Signal Processing - September 2016 - 42

properly exposed, as given by the a ref term, which is a trapezoidal function in the pixel value domain [similar to the
weighting function in (2)] that favors intensities near the middle of the pixel value range.
In the regions where the reference image Z ref is poorly
exposed (indicated by 1 - a ref ), the algorithm draws information from the other images in the stack using a bidirectional
similarity metric, given by the E BDS term. This energy term
enforces that for every pixel patch in the image stack (given by
Z 1, f, Z N ), there must be a similar patch in the final result E,
and vice versa. The first similarity ensures that as much wellexposed content from the image stack is included in the final
HDR result, while the second ensures that the final result does
not contain objectionable artifacts, as these artifacts would
not be found anywhere in the stack. This energy equation is
optimized with an iterative method that solves for the aligned
LDR images and the HDR image simultaneously, producing
high-quality results (Figure 6).
Patch-based optimization algorithms like this are fundamentally different from those discussed in the "Algorithms
that Align the Different Exposures" section, which warp the
images to match based on correspondences. As was pointed
out earlier, alignment methods fail in cases of occlusion or parallax (which happen commonly in dynamic scenes) because

object are well exposed in disjoint regions of the different
images, these parts cannot be brought together to produce an
acceptable result.

Patch-based optimization algorithms
Recently, Sen et al. [1] proposed a new alternative for HDR
deghosting that uses patch-based optimization, which
addresses the problems of both the rejection and alignment
methods. Specifically, a formulated equation codifies the
objective of most reference-based HDR reconstruction algorithms: 1) to produce an HDR result that resembles the reference image in the parts where the reference is well exposed
and 2) to leverage well-exposed information from other images in the stack wherever the reference is poorly exposed. This
HDR synthesis equation can be written as
Energy (E ) =

/

[a ref (p) · ( f - 1 (Z ref ( p)) /t ref - E (p)) 2

p ! pixels

+ (1 - a ref (p)) ·E BDS (E | Z 1, f, Z N )] .

(3)

The first term states that the desired HDR image E should be
close in an L2 sense to the LDR reference Z ref mapped to the
linear irradiance domain by applying the inverse camera
response function f -1 and dividing by the exposure time t ref.
This is only to be done for the pixels where the reference is

(a)

(b)

Figure 6. (a) and (b) show sample HDR results (right) from the input LDR images (left) using the patch-based optimization of Sen et al. [1].
42

IEEE SIgnal ProcESSIng MagazInE

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September 2016

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Table of Contents for the Digital Edition of Signal Processing - September 2016

