I'm using Gaussian equation for a particular photo effect in an iOS application.
I use:
double sigmaX = ...; //some value here
for(int i=0;i<height;i++)
{
double F = 0;
double step = -(pos)*width/20;
/*height,width,pos - all predefined, no problem there*/
for(int j=0;j<4*width;j+=4)
{
F = (double) ((1/1)*exp(-sigmaX*(pow((step++)/1, 2.0)))) ;
//do some operation here...
}
}
and the value of F is used to determine a particular intensity which is used up elsewhere.
So far so good.... F is the typical bell curve as expected.
But, the question is, I want to scale the standard deviation of this curve as per user input.
For example, in the following image, I'd like to shift the curve from the green to the red line (blue maybe an intermediate), hopefully in linear steps:
Now, given the standard notation of:
and comparing it with the way I implemented it in my code, I got the idea to vary 1/sqrt(sigmaX) to alter the scale/SD. I tried incrementing 1/sqrt(sigmaX) in linear steps (to get linear increment) or by x^n to get power of n increment in SD, but none of that worked.
I am a bit stuck with the concept.
Can you please let me know how to scale the Standard Deviation by a predefined ratio, i.e I may want it 1.34 or 3.78 times the oirginal SD and it will scale up the the +3sigma to -3sigma span accordingly.
Your calculation here:
F = (double) ((1/1)*exp(-sigmaX*(pow((step++)/1, 2.0)))) ;
Is not reflecting the Gaussian formula you showed. It should be something like this:
double dSigma = 1.0;
static const double dRootTwoPi = sqrt(2.0 * M_PI);
F = (1.0 / (dSigma * dRootTwoPi)) * exp(-0.5 * pow(step++ / dSigma, 2.0));
Then you can vary dSigma from 1.0 to 3.0 (or whatever) to get the effect you want.
Thanks Roger Rowland, for the help... I finally got this to work:
Changed the gaussian function to:
sigmaX*=scaling;
F = (double) ((scaling / (sigmaX))*exp(-0.0005*(powf((step++/sigmaX), 2.0)))) ;
Indeed, what I had done before wasn't exactly Gaussian. This works fine and scales fine, based on the scaling parameter.
Thanks again.
Related
I am trying to backpropogate a very primitive / simple ANN.
I've almost got it working. I'm trying to implement the formulas and the article I'm reading does not specify whether to use dot product or element wise multiplication or some other multiplication.
Article: https://ml-cheatsheet.readthedocs.io/en/latest/backpropagation.html
Here's the formula for calculating the error (or delta) of a single Hidden layer:
Or, as I read it in the context of my algorithm,
Delta = prev_delta * prev_weight * zprime
Where delta is the error of this layer, prev_delta is the delta of the previous layer, prev_weight is the weight of the previous layer, and zprime is the derivative of the activation function of the current layer.
Also, for a single Output Layer:
Or, as I read it in the context of my algorithm,
Delta = (output - target) % zprime;
Where output is the final output of the feed-forward and target is the target values.
I've written this code to run this calculation:
void Layer::backward(Matrix & prev_delta, Matrix & prev_weight) {
// all variables are matrices
// except for prev_layer, that's a pointer to a layer object.
// I'm using Armadillo for linear algebra / matrices
// delta, weight, output, and zprime refer to the current layer.
// prev_delta, prev_weight belong the the previous layer.
if (next_layer == nullptr) {
// if next layer is null, this is the output layer.
// in that case, prev_delta is target.
// yHat - y * R'(Zo)
delta = (output - prev_delta) * zprime;
}
else {
// Eo * Wo * R'(Zh)
delta = prev_delta * prev_weight * zprime;
}
// tell the next layer to backpropogate
if (prev_layer != nullptr)
prev_layer -> backward(delta, weight);
}
matrix * matrix indicates a matrix multiplication (dot product)
matrix % matrix indicates element-wise multiplication
The issue I'm having is that these matrices don't seem to multiply properly. I've made sure everything lines up the same way the article has it, but these pieces just don't seem to fit. How should these matrices be multiplied to get the result?
Edit: to clarify, I get errors when I try to take the dot product of these matrices. "invalid size". I've tried using element wise multiplication but then things get weird there too.
