BE 400/500
Introduction to Biomedical Image Analysis
Homework 6
Due: 10/24/2016, Noon
Assume that we have measured a single observation of a random variable X . The model for X
is
X=
(1 B)G1 + BG2
where B has the following distribution:
P[ B= 0]= P[ B= 1]

BE 400/500
Introduction to Biomedical Image Analysis
Homework 4
Due: 10/05/2016, Noon
1. The need for image padding when filtering in the frequency domain was discussed in the
lecture. We discussed that images needed to be padded by appending zeros to the

In a given application, a median mask is applied to input images to reduce noise, and then a Laplacian
mask is applied to enhance small details. Would the result be the same if the order of these operations
were reversed?
The result will not be the same i

BE 400/500
Introduction to Biomedical Image Analysis
Homework 5
Due: 10/17/2016, Noon
1. Let X 1 , X 2 , , X N be independent random samples of size N from a distribution that is
( , 2 ) . Assume that is known.
a. Derive the maximum likelihood estimator

BE 400/500
Introduction to Biomedical Image Analysis
Homework 1
Due: 09/14/2016, Noon
1. One dimensional object, s ( x), and PSF, h( x), are defined as:
1 for 0 < x 5
s ( x) =
otherwise,
0
1 for 3 < x 7
h( x ) =
otherwise.
0
Derive s =
( x) s ( x) h(

BE 400/500 (Fall 2016)
Introduction to Biomedical Image Analysis
Fall Semester
Description: Quantification of biologically/clinically relevant information from biomedical images using
computational tools is an important topic. This knowledge is needed in

Question 1
The source of the image is from the article below:
Kuru K. Optimization and enhancement of H&E stained microscopical images by
applying bilinear interpolation method on lab color mode.Theoretical Biology &
Medical Modelling. 2014;11:9. doi:10.1

1. Let X1, X2, , XN be independent random samples of size N from a
distribution that is N(, ). Assume that is known.
a. Derive the maximum likelihood estimator (MLE) of .
b. Is the MLE of derived in (a) unbiased?
Answer:
a.
The probability density of X is

1The need for image padding when filtering in the frequency domain was discussed
in the lecture. We discussed that images needed to be padded by appending zeros to
the end of rows and columns in the image (see the following image on the left). Do
you thin

BE 400/500
Introduction to Biomedical Image Analysis
Homework 2
Due: 09/21/2016, Noon
1. Using one_sphere.m, generate three object images with object intensities of 10, 5, and 1,
and construct an RGB image by assigning the resulted intensity images as R,

BE 400/500
Introduction to Biomedical Image Analysis
Homework 3
Due: 09/28/2016, Noon
1. Find your favorite histopathological image from a peer-reviewed journal article. Report the
source of the image. Apply principal component projection and color deconv

BE 400/500
Introduction to Biomedical Image Analysis
Fall 2016
Description: This course will focus on quantification of biologically and clinically relevant data obtained
from biomedical images using computational tools. Students will learn to i) apply st