Without a complete example, it is impossible to be sure. However, I suspect the problem is the result of the following 2 points:
- without a
\caption or \phantomcaption, \ContinuedFloat will not work;
\phantomcaption is defined by caption which you have told subfig ought not be loaded - hence, it is undefined.
Note that compiling non-stop is great but it is not the way to diagnose problems. Ignore errors at your peril. In this case, LaTeX will have failed compilation with an error which would have told you precisely the problem. If you must ignore errors, you have to read the .log assiduously not only when there is an obvious problem, but to find problems of a more subtle variety.
Here's my version of your example, borrowing code from Zarko's efforts:
\documentclass{article}
\usepackage[labelsep=space,
labelfont={sf,bf},
textfont=sf,
caption=false]{subfig}
\usepackage{graphicx,kantlipsum}
\begin{document}
\begin{figure}[!ht]
% \centering
%%image-1
\subfloat[]{\includegraphics[width=0.24\hsize,height=1cm]{example-image}}\hfill
\subfloat[]{\includegraphics[width=0.24\hsize,height=1cm]{example-image}}\hfill
\subfloat[]{\includegraphics[width=0.24\hsize,height=1cm]{example-image}}\hfill
\subfloat[]{\includegraphics[width=0.24\hsize,height=1cm]{example-image}}
\caption{Assignment of pixels 1.}
\label{image:assignSP1}
\end{figure}
\begin{figure}[!ht]
% \centering
%%image-1
\subfloat[]{\includegraphics[width=0.24\hsize,height=1cm]{example-image}}\hfill
\subfloat[]{\includegraphics[width=0.24\hsize,height=1cm]{example-image}}\hfill
\subfloat[]{\includegraphics[width=0.24\hsize,height=1cm]{example-image}}\hfill
\subfloat[]{\includegraphics[width=0.24\hsize,height=1cm]{example-image}}
\caption{Assignment of pixels 2.}
\label{image:assignSP2}
\end{figure}
\begin{figure}[!ht]
% \centering
%%image-1
\subfloat[]{\includegraphics[width=0.24\hsize,height=1cm]{example-image}}\hfill
\subfloat[]{\includegraphics[width=0.24\hsize,height=1cm]{example-image}}\hfill
\subfloat[]{\includegraphics[width=0.24\hsize,height=1cm]{example-image}}\hfill
\subfloat[]{\includegraphics[width=0.24\hsize,height=1cm]{example-image}}
\caption{Assignment of pixels 3.}
\label{image:assignSP3}
\end{figure}
\kant[1]
\begin{figure}[!ht]
%%image-2
\subfloat[Original image1] {\includegraphics[width=0.24\hsize,height=1cm]{example-image}}\hfill
\subfloat[Layer-11, Subgraph-1] {\includegraphics[width=0.24\hsize,height=1cm]{example-image}}\hfill
\subfloat[Layer-11, Segmentation] {\includegraphics[width=0.24\hsize,height=1cm]{example-image}}\hfill
\subfloat[Layer-11, Saliency] {\includegraphics[width=0.24\hsize,height=1cm]{example-image}}\\
%%Layer-2
\subfloat[Layer-12, Subgraph-1] {\includegraphics[width=0.24\hsize,height=1cm]{example-image}}\hfill
\subfloat[Layer-12, Subgraph-2] {\includegraphics[width=0.24\hsize,height=1cm]{example-image}}\hfill
\subfloat[Layer-12, Segmentation] {\includegraphics[width=0.24\hsize,height=1cm]{example-image}}\hfill
\subfloat[Layer-12, Saliency] {\includegraphics[width=0.24\hsize,height=1cm]{example-image}}
\phantomcaption
\end{figure}
\vfill
%%mages on the new page
\begin{figure}[!ht]
\ContinuedFloat
\subfloat[Layer-14, Segmentation] {\includegraphics[width=0.48\hsize,height=1cm]{example-image}}\hfill
\subfloat[Layer-14, Saliency] {\includegraphics[width=0.48\hsize,height=1cm]{example-image}}
\caption{corresponding maps 1.}
\label{image:Hierarchy1}
\end{figure}
\kant[2-3]
\begin{figure}[!ht]
%%image-2
\subfloat[Original image2] {\includegraphics[width=0.24\hsize,height=1cm]{example-image}}\hfill
\subfloat[Layer-21, Subgraph-1] {\includegraphics[width=0.24\hsize,height=1cm]{example-image}}\hfill
\subfloat[Layer-21, Segmentation] {\includegraphics[width=0.24\hsize,height=1cm]{example-image}}\hfill
\subfloat[Layer-21, Saliency] {\includegraphics[width=0.24\hsize,height=1cm]{example-image}}\\
%%Layer-2
\subfloat[Layer-22, Subgraph-1] {\includegraphics[width=0.24\hsize,height=1cm]{example-image}}\hfill
\subfloat[Layer-22, Subgraph-2] {\includegraphics[width=0.24\hsize,height=1cm]{example-image}}\hfill
\subfloat[Layer-22, Segmentation] {\includegraphics[width=0.24\hsize,height=1cm]{example-image}}\hfill
\subfloat[Layer-22, Saliency] {\includegraphics[width=0.24\hsize,height=1cm]{example-image}}
\phantomcaption
\end{figure}
\vfill
%%mages on the new page
\begin{figure}[!ht]
\ContinuedFloat
\subfloat[Layer-24, Segmentation] {\includegraphics[width=0.48\hsize,height=1cm]{example-image}}\hfill
\subfloat[Layer-24, Saliency] {\includegraphics[width=0.48\hsize,height=1cm]{example-image}}
\caption{corresponding maps 2.}
\label{image:Hierarchy2}
\end{figure}
\end{document}

