Adaptive Median Filter - image-processing

I am constructing code for adaptive median filter . When i execute it it gives me error at line No 12. Not enough arguments. and on line 28.Unexpected MATLAB Expression.
function f = adpmedian(g, Smax)
%ADPMEDIAN Perform adaptive median filtering.
% F = ADPMEDIAN(G, SMAX) performs adaptive median filtering of
% image G. The median filter starts at size 3-by-3 and iterates up
% to size SMAX-by-SMAX. SMAX must be an odd integer greater than 1.
% SMAX must be an odd, positive integer greater than 1.
**12>>**if (Smax <= 1) || (Smax/2 == round(Smax/2)) || (Smax ~= round(Smax))
error('SMAX must be an odd integer > 1.')
end
[M, N] = size(g);
% Initial setup.
f = g;
f(:) = 0;
alreadyProcessed = false(size(g));
% Begin filtering.
for k = 3:2:Smax
zmin = ordfilt2(g, 1, ones(k, k), 'symmetric');
zmax = ordfilt2(g, k * k, ones(k, k), 'symmetric');
zmed = medfilt2(g, [k k], 'symmetric');
`28>>` processUsingLevelB = (zmed > zmin) & (zmax > zmed) & ...
~alreadyProcessed;
zB = (g > zmin) & (zmax > g);
outputZxy = processUsingLevelB & zB;
outputZmed = processUsingLevelB & ~zB;
f(outputZxy) = g(outputZxy);
f(outputZmed) = zmed(outputZmed);
alreadyProcessed = alreadyProcessed | processUsingLevelB;
if all(alreadyProcessed(:))
break;
end
end
% Output zmed for any remaining unprocessed pixels. Note that this
% zmed was computed using a window of size Smax-by-Smax, which is
% the final value of k in the loop.
f(~alreadyProcessed) = zmed(~alreadyProcessed);