I found this code on the internet and would like to know the theory behind it, can anybody point me in the right direction?
Here is the code:
float4 SHCNormalize(in float4 res)
{
// extract direction
float l = dot(res.gba, res.gba);
res.gba /= max(0.05f, sqrt(l));
res.r = 1.0;
return res;
}
To give you a little context, this code gets passed in 4 zonal harmonics coefficients representing a clamped cosine lobe in SH space.
Thanks!
the max in the function is to avoid devision by 0.0. the res.r = 1.0f is an implementation detail that only applies to the code was looking at and has no theoretical basis.
I am currently using a Project Tango tablet for robotic obstacle avoidance. I want to create a matrix of z-values as they would appear on the Tango screen, so that I can use OpenCV to process the matrix. When I say z-values, I mean the distance each point is from the Tango. However, I don't know how to extract the z-values from the TangoXyzIjData and organize the values into a matrix. This is the code I have so far:
public void action(TangoPoseData poseData, TangoXyzIjData depthData) {
byte[] buffer = new byte[depthData.xyzCount * 3 * 4];
FileInputStream fileStream = new FileInputStream(
depthData.xyzParcelFileDescriptor.getFileDescriptor());
try {
fileStream.read(buffer, depthData.xyzParcelFileDescriptorOffset, buffer.length);
fileStream.close();
} catch (IOException e) {
e.printStackTrace();
}
Mat m = new Mat(depthData.ijRows, depthData.ijCols, CvType.CV_8UC1);
m.put(0, 0, buffer);
}
Does anyone know how to do this? I would really appreciate help.
The short answer is it can't be done, at least not simply. The XYZij struct in the Tango API does not work completely yet. There is no "ij" data. Your retrieval of buffer will work as you have it coded. The contents are a set of X, Y, Z values for measured depth points, roughly 10000+ each callback. Each X, Y, and Z value is of type float, so not CV_8UC1. The problem is that the points are not ordered in any way, so they do not correspond to an "image" or xy raster. They are a random list of depth points. There are ways to get them into some xy order, but it is not straightforward. I have done both of these:
render them to an image, with the depth encoded as color, and pull out the image as pixels
use the model/view/perspective from OpenGL and multiply out the locations of each point and then figure out their screen space location (like OpenGL would during rendering). Sort the points by their xy screen space. Instead of the calculated screen-space depth just keep the Z value from the original buffer.
or
wait until (if) the XYZij struct is fixed so that it returns ij values.
I too wish to use Tango for object avoidance for robotics. I've had some success by simplifying the use case to be only interested in the distance of any object located at the center view of the Tango device.
In Java:
private Double centerCoordinateMax = 0.020;
private TangoXyzIjData xyzIjData;
final FloatBuffer xyz = xyzIjData.xyz;
double cumulativeZ = 0.0;
int numberOfPoints = 0;
for (int i = 0; i < xyzIjData.xyzCount; i += 3) {
float x = xyz.get(i);
float y = xyz.get(i + 1);
if (Math.abs(x) < centerCoordinateMax &&
Math.abs(y) < centerCoordinateMax) {
float z = xyz.get(i + 2);
cumulativeZ += z;
numberOfPoints++;
}
}
Double distanceInMeters;
if (numberOfPoints > 0) {
distanceInMeters = cumulativeZ / numberOfPoints;
} else {
distanceInMeters = null;
}
Said simply this code is taking the average distance of a small square located at the origin of x and y axes.
centerCoordinateMax = 0.020 was determined to work based on observation and testing. The square typically contains 50 points in ideal conditions and fewer when held close to the floor.
I've tested this using version 2 of my tango-caminada application and the depth measuring seems quite accurate. Standing 1/2 meter from a doorway I slid towards the open door and the distance changed form 0.5 meters to 2.5 meters which is the wall at the end of the hallway.
Simulating a robot being navigated I moved the device towards a trash can in the path until 0.5 meters separation and then rotated left until the distance was more than 0.5 meters and proceeded forward. An oversimplified simulation, but the basis for object avoidance using Tango depth perception.
