one of the first widely accepted fast algorithms and frequently used for implementing earlier standards like MPEG 1 and H.261.

Simple and Efficient Search (SES)

The idea behind TSS is that the error surface due to motion in every macro block is unimodal. A unimodal surface is a bowl shaped surface such that the weights generated by the cost function increase monotonically from the global minimum. However a unimodal surface cannot have two minimums in opposite directions and hence the 8 point fixed pattern search of TSS can be further modified to incorporate this and save computations. SES  is the extension of TSS that incorporates this assumption.

Four Step Search (4SS)

Four Step Search is an improvement over TSS in terms of lower computational cost and better peak signal-to-noise ratio. Similar to NTSS, FSS  also employs center biased searching and has a halfway stop provision.

Diamond Search (DS)

DS algorithm is exactly the same as 4SS, but the search point pattern is changed from a square to a diamond, and there is no limit on the number of steps that the algorithm can take. DS uses two different types of fixed patterns, one is Large Diamond Search Pattern (LDSP) and the other is Small Diamond Search Pattern (SDSP).

This algorithm finds the global minimum very accurately as the search pattern is neither too big nor too small. Diamond Search algorithm has a peak signal-to-noise ratio close to that of Exhaustive Search with significantly less computational expense.

Adaptive Rood Pattern Search (ARPS)

Adaptive rood pattern search (ARPS)  algorithm makes use of the fact that the general motion in a frame is usually coherent,  if the macro blocks around the current macro block moved in a particular direction then there is a high probability that the current macro block will also have a similar motion vector. This algorithm uses the motion vector of the macro block to its immediate left to predict its own motion vector.

Image Enhancement

 Image Enhancement 

Image enhancement is the process of adjusting digital images so that the results are more suitable for display or  further image analysis.

Here are some useful examples and methods of image enhancement:

• Filtering with morphological operators
• Histogram equalization
• Noise removal using a Wiener filter
• Linear contrast adjustment
• Median filtering
• Unsharp mask filtering
• Contrast-limited adaptive histogram equalization (CLAHE)
• Decorrelation stretch

The aim of image enhancement is to improve the interpretability or perception of information in images for human viewers, or to provide `better' input for other automated image processing techniques.

Image enhancement techniques can be divided into two broad categories:

1. Spatial domain methods, which operate directly on pixels
2. frequency domain methods, which operate on the Fourier transform of an image.

Unfortunately, there is no general theory for determining what is `good' image enhancement when it comes to human perception. If it looks good, it is good! However, when image enhancement techniques are used as pre-processing  tools for other image processing techniques, then quantitative measures can determine which techniques are most appropriate.

How reduce gradient motion?

How reduce gradient  motion?

1.      Minimize the degree of motion. 

     a.  The importance of simple instruction/education of the patient to hold still        while the scanner is making noise should not be underestimated. Pre-scan training and practice with breath holding may be helpful.

     b.  The patient should be made as comfortable in the scanner as possible, including back, leg, or head supports. Stabilization measures including the use foam pads, taping, snug wrapping with sheets, or even bite bars may be useful. Infants should be swaddled and their heads supported.

     c.  For uncooperative patients or those with high anxiety or pain, sedation or general anesthesia may be required.

     d. Some physiologic motions such as peristalsis can be reduced with appropriate pharmacologicagents (e.g., glucagon 1 mg) given IM to prolong their action. 

2.      Suppress signal from moving tissues.

      a. Using surface coils confined to the area of interest will minimize unwanted signals from moving tissues located farther away. A good example is the use of a spine coil array which will naturally attenuate signals from the moving anterior abdominal wall due to distance. 

     b.  Spatial saturation pulses can null signals from unwanted moving anatomical objects.

     c.  Fat suppression techniques (STIR, CHESS, etc) will null high signal from subcutaneous and juxtadiaphragmatic fat stores that are often responsible for motion artifact.

     d.  Flow saturation pulses will suppress signals from arterial or venous blood entering a slice.

3.        Adjust imaging sequences and parameters.

     a.  Increasing number of signals averaged (NSA, NEX) will reduce artifacts and increase signal-to-noise but at expense of increased imaging time.

     b.  Swapping frequency- and phase-encoding directions will shift direction of artefacts but will not reduce them.

     c.  Single-slice ultrafast sequences (HASTE, EPI, TrueFISP) may acquire images rapidly enough (2-5 sec) to freeze bulk motion without breath holding or any additional special techniques.

     d.  Radial/spiral sequences are more effective than those using Cartesian trajectories at dispersing motion artifacts throughout an image.

     e.  Flow compensation (FlowComp, GMN) techniques reduce artifacts from flowing blood and spinal fluid by gradient refocusing of signal.

4.      Detect and compensate for motion. 

     a.  Hardware-based gating methods for respiratory or cardiovascular motion are widely available. Respiratory expansion may be detected by use of a thoracic belt or bellows. Cardiovascular motion can be detected by EKG or peripheral pulse device. Once detected, the MR pulse sequence can be prospectively triggered to a specific time in the cardiac cycle, respiratory cycle, or both. Retrospective gating can also be performed. In this technique MR data is continuously acquired and points are reordered or discarded retroactively based on their timing within the cardiorespiratory cycle.

     b.  Navigator echo techniques (e.g., PACE) use additional RF-pulses to track cardiac or diaphragmatic position. Information from the navigator echo can be used prospectively to trigger data acquisition or retrospectively to adjust the location of a group of slices already acquired.

     c.  Self-correcting sequences (PROPELLER, BLADE) oversample the center of k-space and can detect in-plane rotation or translation. Aberrant slices can be rejected or realigned with the others through an iterative procedure.

     d.  Co-registration to external landmarks or a reference image can control motion artifacts over a 3-dimensional volume. Images are transformed by spatial translations, rotations, and interpolations.

Optical flow

Optical flow is the pattern of apparent motion of image objects between two consecutive frames caused by the movemement of object or camera. It is 2D vector field where each vector is a displacement vector showing the movement of points from first frame to second.

Optical flow has many applications in areas like :

• Structure from Motion
• Video Compression
• Video Stabilization 

Optical flow works on several assumptions:

1. The pixel intensities of an object do not change between consecutive frames.
2. Neighbouring pixels have similar motion.

Angiography

Motion stabilization of direct coronary cine-angiogram for vessel alignment

Angiography :-

•  Angiography is a medical imaging technique.
•  It uses to visualize the inside, or lumen,of blood vessels and organs of the body with particular  interest in the arteries,veins and the heart chambers.
• This is done by injecting a radio-opque contrast agent into the blood vessel and imaging using X-ray based technique.

Cine-angiography :-

Cine-angiography is the technique of taking moving pictures to show how a dye visible by X-ray passes through blood vessels. It allows doctors to see blockages and obstructions.