Related

Precision and recall missunderstanding

In pycocotools in cocoeval.py sctipt there is COCOeval class and in this class there is accumulate function for calculating Precision and Recall. Does anyone know what is this npig variable? Is this negative-positive or?
Because I saw this formula for recall: Recall = (True Positive)/(True Positive + False Negative)
Can I just use this precision and recall variable inside dictionary self.eval to get precision and recall of my model which I'm testing, and plot a precision-recall curve?
And the variable scores is this F1 score?
Because I'm not very well understand this T,R,K,A,M what is happening with this.
How can I print precision and recall in terminal?
def accumulate(self, p = None):
'''
Accumulate per image evaluation results and store the result in self.eval
:param p: input params for evaluation
:return: None
'''
print('Accumulating evaluation results...')
tic = time.time()
if not self.evalImgs:
print('Please run evaluate() first')
# allows input customized parameters
if p is None:
p = self.params
p.catIds = p.catIds if p.useCats == 1 else [-1]
T = len(p.iouThrs)
R = len(p.recThrs)
K = len(p.catIds) if p.useCats else 1
A = len(p.areaRng)
M = len(p.maxDets)
precision = -np.ones((T,R,K,A,M)) # -1 for the precision of absent categories
recall = -np.ones((T,K,A,M))
scores = -np.ones((T,R,K,A,M))
# create dictionary for future indexing
_pe = self._paramsEval
catIds = _pe.catIds if _pe.useCats else [-1]
setK = set(catIds)
setA = set(map(tuple, _pe.areaRng))
setM = set(_pe.maxDets)
setI = set(_pe.imgIds)
# get inds to evaluate
k_list = [n for n, k in enumerate(p.catIds) if k in setK]
m_list = [m for n, m in enumerate(p.maxDets) if m in setM]
a_list = [n for n, a in enumerate(map(lambda x: tuple(x), p.areaRng)) if a in setA]
i_list = [n for n, i in enumerate(p.imgIds) if i in setI]
I0 = len(_pe.imgIds)
A0 = len(_pe.areaRng)
# retrieve E at each category, area range, and max number of detections
for k, k0 in enumerate(k_list):
Nk = k0*A0*I0
for a, a0 in enumerate(a_list):
Na = a0*I0
for m, maxDet in enumerate(m_list):
E = [self.evalImgs[Nk + Na + i] for i in i_list]
E = [e for e in E if not e is None]
if len(E) == 0:
continue
dtScores = np.concatenate([e['dtScores'][0:maxDet] for e in E])
# different sorting method generates slightly different results.
# mergesort is used to be consistent as Matlab implementation.
inds = np.argsort(-dtScores, kind='mergesort')
dtScoresSorted = dtScores[inds]
dtm = np.concatenate([e['dtMatches'][:,0:maxDet] for e in E], axis=1)[:,inds]
dtIg = np.concatenate([e['dtIgnore'][:,0:maxDet] for e in E], axis=1)[:,inds]
gtIg = np.concatenate([e['gtIgnore'] for e in E])
npig = np.count_nonzero(gtIg==0 )
if npig == 0:
continue
tps = np.logical_and( dtm, np.logical_not(dtIg) )
fps = np.logical_and(np.logical_not(dtm), np.logical_not(dtIg) )
tp_sum = np.cumsum(tps, axis=1).astype(dtype=np.float)
fp_sum = np.cumsum(fps, axis=1).astype(dtype=np.float)
for t, (tp, fp) in enumerate(zip(tp_sum, fp_sum)):
tp = np.array(tp)
fp = np.array(fp)
nd = len(tp)
rc = tp / npig
pr = tp / (fp+tp+np.spacing(1))
q = np.zeros((R,))
ss = np.zeros((R,))
if nd:
recall[t,k,a,m] = rc[-1]
else:
recall[t,k,a,m] = 0
# numpy is slow without cython optimization for accessing elements
# use python array gets significant speed improvement
pr = pr.tolist(); q = q.tolist()
for i in range(nd-1, 0, -1):
if pr[i] > pr[i-1]:
pr[i-1] = pr[i]
inds = np.searchsorted(rc, p.recThrs, side='left')
try:
for ri, pi in enumerate(inds):
q[ri] = pr[pi]
ss[ri] = dtScoresSorted[pi]
except:
pass
precision[t,:,k,a,m] = np.array(q)
scores[t,:,k,a,m] = np.array(ss)
self.eval = {
'params': p,
'counts': [T, R, K, A, M],
'date': datetime.datetime.now().strftime('%Y-%m-%d %H:%M:%S'),
'precision': precision,
'recall': recall,
'scores': scores,
}
toc = time.time()
print('DONE (t={:0.2f}s).'.format( toc-tic))

Max and Min of a set of variables in z3py

I have a problem where I want to limit the range of a real variable between the maximum and minimum value of another set of real variables.
s = Solver()
y = Real('y')
Z = RealVector('z', 10)
s.add(And(y >= min(Z), y <= max(Z)))
Is there a way to do this in z3py?
You can use Axel's solution; though that one requires you to create an extra variable and also asserts more constraints than needed. Moreover, it doesn't let you use min and max as simple functions. It might be easier to just program this in a functional way, like this:
# Return minimum of a vector; error if empty
def min(vs):
m = vs[0]
for v in vs[1:]:
m = If(v < m, v, m)
return m
# Return maximum of a vector; error if empty
def max(vs):
m = vs[0]
for v in vs[1:]:
m = If(v > m, v, m)
return m
Another difference is that in the functional style we throw an error if the vector is empty. In the other style, the result will essentially be unconstrained. (i.e., min/max can take any value.) You should consider which semantics is right for your application, in case the vector you're passing might be empty. (At the least, you should change it so it prints out a nicer error message. Currently it'll throw an IndexError: list index out of range error if given an empty vector.)
Now you can say:
s = Solver()
y = Real('y')
Z = RealVector('z', 10)
s.add(And(y >= min(Z), y <= max(Z)))
print (s.check())
print (s.model())
This prints:
sat
[z__7 = -1,
z__0 = -7/2,
z__4 = -5/2,
z__5 = -2,
z__3 = -9/2,
z__2 = -4,
z__8 = -1/2,
y = 0,
z__9 = 0,
z__6 = -3/2,
z__1 = -3]
You could benefit from Hakan Kjellerstrand's collection of useful z3py definitions:
from z3 import *
# Functions written by Hakan Kjellerstrand
# http://hakank.org/z3/
# The following can be used by importing http://www.hakank.org/z3/z3_utils_hakank.py
# v is the maximum value of x
def maximum(sol, v, x):
sol.add(Or([v == x[i] for i in range(len(x))])) # v is an element in x)
for i in range(len(x)):
sol.add(v >= x[i]) # and it's the greatest
# v is the minimum value of x
def minimum(sol, v, x):
sol.add(Or([v == x[i] for i in range(len(x))])) # v is an element in x)
for i in range(len(x)):
sol.add(v <= x[i]) # and it's the smallest
s = Solver()
y = Real('y')
zMin = Real('zMin')
zMax = Real('zMax')
Z = RealVector('z', 10)
maximum(s, zMin, Z)
minimum(s, zMax, Z)
s.add(And(y >= zMin, y <= zMax))
print(s.check())
print(s.model())

