It's hard to give any detailed answer as I don't know what you are looking for or expecting. I guess you may need some sort of Perceptual Hash if you are looking for images that people would perceive as similar or dissimilar, or maybe a Scale/Rotation/Translation Invariant technique that identifies similar images independently of resizes, shifts and rotations.
You could look at the Perceptual Hash and Image Moments with ImageMagick like this:
identify -verbose -features 1 -moments 1.png
Image: 1.png
Format: PNG (Portable Network Graphics)
Mime type: image/png
Class: PseudoClass
Geometry: 103x115+0+0
Resolution: 37.79x37.79
Print size: 2.72559x3.04313
Units: PixelsPerCentimeter
Type: Grayscale
Base type: Grayscale
Endianess: Undefined
Colorspace: Gray
Depth: 8-bit
Channel depth:
gray: 8-bit
Channel statistics:
Pixels: 11845
Gray:
min: 62 (0.243137)
max: 255 (1)
mean: 202.99 (0.79604)
standard deviation: 85.6322 (0.335812)
kurtosis: -0.920271
skewness: -1.0391
entropy: 0.840719
Channel moments:
Gray:
Centroid: 51.6405,57.1281
Ellipse Semi-Major/Minor axis: 66.5375,60.336
Ellipse angle: 0.117192
Ellipse eccentricity: 0.305293
Ellipse intensity: 190.641 (0.747614)
I1: 0.000838838 (0.213904)
I2: 6.69266e-09 (0.00043519)
I3: 3.34956e-15 (5.55403e-08)
I4: 5.38335e-15 (8.92633e-08)
I5: 2.27572e-29 (6.25692e-15)
I6: -4.33202e-19 (-1.83169e-09)
I7: -2.16323e-30 (-5.94763e-16)
I8: 3.96612e-20 (1.67698e-10)
Channel perceptual hash:
Red, Hue:
PH1: 0.669868, 11
PH2: 3.35965, 11
PH3: 7.27735, 11
PH4: 7.05343, 11
PH5: 11, 11
PH6: 8.746, 11
PH7: 11, 11
Green, Chroma:
PH1: 0.669868, 11
PH2: 3.35965, 11
PH3: 7.27735, 11
PH4: 7.05343, 11
PH5: 11, 11
PH6: 8.746, 11
PH7: 11, 11
Blue, Luma:
PH1: 0.669868, 0.669868
PH2: 3.35965, 3.35965
PH3: 7.27735, 7.27735
PH4: 7.05343, 7.05343
PH5: 11, 11
PH6: 8.746, 8.746
PH7: 11, 11
Channel features (horizontal, vertical, left and right diagonals, average):
Gray:
Angular Second Moment:
0.364846, 0.615673, 0.372224, 0.372224, 0.431242
Contrast:
0.544246, 0.0023846, 0.546612, 0.546612, 0.409963
Correlation:
-0.406263, 0.993832, -0.439964, -0.439964, -0.07309
Sum of Squares Variance:
1.19418, 1.1939, 1.19101, 1.19101, 1.19253
Inverse Difference Moment:
0.737681, 1.00758, 0.745356, 0.745356, 0.808993
Sum Average:
1.63274, 0.546074, 1.63983, 1.63983, 1.36462
Sum Variance:
4.43991, 0.938019, 4.46048, 4.46048, 3.57472
Sum Entropy:
0.143792, 0.159713, 0.143388, 0.143388, 0.14757
Entropy:
0.462204, 0.258129, 0.461828, 0.461828, 0.410997
Difference Variance:
0.0645055, 0.189604, 0.0655494, 0.0655494, 0.0963021
Difference Entropy:
0.29837, 0.003471, 0.297282, 0.297282, 0.224101
Information Measure of Correlation 1:
-0.160631, -0.971422, -0.146024, -0.146024, -0.356026
Information Measure of Correlation 2:
0.294281, 0.625514, 0.29546, 0.29546, 0.377679
You could also go on Fred Weinhaus's excellent website (here) and download his script called moments
which will calculate the Hu and Maitra moments and see if those will tell you what you want. Basically, you could run the script on each of your images like this:
./moments image1.png > 1.txt
./moments image2.png > 2.txt
and then use your favourite diff
tool to see what has changed between the two images you wish to compare.