Signal Processing - September 2016 - Cover1
Signal Processing - September 2016 - Cover2
Signal Processing - September 2016 - 1
Signal Processing - September 2016 - 2
Signal Processing - September 2016 - 3
Signal Processing - September 2016 - 4
Signal Processing - September 2016 - 5
Signal Processing - September 2016 - 6
Signal Processing - September 2016 - 7
Signal Processing - September 2016 - 8
Signal Processing - September 2016 - 9
Signal Processing - September 2016 - 10
Signal Processing - September 2016 - 11
Signal Processing - September 2016 - 12
Signal Processing - September 2016 - 13
Signal Processing - September 2016 - 14
Signal Processing - September 2016 - 15
Signal Processing - September 2016 - 16
Signal Processing - September 2016 - 17
Signal Processing - September 2016 - 18
Signal Processing - September 2016 - 19
Signal Processing - September 2016 - 20
Signal Processing - September 2016 - 21
Signal Processing - September 2016 - 22
Signal Processing - September 2016 - 23
Signal Processing - September 2016 - 24
Signal Processing - September 2016 - 25
Signal Processing - September 2016 - 26
Signal Processing - September 2016 - 27
Signal Processing - September 2016 - 28
Signal Processing - September 2016 - 29
Signal Processing - September 2016 - 30
Signal Processing - September 2016 - 31
Signal Processing - September 2016 - 32
Signal Processing - September 2016 - 33
Signal Processing - September 2016 - 34
Signal Processing - September 2016 - 35
Signal Processing - September 2016 - 36
Signal Processing - September 2016 - 37
Signal Processing - September 2016 - 38
Signal Processing - September 2016 - 39
Signal Processing - September 2016 - 40
Signal Processing - September 2016 - 41
Signal Processing - September 2016 - 42
Signal Processing - September 2016 - 43
Signal Processing - September 2016 - 44
Signal Processing - September 2016 - 45
Signal Processing - September 2016 - 46
Signal Processing - September 2016 - 47
Signal Processing - September 2016 - 48
Signal Processing - September 2016 - 49
Signal Processing - September 2016 - 50
Signal Processing - September 2016 - 51
Signal Processing - September 2016 - 52
Signal Processing - September 2016 - 53
Signal Processing - September 2016 - 54
Signal Processing - September 2016 - 55
Signal Processing - September 2016 - 56
Signal Processing - September 2016 - 57
Signal Processing - September 2016 - 58
Signal Processing - September 2016 - 59
Signal Processing - September 2016 - 60
Signal Processing - September 2016 - 61
Signal Processing - September 2016 - 62
Signal Processing - September 2016 - 63
Signal Processing - September 2016 - 64
Signal Processing - September 2016 - 65
Signal Processing - September 2016 - 66
Signal Processing - September 2016 - 67
Signal Processing - September 2016 - 68
Signal Processing - September 2016 - 69
Signal Processing - September 2016 - 70
Signal Processing - September 2016 - 71
Signal Processing - September 2016 - 72
Signal Processing - September 2016 - 73
Signal Processing - September 2016 - 74
Signal Processing - September 2016 - 75
Signal Processing - September 2016 - 76
Signal Processing - September 2016 - 77
Signal Processing - September 2016 - 78
Signal Processing - September 2016 - 79
Signal Processing - September 2016 - 80
Signal Processing - September 2016 - 81
Signal Processing - September 2016 - 82
Signal Processing - September 2016 - 83
Signal Processing - September 2016 - 84
Signal Processing - September 2016 - 85
Signal Processing - September 2016 - 86
Signal Processing - September 2016 - 87
Signal Processing - September 2016 - 88
Signal Processing - September 2016 - 89
Signal Processing - September 2016 - 90
Signal Processing - September 2016 - 91
Signal Processing - September 2016 - 92
Signal Processing - September 2016 - 93
Signal Processing - September 2016 - 94
Signal Processing - September 2016 - 95
Signal Processing - September 2016 - 96
Signal Processing - September 2016 - 97
Signal Processing - September 2016 - 98
Signal Processing - September 2016 - 99
Signal Processing - September 2016 - 100
Signal Processing - September 2016 - 101
Signal Processing - September 2016 - 102
Signal Processing - September 2016 - 103
Signal Processing - September 2016 - 104
Signal Processing - September 2016 - 105
Signal Processing - September 2016 - 106
Signal Processing - September 2016 - 107
Signal Processing - September 2016 - 108
Signal Processing - September 2016 - 109
Signal Processing - September 2016 - 110
Signal Processing - September 2016 - 111
Signal Processing - September 2016 - 112
Signal Processing - September 2016 - 113
Signal Processing - September 2016 - 114
Signal Processing - September 2016 - 115
Signal Processing - September 2016 - 116
Signal Processing - September 2016 - 117
Signal Processing - September 2016 - 118
Signal Processing - September 2016 - 119
Signal Processing - September 2016 - 120
Signal Processing - September 2016 - 121
Signal Processing - September 2016 - 122
Signal Processing - September 2016 - 123
Signal Processing - September 2016 - 124
Signal Processing - September 2016 - 125
Signal Processing - September 2016 - 126
Signal Processing - September 2016 - 127
Signal Processing - September 2016 - 128
Signal Processing - September 2016 - 129
Signal Processing - September 2016 - 130
Signal Processing - September 2016 - 131
Signal Processing - September 2016 - 132
Signal Processing - September 2016 - 133
Signal Processing - September 2016 - 134
Signal Processing - September 2016 - 135
Signal Processing - September 2016 - 136
Signal Processing - September 2016 - 137
Signal Processing - September 2016 - 138
Signal Processing - September 2016 - 139
Signal Processing - September 2016 - 140
Signal Processing - September 2016 - 141
Signal Processing - September 2016 - 142
Signal Processing - September 2016 - 143
Signal Processing - September 2016 - 144
Signal Processing - September 2016 - 145
Signal Processing - September 2016 - 146
Signal Processing - September 2016 - 147
Signal Processing - September 2016 - 148
Signal Processing - September 2016 - 149
Signal Processing - September 2016 - 150
Signal Processing - September 2016 - 151
Signal Processing - September 2016 - 152
Signal Processing - September 2016 - 153
Signal Processing - September 2016 - 154
Signal Processing - September 2016 - 155
Signal Processing - September 2016 - 156
Signal Processing - September 2016 - 157
Signal Processing - September 2016 - 158
Signal Processing - September 2016 - 159
Signal Processing - September 2016 - 160
Signal Processing - September 2016 - 161
Signal Processing - September 2016 - 162
Signal Processing - September 2016 - 163
Signal Processing - September 2016 - 164
Signal Processing - September 2016 - 165
Signal Processing - September 2016 - 166
Signal Processing - September 2016 - 167
Signal Processing - September 2016 - 168
Signal Processing - September 2016 - 169
Signal Processing - September 2016 - 170
Signal Processing - September 2016 - 171
Signal Processing - September 2016 - 172
Signal Processing - September 2016 - 173
Signal Processing - September 2016 - 174
Signal Processing - September 2016 - 175
Signal Processing - September 2016 - 176
Signal Processing - September 2016 - Cover3
Signal Processing - September 2016 - Cover4
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