Attempt to get numbers instead of NaN values when printing

I've a simple program with a for loop where i calculate some value that I print to the screen, but only the first value is printed, the rest is just NaN values. Is there any way to fix this? I suppose the numbers might have a lot of decimals thus the NaN issue.
Output from program:
0.18410
NaN
NaN
NaN
NaN
etc.
This is the code, maybe it helps:
for i=1:30
t = (100*i)*1.1*0.5;
b = factorial(round(100*i)) / (factorial(round((100*i)-t)) * factorial(round(t)));
% binomial distribution
d = b * 0.5^(t) * 0.5^(100*i-(t));
% cumulative
p = binocdf(1.1 * (100*i) * 0.5,100*i,0.5);
% >= AT LEAST
result = 1-p + d;
disp(result);
end
You could do the calculation of the fraction yourself.
Therefore you need to calculate $d$ directly. Then you can get all values of the numerators and the denominators and multiply them by hand and make sure that the result will not get too big. The following code is poorly in terms of speed and memory, but it may be a good start:
for i=1:30
t = (55*i);
b = factorial(100*i) / (factorial(100*i-t) * factorial(t));
% binomial distribution
d = b * 0.5^(t) * 0.5^(100*i-(t));
numerators = 1:(100*i);
denominators = [1:(100*i-t),1:55*i,ones(1,100*i)*2];
value = 1;
while length(numerators) > 0 || length(denominators) > 0
if length(numerators) == 0
value = value/denominators(1);
denominators(1) = [];
elseif length(denominators) == 0
value = value* numerators(1);
numerators(1) = [];
elseif value > 10000
value = value/denominators(1);
denominators(1) = [];
else
value = value* numerators(1);
numerators(1) = [];
end
end
% cumulative
p = binocdf(1.1 * (100*i) * 0.5,100*i,0.5);
% >= AT LEAST
result = 1-p + value;
disp(result);
end
output:
0.1841
0.0895
0.0470
0.0255
0.0142
0.0080
0.0045
...
Take a look at the documentation of factorial:
Note that the factorial function grows large quite quickly, and
even with double precision values overflow will occur if N > 171.
For such cases consider 'gammaln'.
On your second iteration you are already doing factorial (200) which returns Inf and then Inf/Inf returns NaN.