We do not actually need this much. A single figure followed by some filler text, the first part of a figure and the continuation would be quite sufficient to demonstrate the issue:
\documentclass{article}
\usepackage[labelsep=space,
labelfont={sf,bf},
textfont=sf,
caption=false]{subfig}
\usepackage{graphicx}
\begin{document}
\begin{figure}[!ht]
\subfloat[]{\includegraphics[width=\linewidth]{example-image-a}}
\caption{Assignment of pixels 1.}
\label{image:assignSP1}
\end{figure}
\begin{figure}[!ht]
\subfloat[Original image1] {\includegraphics[width=.45\linewidth]{example-image-4x3}}\hfill
\subfloat[Layer-12, Subgraph-1] {\includegraphics[width=.45\linewidth]{example-image-4x3}}
\phantomcaption
\end{figure}
\vfill
%%mages on the new page
\begin{figure}[!ht]
\ContinuedFloat
\subfloat[Layer-14, Segmentation] {\includegraphics[width=\linewidth]{example-image-b}}\hfill
\caption{corresponding maps 1.}
\label{image:Hierarchy1}
\end{figure}
\end{document}
which, if we ignore the errors and carry blithely on, gives us:

which clearly shows the problem: figure 2 on page 2 is numbered 1.
When we try to compile this, compilation fails with the following error:
! Undefined control sequence.
l.24 \phantomcaption
?
That is, it complains that \phantomcaption is not defined. This is bad because \ContinuedFloat requires a \caption to work. subfig assumes that the first part of a figure will always have a \caption. That caption increments the figure counter. No \caption means no increment. Meanwhile, \ContinuedFloat explicitly prevents the \caption in the second part from incrementing the figure counter.
The solution to this is \phantomcaption which ensures that the counter is incremented. But subfig does not provide this command. caption provides it. But by setting caption=false, we have told subfig that caption is not to be loaded.
For further details, see Axel Sommerfeldt's answer on this topic.
So, there are two obvious options:
- set
caption=true;
- use a real
\caption.
In the absence of more details, option 1 seems the better choice. Setting caption=true in the options to subfig resolves the issue nicely:

Option 2, adding \caption{first part} to the first part of the figure achieves precisely the same result for the second part plus, of course, an additional caption for the first.
If for some reason neither of these are options, the only other choice I can see is to implement something yourself. For example adding the following to your preamble:
\newcommand*\phantomfigurecaption{\stepcounter{figure}}
\newcommand*\phantomtablecaption{\stepcounter{table}}
would allow you to use \phantomfigurecaption in the first part of the figure to achieve roughly the same result. But note that this is a hack and will be much less robust than using one of the options provided by the packages. I do not recommend doing it this way unless you really have no better option.
captionandsubfigurepackages? – Mico Jun 03 '15 at 21:10\phantomcaptiondefined? – cfr Aug 03 '15 at 00:55