You can do this by using camera intrinsics to convert XY coordinates to normalized values -- see this post - Google Tango: Aligning Depth and Color Frames - it's talking about texture coordinates but it's exactly the same problem
Once normalized, move to screen space x[1280,720] and then the Z coordinate can be used to generate a pixel value for openCV to chew on. You'll need to decide how to color pixels that don't correspond to depth points on your own, and advisedly, before you use the depth information to further colorize pixels.
The main thing is to remember that the raw coordinates returned are already using the basis vectors you want, i.e. you do not want the pose attitude or location
What I am doing is trying to implement an Skin Probability Maps algorithm for skin detection in OpenCV.
I've stuck in a place where I should compare SkinHistValue / NonSkinHistValue probability of each pixel with Theta threshold according to http://www.cse.unsw.edu.au/~icml2002/workshops/MLCV02/MLCV02-Morales.pdf and this tutorial http://www.morethantechnical.com/2013/03/05/skin-detection-with-probability-maps-and-elliptical-boundaries-opencv-wcode/
My problems lies in calculating the coords for hist value:
From the tutorial:
calcHist(&nRGB_frame,1,channels,mask,skin_Histogram,2,histSize,ranges,uniform,accumulate);
calcHist(&nRGB_frame,1,channels,~mask,non_skin_Histogram,2,histSize,ranges,uniform,accumulate);
Calculates the histograms. Than i normalize them.
And after that:
for (int i=0; i<nrgb.rows; i++) {
int gbin = cvRound((nrgb(i)[1] - 0)/range_dist[0] * hist_bins[0]);
int rbin = cvRound((nrgb(i)[2] - low_range[1])/range_dist[1] * hist_bins[1]);
float skin_hist_val = skin_Histogram.at<float>(gbin,rbin);
};
Where nrgb is my image, and im trying to get skin_hist_value for that. But the gbin and rbin are probably calculated wrong and it throws an exception (i run outside of array?) when it comes to
skin_Histogram.at<float>(gbin,rbin);
I have totally no idea how to calculate it correctly. Any help?
I'm having trouble setting up vectors for an object in my code. I tried modeling my code similarly to the answer in this question: Game enemy move towards player except that I'm using GLKVector2's. I thought my implementation seemed correct, but it's really only my first time using vectors with GLKit and in general I haven't used them too much before.
My current code looks something like:
GLKVector2 vector = GLKVector2Make(self.player.position.x - self.target.position.x, self.player.position.y - self.target.position.y);
float hypo = sqrt(vector.x*vector.x + vector.y*vector.y);
float speed = 0.25;
vector = GLKVector2Make(vector.x/hypo, vector.y/hypo);
vector = GLKVector2MultiplyScalar(vector, speed);
GLKVector2 sum = GLKVector2Add(vector, self.target.position);
self.target.moveVelocity = sum;
Is it possible that my logic just isn't correct here? I'd appreciate any help or suggestions. Thanks!
EDIT: just for clarification since I didn't really explain what happens.. Basically the "enemy" shapes either stutter/jump or just stick. They aren't moving toward the other object at all.
EDIT 2:
If I try using GLKVector2Normalize, then nothing moves. If I do something like:
GLKVector2 vector = GLKVector2Make(self.player.position.x - self.target.position.x, self.player.position.y - self.target.position.y);
float speed = 0.10;
// float distance = GLKVector2Distance(self.player.position, self.target.position);
// vector = GLKVector2Normalize(vector);
vector = GLKVector2MultiplyScalar(vector, speed);
self.target.moveVelocity = vector;
Then the movement works toward the player object, but only updates the one time even though it should be updating every second.
Two things:
There's no need to calculate the magnitude of the vector and divide yourself -- GLKit has a GLKVector2Normalize function, which takes a vector and returns the vector in the same direction with length 1. You can then use GLKVector2MultiplyScalar (as you do) to change the speed.
Your target's velocity should be set to vector, not sum, assuming that in the target's update method (which you should call once per timestep), you add self.moveVelocity.x to self.position.x and self.moveVelocity.y to self.position.y each timestep. As it is now, your sum variable will hold the position that your target should have one timestep in the future, not its velocity.