Projective Transform - matlab code

i can't use any toolbox function i need to build it from scratch.
% load images
img1 = readImage('roadSign.tif');
img2 = readImage('lena.tif');
% call the main function
mapIntoImage(img1,img2)
function [newImage] = mapIntoImage(imageA,imageB)
% Input: imageA, imageB - a grayscale image in the range [0..255].
%
% Output: newImage – imageA into which image B has been mapped.
%
showImage(imageA)
hold on
% Initially, the list of points is empty.
xy = [];
% Loop, picking up the points.
disp('Please enter corners of place to insert image in clockwise order.')
for j = 1:4
[xi,yi] = ginput(1);
%draw a yellow dot
plot(xi,yi,'yo')
xy(:,j) = [xi;yi];
end
% get x1 y1 cordinates - xy(:, 1)
imgRow = size(imageB,1);
imgCol = size(imageB,2);
[X,Y] = meshgrid(1:imgCol,1:imgRow);
imgBcords = [0 size(imageB, 1) size(imageB,1) 0 ;
0 0 size(imageB,2) size(imageB,2)];
coefs = findCoefficients(xy, imgBcords);
A = [coefs(1) coefs(2) coefs(5);coefs(3) coefs(4) coefs(6); coefs(7) coefs(8) 1];
temp = zeros(size(X,1), size(X,2), 3);
new = ones(256);
for i = 1:size(X,1)
for j = 1:size(X,2)
temp(i,j,:) =A*[X(i,j); Y(i,j); new(i,j)];
end
end
end
function [ result ] = findCoefficients( imageA, imageB )
% finds coefficients for inverse mapping algorithem
% takes 2 X 2d vectors each consists of 4 points x,y
% and returns the coef accroding to reverse mapping function
%
% x y 0 0 1 0 -xx' -yx'
% 0 0 x y 0 1 -xy' -yy'
% y' and x' are in the destenation picture;
A = [imageB(1,1) imageB(2,1) 0 0 1 0 -imageB(1,1)*imageA(1,1) -imageB(2,1)*imageA(1,1);
0 0 imageB(1,1) imageB(2,1) 0 1 -imageB(1,1)*imageA(2,1) -imageB(2,1)*imageA(2,1);
imageB(1,2) imageB(2,2) 0 0 1 0 -imageB(1,2)*imageA(1,2) -imageB(2,2)*imageA(1,2);
0 0 imageB(1,2) imageB(2,2) 0 1 -imageB(1,2)*imageA(2,2) -imageB(2,2)*imageA(2,2);
imageB(1,3) imageB(2,3) 0 0 1 0 -imageB(1,3)*imageA(1,3) -imageB(2,3)*imageA(1,3);
0 0 imageB(1,3) imageB(2,3) 0 1 -imageB(1,3)*imageA(2,3) -imageB(2,3)*imageA(2,3);
imageB(1,4) imageB(2,4) 0 0 1 0 -imageB(1,4)*imageA(1,4) -imageB(2,4)*imageA(1,4);
0 0 imageB(1,4) imageB(2,4) 0 1 -imageB(1,4)*imageA(2,4) -imageB(2,4)*imageA(2,4)];
B = [imageB(1,1); imageB(2,1); imageB(1,2); imageB(2,2); imageB(1,3); imageB(2,3); imageB(1,4); imageB(2,4)];
result = pinv(A)*B;
end
i want to build now the transform
[x' y' 1] = A*[X Y 1];
i have figured out that i would need to use repmat, but i can't seem to get to the real syntax without loops.
what's the most efficient way to do it?
A projective transform has the form of
$ x' = \frac {a_{11}x+a_{12}y+a_{13}}{a_{13}x+a_{23}y+a_{33}} \\
y' = \frac {a_{21}x+a_{22}y+a_{23}}{a_{13}x+a_{23}y+a_{33}}
$
Where the coefficients are defined up to some scale factor. One of the ways to ensure a constant scale factor is to set $a_{33}=1$. One easy way to think about it is to use the homogenous coordinates:
$ \left( \begin{array}{ccc} x'\\y'\\S\end{array} \right) =
\left( \begin{array}{ccc} a_{11} & a_{12} & a_{13}\\a_{21} & a_{22} & a_{23}\\ a_{31} & a_{32} & a_{33}\end{array} \right)
\left( \begin{array}{ccc} x\\y\\1\end{array} \right)
$
These coordinates are defined up to scale. That is,
$ \left( \begin{array}{ccc} x'/S\\y'/S\\1\end{array} \right) \equiv
\left( \begin{array}{ccc} x'\\y'\\S\end{array} \right)$
Thus, in your case you should do: (Assuming that x and y are column vectors, and A is the transpose of the matrix that I described above:
XY = A * [x y ones(size(x))];
XY(:,1) = XY(:,1)./XY(:,3);
XY(:,2) = XY(:,2)./XY(:,3);

Ruby/Rails while loop not breaking correctly?

