INTRODUCTION

The aim of this project is to analyze particle flow across images. This is a relatively common technical problem that arises in many disciplines. Obviously fluid dynamics, blood flow, or similarly the motion of surfaces as seen by motion of points. This is a unique project where the particles are sheeps herding in a lush green field. We will determine the flow of sheep gathering to cross through a small opening. For this project we have four sequential frames from the video, taken at interval of 1 sec starting at t = 38 sec.

The main objective of the project is to analyze the particle flow across the images and develop corresponding vectors indicating the direction of flow. To perform the analysis it is first important to convert the sheeps into a size of a particle. This is achived by toning down the sheeps to the level of a single or few pixels. To do so, various operations like thresholding, hit or miss etc are perfomed. The second major objective of the project was to see the movement of the entire sheep flock as a single unit. To do so, all the various operations like convolution, dilatation etc are performed. The work flow of the project and the steps are as follows -

• Images taken as input

• Elementary preprocessing done

• Heat Map created

• Preprocessing images to represent the entire flock of sheep herd as a single unit

• Flow analysis and vector plotting

• Preprocessing images to represent each sheep as a single unit.

• Flow analysis and vector plotting

• Velocity analysis

The images developed show a heat map with white being the coolest (least dense) and black dark red being the hottest (most dense) area.

The results are in line with what we see in the frames. The first few images have few sheep at the gates. In the last frame a large part of the herd is going through the gate hence in the last image there is a dark red spot near the gates. We see the flock moving through the gates and the middle of the flock moving about.

Processing images to represent all sheep as a single unit

The work flow of the algorithm is

• Input image is thresholded

• Converted to binary

• Sheeps are then dilated using ones(3,3) matrix

• This is repeated for 25 times

Since the image is big and sheeps are spread across a wider area, multiple iterations of dialation are needed to convert the image to be treated as a single flock. This number was decided to be 25 by trial

Motion tracking algorithm

• The proposed algorithm intakes a two subsequent frames of the processed images

• Search window size, Template window size and grid dimension are given as input

• Image 1 acts as a template which is searched in Image 2.

• Entire image is broken down into several windows based on the tracking parameters

• Correlations are developed using normxcorr2to see the matching intensities

• Extra developed padding is subtracted

• Quiver plots are taken in account

The above images show a clear movement of the flock in north west direction. The length of the arrow is proportional to the length of the arrow. Since the diluted blob is tracked as a whole hence we can see a general movement in the northwest direction.

Processing images to represent each sheep as a single unit

The input images are first thresholded and then converted to binary images. These images are then further skeleton morphed to reduce the thickness of each sheep and finally different erode and hit/miss commands are taken into account. The sheeps can be assumed to have 4 different orientations namely Horizontal, Vertical, Leading diagnol and Falling diagnol.

Each of the image is first eroded using the hit structural element and then morphed using bwhitmiss(image,hit,miss) command in 4 different ways. All the four different parts are then added to represnt the entire image.

As a result of these operations, we now have the final images which shows the sheep being represented by 1 or 2 pixels.

Zoomed images of top left corner

Velocity Analysis

To calculate the velocity, we first note the exact timestamp of each frame. The first frame is at 0:39, second frame is at 0:41, third frame is 0:43 and last frame is at around 0:45. Next, we need the distance traveled by sheep. This is achieved by plotting 'imagesc' plot and noing the average distance traveled by the pixels.

As seen from the above image (left) the sheep is approximately 15 pixels long and in frame 1 to 2 the head of the sheep moved about 75 pixels up and 45 pixels to the left so the sheep moved around 85 pixels. An adult sheep is approximately 1.5 metres long hence each pixel represents about 1.5/15 m ~= 0.1 m. Therefore, the velocity is 85*0.1/2 ~= 4.25m/s or around 15 kmph.

The MATLAB code is available here