I am working on a client's site, and I'm writing an amortization schedule calculator in in ruby on rails. For longer loan term calculations, it doesn't seem to be breaking when the balance reaches 0
Here is my code:
def calculate_amortization_results
p = params[:price].to_i
i = params[:rate].to_d
l = params[:term].to_i
j = i/(12*100)
n = l * 12
m = p * (j / (1 - (1 + j) ** (-1 * n)))
#loanAmount = p
#rateAmount = i
#monthlyAmount = m
#amort = []
#interestAmount = 0
while p > 0
line = Hash.new
h = p*j
c = m-h
p = p-c
line["interest"] = h
line["principal"] = c
if p <= 0
line["balance"] = 0
else
line["balance"] = p
end
line["payment"] = h+c
#amort.push(line)
#interestAmount += h
end
end
And here is the view:
- #amort.each_with_index do |a, i|
%li
.m
= i+1
.i
= number_to_currency(a["interest"], :unit => "$")
.p
= number_to_currency(a["principal"], :unit => "$")
.pp
= number_to_currency(a["payment"], :unit => "$")
.b
= number_to_currency(a["balance"], :unit => "$")
What I am seeing is, in place of $0.00 in the final payment balance, it shows "-$-inf", iterates one more loop, then displays $0.00, but shows "-$-inf" for interest. It should loop until p gets to 0, then stop and set the balance as 0, but it isn't. Any idea what I've done wrong?
The calculator is here. It seems to work fine for shorter terms, like 5 years, but longer terms cause the above error.
Edit:
Changing the while loop to n.times do
and then changing the balance view to
= number_to_currency(a["balance"], :unit => "$", :negative_format => "$0.00")
Is a workaround, but i'd like to know why the while loop wouldn't work correctly
in Ruby the default for numerical values is Fixnum ... e.g.:
> 15 / 4
=> 3
You will see weird rounding errors if you try to use Fixnum values and divide them.
To make sure that you use Floats, at least one of the numbers in the calculation needs to be a Float
> 15.0 / 4
=> 3.75
> 15 / 4.0
=> 3.75
You do two comparisons against 0 , which should be OK if you make sure that p is a Float.
As the other answer suggests, you should use "decimal" type in your database to represent currency.
Please try if this will work:
def calculate_amortization_results
p = params[:price].to_f # instead of to_i
i = params[:rate].to_f # <-- what is to_d ? use to_f
l = params[:term].to_i
j = i/(12*100.0) # instead of 100
n = l * 12
m = p * (j / (1 - (1 + j) ** (-1 * n))) # division by zero if i==0 ==> j==0
#loanAmount = p
#rateAmount = i
#monthlyAmount = m
#amort = []
#interestAmount = 0.0 # instead of 0
while p > 0
line = Hash.new
h = p*j
c = m-h
p = p-c
line["interest"] = h
line["principal"] = c
if p <= 0
line["balance"] = 0
else
line["balance"] = p
end
line["payment"] = h+c
#amort.push(line)
#interestAmount += h
end
end
If you see "inf" in your output, you are doing a division by zero somewhere.. better check the logic of your calculation, and guard against division by zero.
according to Wikipedia the formula is:
http://en.wikipedia.org/wiki/Amortization_calculator
to improve rounding errors, it's probably better to re-structure the formula like this:
m = (p * j) / (1 - (1 + j) ** (-1 * n) # these are two divisions! x**-1 == 1/x
which is equal to:
m = (p * j) + (p * j) / ((1 + j) ** n) - 1.0)
which is equal to: (use this one)
q = p * j # this is much larger than 1 , so fewer rounding errors when dividing it by something
m = q + q / ((1 + j) ** n) - 1.0) # only one division
I think it has something to do with the floating point operations precision. It has already been discussed here: Ruby number precision with simple arithmetic and it would be better to use decimal format for financial purposes.
The answer could be computing the numbers in the loop, but with precomputed number of iterations and from the scratch.

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